text:
using Rubin
using Tests
using Elliptic
using HypergeometricFunctions
using Polylogarithms
using SpecialFunctions

@test integrate(x^4*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(1//5*d*x^5*(a+b*arcsin(c*x))+-8//175*b*d*c^-5*(1+-1*c^2*x^2)^5//2+-1//7*d*c^2*x^7*(a+b*arcsin(c*x))+1//49*b*d*c^-5*(1+-1*c^2*x^2)^7//2+1//105*b*d*c^-5*(1+-1*c^2*x^2)^3//2+2//35*b*d*c^-5*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^3*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(1//4*d*x^4*(a+b*arcsin(c*x))+-1//6*d*c^2*x^6*(a+b*arcsin(c*x))+-1//24*b*d*c^-4*arcsin(c*x)+-1//36*b*c*d*x^5*(1+-1*c^2*x^2)^(1/2)+1//24*b*d*x*c^-3*(1+-1*c^2*x^2)^(1/2)+1//36*b*d*c^-1*x^3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^2*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(1//3*d*x^3*(a+b*arcsin(c*x))+-1//5*d*c^2*x^5*(a+b*arcsin(c*x))+-1//25*b*d*c^-3*(1+-1*c^2*x^2)^5//2+1//45*b*d*c^-3*(1+-1*c^2*x^2)^3//2+2//15*b*d*c^-3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(-1//4*d*c^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))+3//32*b*d*c^-2*arcsin(c*x)+1//16*b*d*x*c^-1*(1+-1*c^2*x^2)^3//2+3//32*b*d*x*c^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate((a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(d*x*(a+b*arcsin(c*x))+-1//3*d*c^2*x^3*(a+b*arcsin(c*x))+1//9*b*d*c^-1*(1+-1*c^2*x^2)^3//2+2//3*b*d*c^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-1*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(d*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+(1/2)*d*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//4*b*d*arcsin(c*x)+-1//2*im*b*d*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*im*d*b^-1*(a+b*arcsin(c*x))^2+-1//4*b*c*d*x*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-2*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(-1*d*x^-1*(a+b*arcsin(c*x))+-1*b*c*d*(1+-1*c^2*x^2)^(1/2)+-1*b*c*d*arctanh((1+-1*c^2*x^2)^(1/2))+-1*d*x*c^2*(a+b*arcsin(c*x)))
@test integrate(x^-3*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(-1*d*c^2*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+-1//2*b*d*c^2*arcsin(c*x)+-1//2*d*x^-2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+(1/2)*im*b*d*c^2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+(1/2)*im*d*b^-1*c^2*(a+b*arcsin(c*x))^2+-1//2*b*c*d*x^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-4*(a+b*arcsin(c*x))*(d+-1*d*c^2*x^2), x) == :(-1//3*d*x^-3*(a+b*arcsin(c*x))+d*c^2*x^-1*(a+b*arcsin(c*x))+5//6*b*d*c^3*arctanh((1+-1*c^2*x^2)^(1/2))+-1//6*b*c*d*x^-2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^4*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(1//5*d^2*x^5*(a+b*arcsin(c*x))+-10//441*b*c^-5*d^2*(1+-1*c^2*x^2)^7//2+-2//7*c^2*d^2*x^7*(a+b*arcsin(c*x))+1//9*c^4*d^2*x^9*(a+b*arcsin(c*x))+1//81*b*c^-5*d^2*(1+-1*c^2*x^2)^9//2+1//525*b*c^-5*d^2*(1+-1*c^2*x^2)^5//2+4//945*b*c^-5*d^2*(1+-1*c^2*x^2)^3//2+8//315*b*c^-5*d^2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^3*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(1//4*d^2*x^4*(a+b*arcsin(c*x))+-73//3072*b*c^-4*d^2*arcsin(c*x)+-1//3*c^2*d^2*x^6*(a+b*arcsin(c*x))+1//8*c^4*d^2*x^8*(a+b*arcsin(c*x))+-43//1152*b*c*d^2*x^5*(1+-1*c^2*x^2)^(1/2)+1//64*b*c^3*d^2*x^7*(1+-1*c^2*x^2)^(1/2)+73//3072*b*x*c^-3*d^2*(1+-1*c^2*x^2)^(1/2)+73//4608*b*c^-1*d^2*x^3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^2*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(1//3*d^2*x^3*(a+b*arcsin(c*x))+-2//5*c^2*d^2*x^5*(a+b*arcsin(c*x))+-1//49*b*c^-3*d^2*(1+-1*c^2*x^2)^7//2+1//7*c^4*d^2*x^7*(a+b*arcsin(c*x))+1//175*b*c^-3*d^2*(1+-1*c^2*x^2)^5//2+4//315*b*c^-3*d^2*(1+-1*c^2*x^2)^3//2+8//105*b*c^-3*d^2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(-1//6*c^-2*d^2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))+5//96*b*c^-2*d^2*arcsin(c*x)+1//36*b*x*c^-1*d^2*(1+-1*c^2*x^2)^5//2+5//96*b*x*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)+5//144*b*x*c^-1*d^2*(1+-1*c^2*x^2)^3//2)
@test integrate((d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(x*d^2*(a+b*arcsin(c*x))+-2//3*c^2*d^2*x^3*(a+b*arcsin(c*x))+1//5*c^4*d^2*x^5*(a+b*arcsin(c*x))+1//25*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2+4//45*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2+8//15*b*c^-1*d^2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(d^2*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+(1/2)*d^2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-11//32*b*d^2*arcsin(c*x)+1//4*d^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))+-1//2*im*b*d^2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*im*b^-1*d^2*(a+b*arcsin(c*x))^2+-11//32*b*c*x*d^2*(1+-1*c^2*x^2)^(1/2)+-1//16*b*c*x*d^2*(1+-1*c^2*x^2)^3//2)
@test integrate(x^-2*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(-1*d^2*x^-1*(a+b*arcsin(c*x))+-1*b*c*d^2*arctanh((1+-1*c^2*x^2)^(1/2))+-2*x*c^2*d^2*(a+b*arcsin(c*x))+-5//3*b*c*d^2*(1+-1*c^2*x^2)^(1/2)+-1//9*b*c*d^2*(1+-1*c^2*x^2)^3//2+1//3*c^4*d^2*x^3*(a+b*arcsin(c*x)))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(-1*c^2*d^2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-2*c^2*d^2*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+-1//2*d^2*x^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))+-1//4*b*c^2*d^2*arcsin(c*x)+im*b*c^2*d^2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+im*b^-1*c^2*d^2*(a+b*arcsin(c*x))^2+-1//2*b*c*d^2*x^-1*(1+-1*c^2*x^2)^3//2+-1//4*b*x*c^3*d^2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^2*(a+b*arcsin(c*x)), x) == :(-1//3*d^2*x^-3*(a+b*arcsin(c*x))+b*c^3*d^2*(1+-1*c^2*x^2)^(1/2)+x*c^4*d^2*(a+b*arcsin(c*x))+2*c^2*d^2*x^-1*(a+b*arcsin(c*x))+11//6*b*c^3*d^2*arctanh((1+-1*c^2*x^2)^(1/2))+-1//6*b*c*d^2*x^-2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^4*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(1//5*d^3*x^5*(a+b*arcsin(c*x))+-4//297*b*c^-5*d^3*(1+-1*c^2*x^2)^9//2+-3//7*c^2*d^3*x^7*(a+b*arcsin(c*x))+-1//11*c^6*d^3*x^11*(a+b*arcsin(c*x))+1//3*c^4*d^3*x^9*(a+b*arcsin(c*x))+1//121*b*c^-5*d^3*(1+-1*c^2*x^2)^11//2+1//1617*b*c^-5*d^3*(1+-1*c^2*x^2)^7//2+2//1925*b*c^-5*d^3*(1+-1*c^2*x^2)^5//2+8//3465*b*c^-5*d^3*(1+-1*c^2*x^2)^3//2+16//1155*b*c^-5*d^3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^3*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(-1//8*c^-4*d^3*(1+-1*c^2*x^2)^4*(a+b*arcsin(c*x))+1//10*c^-4*d^3*(1+-1*c^2*x^2)^5*(a+b*arcsin(c*x))+49//5120*b*c^-4*d^3*arcsin(c*x)+-1//100*b*x*c^-3*d^3*(1+-1*c^2*x^2)^9//2+7//1600*b*x*c^-3*d^3*(1+-1*c^2*x^2)^7//2+49//5120*b*x*c^-3*d^3*(1+-1*c^2*x^2)^(1/2)+49//7680*b*x*c^-3*d^3*(1+-1*c^2*x^2)^3//2+49//9600*b*x*c^-3*d^3*(1+-1*c^2*x^2)^5//2)
@test integrate(x^2*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(1//3*d^3*x^3*(a+b*arcsin(c*x))+-3//5*c^2*d^3*x^5*(a+b*arcsin(c*x))+-1//9*c^6*d^3*x^9*(a+b*arcsin(c*x))+-1//81*b*c^-3*d^3*(1+-1*c^2*x^2)^9//2+1//441*b*c^-3*d^3*(1+-1*c^2*x^2)^7//2+2//525*b*c^-3*d^3*(1+-1*c^2*x^2)^5//2+3//7*c^4*d^3*x^7*(a+b*arcsin(c*x))+8//945*b*c^-3*d^3*(1+-1*c^2*x^2)^3//2+16//315*b*c^-3*d^3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(-1//8*c^-2*d^3*(1+-1*c^2*x^2)^4*(a+b*arcsin(c*x))+35//1024*b*c^-2*d^3*arcsin(c*x)+1//64*b*x*c^-1*d^3*(1+-1*c^2*x^2)^7//2+7//384*b*x*c^-1*d^3*(1+-1*c^2*x^2)^5//2+35//1024*b*x*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)+35//1536*b*x*c^-1*d^3*(1+-1*c^2*x^2)^3//2)
@test integrate((d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(x*d^3*(a+b*arcsin(c*x))+-1*c^2*d^3*x^3*(a+b*arcsin(c*x))+-1//7*c^6*d^3*x^7*(a+b*arcsin(c*x))+1//49*b*c^-1*d^3*(1+-1*c^2*x^2)^7//2+3//5*c^4*d^3*x^5*(a+b*arcsin(c*x))+6//175*b*c^-1*d^3*(1+-1*c^2*x^2)^5//2+8//105*b*c^-1*d^3*(1+-1*c^2*x^2)^3//2+16//35*b*c^-1*d^3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(d^3*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+(1/2)*d^3*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-19//48*b*d^3*arcsin(c*x)+1//4*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))+1//6*d^3*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))+-1//2*im*b*d^3*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*im*b^-1*d^3*(a+b*arcsin(c*x))^2+-19//48*b*c*x*d^3*(1+-1*c^2*x^2)^(1/2)+-7//72*b*c*x*d^3*(1+-1*c^2*x^2)^3//2+-1//36*b*c*x*d^3*(1+-1*c^2*x^2)^5//2)
@test integrate(x^-2*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(-1*d^3*x^-1*(a+b*arcsin(c*x))+c^4*d^3*x^3*(a+b*arcsin(c*x))+-1*b*c*d^3*arctanh((1+-1*c^2*x^2)^(1/2))+-3*x*c^2*d^3*(a+b*arcsin(c*x))+-11//5*b*c*d^3*(1+-1*c^2*x^2)^(1/2)+-1//5*b*c*d^3*(1+-1*c^2*x^2)^3//2+-1//5*c^6*d^3*x^5*(a+b*arcsin(c*x))+-1//25*b*c*d^3*(1+-1*c^2*x^2)^5//2)
@test integrate(x^-3*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(-3*c^2*d^3*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+-3//2*c^2*d^3*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-3//4*c^2*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))+-1//2*d^3*x^-2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))+3//32*b*c^2*d^3*arcsin(c*x)+-7//16*b*x*c^3*d^3*(1+-1*c^2*x^2)^3//2+-1//2*b*c*d^3*x^-1*(1+-1*c^2*x^2)^5//2+3//2*im*b*c^2*d^3*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+3//2*im*b^-1*c^2*d^3*(a+b*arcsin(c*x))^2+3//32*b*x*c^3*d^3*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^3*(a+b*arcsin(c*x)), x) == :(-1//3*d^3*x^-3*(a+b*arcsin(c*x))+3*x*c^4*d^3*(a+b*arcsin(c*x))+3*c^2*d^3*x^-1*(a+b*arcsin(c*x))+-1//3*c^6*d^3*x^3*(a+b*arcsin(c*x))+1//9*b*c^3*d^3*(1+-1*c^2*x^2)^3//2+8//3*b*c^3*d^3*(1+-1*c^2*x^2)^(1/2)+17//6*b*c^3*d^3*arctanh((1+-1*c^2*x^2)^(1/2))+-1//6*b*c*d^3*x^-2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^4*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1*x*c^-4*d^-1*(a+b*arcsin(c*x))+-4//3*b*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)+-1//3*c^-2*d^-1*x^3*(a+b*arcsin(c*x))+1//9*b*c^-5*d^-1*(1+-1*c^2*x^2)^3//2+im*b*c^-5*d^-1*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*b*c^-5*d^-1*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*c^-5*d^-1*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^3*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1*c^-4*d^-1*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-1//2*c^-2*d^-1*x^2*(a+b*arcsin(c*x))+1//4*b*c^-4*d^-1*arcsin(c*x)+(1/2)*im*b*c^-4*d^-1*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+(1/2)*im*b^-1*c^-4*d^-1*(a+b*arcsin(c*x))^2+-1//4*b*x*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^2*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1*b*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)+-1*x*c^-2*d^-1*(a+b*arcsin(c*x))+im*b*c^-3*d^-1*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*b*c^-3*d^-1*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*c^-3*d^-1*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1*c^-2*d^-1*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+(1/2)*im*b*c^-2*d^-1*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+(1/2)*im*b^-1*c^-2*d^-1*(a+b*arcsin(c*x))^2)
@test integrate((d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(im*b*c^-1*d^-1*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*b*c^-1*d^-1*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*c^-1*d^-1*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1*d^-1*(2a+2*b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+(1/2)*im*b*d^-1*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//2*im*b*d^-1*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x))))
@test integrate(x^-2*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arcsin(c*x))+-1*b*c*d^-1*arctanh((1+-1*c^2*x^2)^(1/2))+im*b*c*d^-1*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*b*c*d^-1*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*c*d^-1*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arcsin(c*x))+-2*c^2*d^-1*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+(1/2)*im*b*c^2*d^-1*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//2*im*b*c^2*d^-1*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*b*c*d^-1*x^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^-1*(a+b*arcsin(c*x)), x) == :(-1//3*d^-1*x^-3*(a+b*arcsin(c*x))+-1*c^2*d^-1*x^-1*(a+b*arcsin(c*x))+-7//6*b*c^3*d^-1*arctanh((1+-1*c^2*x^2)^(1/2))+im*b*c^3*d^-1*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*b*c^3*d^-1*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*c^3*d^-1*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-1//6*b*c*d^-1*x^-2*(1+-1*c^2*x^2)^(1/2))
@test integrate(x^4*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :(b*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)+-1//2*b*c^-5*d^-2*(1+-1*c^2*x^2)^-1//2+3//2*x*c^-4*d^-2*(a+b*arcsin(c*x))+(1/2)*c^-2*d^-2*x^3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+3*im*c^-5*d^-2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-3//2*im*b*c^-5*d^-2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+3//2*im*b*c^-5*d^-2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate(x^3*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :(c^-4*d^-2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+(1/2)*b*c^-4*d^-2*arcsin(c*x)+(1/2)*c^-2*d^-2*x^2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1//2*im*b*c^-4*d^-2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//2*im*b^-1*c^-4*d^-2*(a+b*arcsin(c*x))^2+-1//2*b*x*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2)
@test integrate(x^2*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :(-1//2*b*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2+im*c^-3*d^-2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+(1/2)*im*b*c^-3*d^-2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+(1/2)*x*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1//2*im*b*c^-3*d^-2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :((1/2)*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1//2*b*x*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2)
@test integrate((d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :((1/2)*x*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1//2*b*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2+(1/2)*im*b*c^-1*d^-2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*c^-1*d^-2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-1//2*im*b*c^-1*d^-2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :((1/2)*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1*d^-2*(2a+2*b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+(1/2)*im*b*d^-2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//2*im*b*d^-2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*b*c*x*d^-2*(1+-1*c^2*x^2)^-1//2)
@test integrate(x^-2*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :(-1*b*c*d^-2*arctanh((1+-1*c^2*x^2)^(1/2))+-1*d^-2*x^-1*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1//2*b*c*d^-2*(1+-1*c^2*x^2)^-1//2+-3*im*c*d^-2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-3//2*im*b*c*d^-2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+3//2*im*b*c*d^-2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+3//2*x*c^2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x)))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :(c^2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-4*c^2*d^-2*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+-1//2*d^-2*x^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+im*b*c^2*d^-2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*b*c^2*d^-2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*b*c*d^-2*x^-1*(1+-1*c^2*x^2)^-1//2)
@test integrate(x^-4*(d+-1*d*c^2*x^2)^-2*(a+b*arcsin(c*x)), x) == :(-13//6*b*c^3*d^-2*arctanh((1+-1*c^2*x^2)^(1/2))+-1//3*b*c^3*d^-2*(1+-1*c^2*x^2)^-1//2+-1//3*d^-2*x^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-5*im*c^3*d^-2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-5//2*im*b*c^3*d^-2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-5//3*c^2*d^-2*x^-1*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1//6*b*c*d^-2*x^-2*(1+-1*c^2*x^2)^-1//2+5//2*im*b*c^3*d^-2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+5//2*x*c^4*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x)))
@test integrate(x^4*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-1//12*b*c^-5*d^-3*(1+-1*c^2*x^2)^-3//2+5//8*b*c^-5*d^-3*(1+-1*c^2*x^2)^-1//2+-3//4*im*c^-5*d^-3*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-3//8*im*b*c^-5*d^-3*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-3//8*x*c^-4*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+1//4*c^-2*d^-3*x^3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+3//8*im*b*c^-5*d^-3*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^3*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-1//4*b*c^-4*d^-3*arcsin(c*x)+1//4*d^-3*x^4*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+-1//12*b*c^-1*d^-3*x^3*(1+-1*c^2*x^2)^-3//2+1//4*b*x*c^-3*d^-3*(1+-1*c^2*x^2)^-1//2)
@test integrate(x^2*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-1//12*b*c^-3*d^-3*(1+-1*c^2*x^2)^-3//2+1//8*b*c^-3*d^-3*(1+-1*c^2*x^2)^-1//2+-1//8*im*b*c^-3*d^-3*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1//8*x*c^-2*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+1//4*im*c^-3*d^-3*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+1//4*x*c^-2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+1//8*im*b*c^-3*d^-3*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate(x*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(1//4*c^-2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+-1//6*b*x*c^-1*d^-3*(1+-1*c^2*x^2)^-1//2+-1//12*b*x*c^-1*d^-3*(1+-1*c^2*x^2)^-3//2)
@test integrate((d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-3//8*b*c^-1*d^-3*(1+-1*c^2*x^2)^-1//2+-1//12*b*c^-1*d^-3*(1+-1*c^2*x^2)^-3//2+1//4*x*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+3//8*x*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-3//4*im*c^-1*d^-3*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-3//8*im*b*c^-1*d^-3*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+3//8*im*b*c^-1*d^-3*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :((1/2)*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+-1*d^-3*(2a+2*b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+1//4*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+(1/2)*im*b*d^-3*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//2*im*b*d^-3*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-2//3*b*c*x*d^-3*(1+-1*c^2*x^2)^-1//2+-1//12*b*c*x*d^-3*(1+-1*c^2*x^2)^-3//2)
@test integrate(x^-2*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-1*b*c*d^-3*arctanh((1+-1*c^2*x^2)^(1/2))+-1*d^-3*x^-1*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+-7//8*b*c*d^-3*(1+-1*c^2*x^2)^-1//2+-1//12*b*c*d^-3*(1+-1*c^2*x^2)^-3//2+-15//4*im*c*d^-3*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-15//8*im*b*c*d^-3*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+5//4*x*c^2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+15//8*im*b*c*d^-3*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+15//8*x*c^2*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x)))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-6*c^2*d^-3*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+-1//2*d^-3*x^-2*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+3//2*c^2*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+3//4*c^2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+-3//2*im*b*c^2*d^-3*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-2//3*b*x*c^3*d^-3*(1+-1*c^2*x^2)^-1//2+-1//2*b*c*d^-3*x^-1*(1+-1*c^2*x^2)^-3//2+3//2*im*b*c^2*d^-3*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+5//12*b*x*c^3*d^-3*(1+-1*c^2*x^2)^-3//2)
@test integrate(x^-4*(d+-1*d*c^2*x^2)^-3*(a+b*arcsin(c*x)), x) == :(-29//24*b*c^3*d^-3*(1+-1*c^2*x^2)^-1//2+-19//6*b*c^3*d^-3*arctanh((1+-1*c^2*x^2)^(1/2))+-1//3*d^-3*x^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+1//12*b*c^3*d^-3*(1+-1*c^2*x^2)^-3//2+-35//4*im*c^3*d^-3*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x)))+-35//8*im*b*c^3*d^-3*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-7//3*c^2*d^-3*x^-1*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))+-1//6*b*c*d^-3*x^-2*(1+-1*c^2*x^2)^-3//2+35//8*im*b*c^3*d^-3*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+35//8*x*c^4*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))+35//12*x*c^4*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x)))
@test integrate(x^4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(1//6*x^5*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//16*x*c^-4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//24*c^-2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//36*b*c*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//32*b*c^-3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//32*b^-1*c^-5*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//96*b*c^-1*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(1//4*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//8*x*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//16*b*c*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//16*b*c^-1*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//16*b^-1*c^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate((d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :((1/2)*x*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//4*b*c*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//4*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1*x^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*c*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//2*c*b^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//3*d^-1*x^-3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//3*b*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//6*b*c*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-6*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//5*d^-1*x^-5*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-2//15*b*c^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-2//15*c^2*d^-1*x^-3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//20*b*c*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//30*b*c^3*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-8*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//7*d^-1*x^-7*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-8//105*b*c^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-8//105*c^4*d^-1*x^-3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-4//35*c^2*d^-1*x^-5*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//42*b*c*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//140*b*c^3*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//105*b*c^5*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^5*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//3*c^-6*d^-1*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//7*c^-6*d^-3*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+2//5*c^-6*d^-2*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-1//49*b*c*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//175*b*c^-1*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//315*b*c^-3*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+8//105*b*x*c^-5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//3*c^-4*d^-1*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+1//5*c^-4*d^-2*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-1//25*b*c*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//45*b*c^-1*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//15*b*x*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//3*c^-2*d^-1*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//9*b*c*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//3*b*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :((d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+im*b*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-1*b*c*x*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//2*x^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//2*b*c*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+(1/2)*im*b*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-1//2*im*b*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-5*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)), x) == :(-1//4*x^-4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//8*c^2*x^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//12*b*c*x^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//4*c^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+1//8*b*c^3*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//8*im*b*c^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+1//8*im*b*c^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^4*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(1//8*x^5*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+1//16*d*x^5*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-3//128*d*x*c^-4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//64*d*c^-2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//32*b*c*d*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//64*b*d*c^3*x^8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//256*b*d*c^-1*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//256*b*d*c^-3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//256*d*b^-1*c^-5*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^2*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(1//6*x^3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+1//8*d*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//16*d*x*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-7//96*b*c*d*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//32*b*d*c^-1*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//32*d*b^-1*c^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//36*b*d*c^3*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate((d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(1//4*x*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+3//8*d*x*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5//16*b*c*d*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//16*b*d*c^3*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//16*d*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-2*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1*x^-1*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-3//2*d*x*c^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*c*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-3//4*c*d*b^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//4*b*d*c^3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//3*x^-3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+d*c^2*x^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+(1/2)*d*b^-1*c^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-4//3*b*d*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//6*b*c*d*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-6*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//5*d^-1*x^-5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-1//20*b*c*d*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//5*b*d*c^3*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//5*b*d*c^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^-8*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//7*d^-1*x^-7*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-2//35*c^2*d^-1*x^-5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-1//42*b*c*d*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//70*b*d*c^5*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//35*b*d*c^3*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//35*b*d*c^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^-10*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//9*d^-1*x^-9*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-8//315*c^4*d^-1*x^-5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-4//63*c^2*d^-1*x^-7*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-2//315*b*d*c^7*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//72*b*c*d*x^-8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//420*b*d*c^5*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//189*b*d*c^3*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+8//315*b*d*c^9*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^-12*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//11*d^-1*x^-11*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-16//1155*c^6*d^-1*x^-5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-8//231*c^4*d^-1*x^-7*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-2//33*c^2*d^-1*x^-9*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-4//1155*b*d*c^9*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//110*b*c*d*x^-10*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//770*b*d*c^7*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//1386*b*d*c^5*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//66*b*d*c^3*x^-8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+16//1155*b*d*c^11*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^7*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//3*c^-8*d^-3*(d+-1*d*c^2*x^2)^9//2*(a+b*arcsin(c*x))+-1//5*c^-8*d^-1*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+1//11*c^-8*d^-4*(d+-1*d*c^2*x^2)^11//2*(a+b*arcsin(c*x))+3//7*c^-8*d^-2*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-4//297*b*c*d*x^9*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//121*b*d*c^3*x^11*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//1617*b*d*c^-1*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//1925*b*d*c^-3*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+8//3465*b*d*c^-5*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+16//1155*b*d*x*c^-7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^5*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//5*c^-6*d^-1*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-1//9*c^-6*d^-3*(d+-1*d*c^2*x^2)^9//2*(a+b*arcsin(c*x))+2//7*c^-6*d^-2*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-10//441*b*c*d*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//81*b*d*c^3*x^9*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//525*b*d*c^-1*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//945*b*d*c^-3*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+8//315*b*d*x*c^-5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//5*c^-4*d^-1*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+1//7*c^-4*d^-2*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-8//175*b*c*d*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//49*b*d*c^3*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//105*b*d*c^-1*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//35*b*d*x*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//5*c^-2*d^-1*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-2//15*b*c*d*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//5*b*d*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//25*b*d*c^3*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(1//3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+d*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+im*b*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-4//3*b*c*d*x*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//9*b*d*c^3*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//2*x^-2*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-3//2*d*c^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*d*x*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3*d*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//2*b*c*d*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//2*im*b*d*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+3//2*im*b*d*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-5*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x)), x) == :(-1//4*x^-4*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+3//8*d*c^2*x^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-3//4*d*c^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//12*b*c*d*x^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//8*b*d*c^3*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//8*im*b*d*c^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+3//8*im*b*d*c^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^4*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(1//10*x^5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+1//16*d*x^5*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+1//32*d^2*x^5*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-3//256*x*c^-4*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//128*c^-2*d^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-31//960*b*c*d^2*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//100*b*c^5*d^2*x^10*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//512*b*c^-1*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//512*b*c^-3*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//512*b^-1*c^-5*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+21//640*b*c^3*d^2*x^8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^2*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(1//8*x^3*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+5//48*d*x^3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+5//64*d^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5//128*x*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-59//768*b*c*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//64*b*c^5*d^2*x^8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//256*b*c^-1*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//256*b^-1*c^-3*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+17//288*b*c^3*d^2*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate((d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(1//6*x*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+5//16*x*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//24*d*x*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+1//36*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)+-25//96*b*c*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//32*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//96*b*c^3*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-2*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1*x^-1*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-15//8*x*c^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5//4*d*x*c^2*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+b*c*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-15//16*c*b^-1*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//16*b*c^5*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+9//16*b*c^3*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//3*x^-3*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+5//2*x*c^4*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//3*d*c^2*x^-1*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-7//3*b*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//4*b*c^5*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//6*b*c*d^2*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//4*b^-1*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-6*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//5*x^-5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-1*c^4*d^2*x^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//3*d*c^2*x^-3*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//2*b^-1*c^5*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//20*b*c*d^2*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+11//30*b*c^3*d^2*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+23//15*b*c^5*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^-8*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//7*d^-1*x^-7*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-3//14*b*c^5*d^2*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//7*b*c^7*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//42*b*c*d^2*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//28*b*c^3*d^2*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-10*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//9*d^-1*x^-9*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-2//63*c^2*d^-1*x^-7*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-2//63*b*c^9*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//21*b*c^7*d^2*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//72*b*c*d^2*x^-8*(1+-1*c^2*x^2)^7//2*(d+-1*d*c^2*x^2)^(1/2)+-1//189*b*c^3*d^2*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//42*b*c^5*d^2*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-12*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//11*d^-1*x^-11*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-8//693*c^4*d^-1*x^-7*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-4//99*c^2*d^-1*x^-9*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-113//4158*b*c^5*d^2*x^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-8//693*b*c^11*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(x)+-1//110*b*c*d^2*x^-10*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//924*b*c^7*d^2*x^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//693*b*c^9*d^2*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+23//792*b*c^3*d^2*x^-8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//7*c^-6*d^-1*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-1//11*c^-6*d^-3*(d+-1*d*c^2*x^2)^11//2*(a+b*arcsin(c*x))+2//9*c^-6*d^-2*(d+-1*d*c^2*x^2)^9//2*(a+b*arcsin(c*x))+-113//4851*b*c*d^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//121*b*c^5*d^2*x^11*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//1155*b*c^-1*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//2079*b*c^-3*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+8//693*b*x*c^-5*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+23//891*b*c^3*d^2*x^9*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^3*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//7*c^-4*d^-1*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+1//9*c^-4*d^-2*(d+-1*d*c^2*x^2)^9//2*(a+b*arcsin(c*x))+-1//21*b*c*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//81*b*c^5*d^2*x^9*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//189*b*c^-1*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//63*b*x*c^-3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+19//441*b*c^3*d^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//7*c^-2*d^-1*(d+-1*d*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-1//7*b*c*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//49*b*c^5*d^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//7*b*x*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//35*b*c^3*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(1//5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//3*d*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+im*b*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-23//15*b*c*x*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//25*b*c^5*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+11//45*b*c^3*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//2*x^-2*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+-5//2*c^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5//6*d*c^2*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+5*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//2*b*c*d^2*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//9*b*c^5*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+7//3*b*x*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-5//2*im*b*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+5//2*im*b*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-5*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x)), x) == :(-1//4*x^-4*(d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))+15//8*c^4*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//8*d*c^2*x^-2*(d+-1*d*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1*b*x*c^5*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-15//4*c^4*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//12*b*c*d^2*x^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+9//8*b*c^3*d^2*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-15//8*im*b*c^4*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+15//8*im*b*c^4*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate((1+-1*x^2)^(1/2)*arcsin(x), x) == :(-1//4*x^2+1//4*arcsin(x)^2+(1/2)*x*(1+-1*x^2)^(1/2)*arcsin(x))
@test integrate(x^4*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(1//16*a^-1*x^4+3//16*a^-5*arcsin(a*x)^2+3//16*a^-3*x^2+-3//8*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)+-1//4*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(1//9*a^-1*x^3+2//3*x*a^-3+-2//3*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(1//4*a^-1*x^2+1//4*a^-3*arcsin(a*x)^2+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(x*a^-1+-1*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate((1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :((1/2)*a^-1*arcsin(a*x)^2)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(im*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x)))+-1*im*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))+-2*arcsin(a*x)*arctanh(exp(im*arcsin(a*x))))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(a*log(x)+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x), x) == :(-1//2*a*x^-1+(1/2)*im*a^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x)))+-1*a^2*arcsin(a*x)*arctanh(exp(im*arcsin(a*x)))+-1//2*im*a^2*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x^5*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-8//15*c^-6*d^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-4//15*c^-4*d^-1*x^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//5*c^-2*d^-1*x^4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//25*b*c^-1*x^5*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+4//45*b*c^-3*x^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+8//15*b*x*c^-5*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^4*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-3//8*x*c^-4*d^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//4*c^-2*d^-1*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//16*b*c^-1*x^4*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+3//16*b*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+3//16*b^-1*c^-5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^3*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-2//3*c^-4*d^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//3*c^-2*d^-1*x^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//9*b*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+2//3*b*x*c^-3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-1//2*x*c^-2*d^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//4*b*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+1//4*b^-1*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-1*c^-2*d^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2)
@test integrate((d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :((1/2)*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+im*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-1*d^-1*x^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*c*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(x))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-1//2*d^-1*x^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//2*b*c*x^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+(1/2)*im*b*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1//2*im*b*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)), x) == :(-1//3*d^-1*x^-3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2//3*c^2*d^-1*x^-1*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//6*b*c*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+2//3*b*c^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(x))
@test integrate(x^5*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(8//3*c^-6*d^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+c^-2*d^-1*x^4*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+4//3*c^-4*d^-2*x^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*b*c^-6*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x)+-5//3*b*x*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-1//9*b*c^-3*d^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^4*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(c^-2*d^-1*x^3*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+3//2*x*c^-4*d^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+(1/2)*b*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2)+-3//4*b^-1*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1//4*b*c^-3*d^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^3*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(2*c^-4*d^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+c^-2*d^-1*x^2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1*b*x*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-1*b*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x))
@test integrate(x^2*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(x*c^-2*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+(1/2)*b*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2)+-1//2*b^-1*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(c^-2*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1*b*c^-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x))
@test integrate((d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(x*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+(1/2)*b*c^-1*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x)+-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+im*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-2*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(-1*d^-1*x^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+2*x*c^2*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+b*c*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(x)+(1/2)*b*c*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(-1//2*d^-1*x^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+3//2*c^2*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1*b*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x)+-3*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//2*b*c*d^-1*x^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-3//2*im*b*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+3//2*im*b*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x)), x) == :(-1//3*d^-1*x^-3*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-4//3*c^2*d^-1*x^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+8//3*x*c^4*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+(1/2)*b*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2)+-1//6*b*c*d^-1*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+5//3*b*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(x))
@test integrate(x^6*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-5//2*x*c^-6*d^-3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5//3*c^-4*d^-2*x^3*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c^-7*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^5*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-7//6*b*c^-7*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2)+1//4*b*c^-5*d^-2*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+5//4*b^-1*c^-7*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^5*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-8//3*c^-6*d^-3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-4//3*c^-4*d^-2*x^2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+1//3*c^-2*d^-1*x^4*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//6*b*c^-3*d^-2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+5//6*b*x*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+11//6*b*c^-6*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x))
@test integrate(x^4*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-1*x*c^-4*d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c^-5*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^3*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+(1/2)*b^-1*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2//3*b*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2))
@test integrate(x^3*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-1//3*c^-4*d^-2*(d+-1*d*c^2*x^2)^-1//2*(2a+2*b*arcsin(c*x))+1//3*c^-2*d^-1*x^2*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//6*b*x*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+5//6*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x))
@test integrate(x^2*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(1//3*d^-1*x^3*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//6*b*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+-1//6*b*c^-3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2))
@test integrate(x*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(1//3*c^-2*d^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//6*b*x*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+-1//6*b*c^-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x))
@test integrate((d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(1//3*x*d^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+2//3*x*d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+1//3*b*c^-1*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2))
@test integrate(x^-1*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+1//3*d^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-7//6*b*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x)+im*b*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-1//6*b*c*x*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^-2*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-1*d^-1*x^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//6*b*c*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+4//3*x*c^2*d^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+8//3*x*c^2*d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+b*c*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(x)+5//6*b*c*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2))
@test integrate(x^-3*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-1//2*d^-1*x^-2*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+5//2*c^2*d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+5//6*c^2*d^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-5*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-13//6*b*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x)+-5//12*b*x*c^3*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+-3//4*b*c*d^-2*x^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+1//4*b*c*d^-2*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+-5//2*im*b*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+5//2*im*b*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-4*(d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x)), x) == :(-1//3*d^-1*x^-3*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-2*c^2*d^-1*x^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//6*b*c^3*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2+8//3*x*c^4*d^-1*(d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+16//3*x*c^4*d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c*d^-2*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+4//3*b*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(1+-1*c^2*x^2)+8//3*b*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*log(x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*arcsin(a*x), x) == :(-2//15*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^-1//2+-1//20*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^2*x^2)^-1//2+1//5*x*c^-1*(c+-1*c*a^2*x^2)^-5//2*arcsin(a*x)+4//15*x*c^-2*(c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)+8//15*x*c^-3*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+4//15*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a^2*x^2))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-38//6125*d*b^2*x^5+2//35*d*x^5*(a+b*arcsin(c*x))^2+-304//3675*d*x*b^2*c^-4+-152//11025*d*b^2*c^-2*x^3+1//7*d*x^5*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+2//343*d*b^2*c^2*x^7+-4//35*b*d*c^-5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+2//21*b*d*c^-5*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+2//49*b*d*c^-5*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+32//525*b*d*c^-5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//175*b*d*c^-1*x^4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+16//525*b*d*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-1//24*d*c^-4*(a+b*arcsin(c*x))^2+-1//72*d*b^2*x^4+1//12*d*x^4*(a+b*arcsin(c*x))^2+-1//24*d*b^2*c^-2*x^2+1//6*d*x^4*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+1//108*d*b^2*c^2*x^6+-1//18*b*c*d*x^5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//12*b*d*x*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//18*b*d*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-26//675*d*b^2*x^3+2//15*d*x^3*(a+b*arcsin(c*x))^2+-52//225*d*x*b^2*c^-2+1//5*d*x^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+2//125*d*b^2*c^2*x^5+-2//25*b*d*c^-3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+2//15*b*d*c^-3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+8//45*b*d*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//45*b*d*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-5//32*d*b^2*x^2+3//32*d*c^-2*(a+b*arcsin(c*x))^2+-1//4*d*c^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+1//32*d*b^2*c^2*x^4+1//8*b*d*x*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+3//16*b*d*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-14//9*d*x*b^2+2//3*d*x*(a+b*arcsin(c*x))^2+1//3*d*x*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+2//27*d*b^2*c^2*x^3+2//9*b*d*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+4//3*b*d*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-1//4*d*(a+b*arcsin(c*x))^2+d*(a+b*arcsin(c*x))^2*log(1+-1*exp(2*im*arcsin(c*x)))+(1/2)*d*b^2*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+(1/2)*d*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-1//3*im*d*b^-1*(a+b*arcsin(c*x))^3+1//4*d*b^2*c^2*x^2+-1*im*b*d*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*b*c*d*x*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-1*d*x^-1*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-2*d*x*c^2*(a+b*arcsin(c*x))^2+2*d*x*b^2*c^2+-4*b*c*d*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-2*im*c*d*b^2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*b*c*d*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2*im*c*d*b^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-1//2*d*c^2*(a+b*arcsin(c*x))^2+d*b^2*c^2*log(x)+-1*d*c^2*(a+b*arcsin(c*x))^2*log(1+-1*exp(2*im*arcsin(c*x)))+-1//2*d*b^2*c^2*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+-1//2*d*x^-2*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+1//3*im*d*b^-1*c^2*(a+b*arcsin(c*x))^3+im*b*d*c^2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1*b*c*d*x^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2), x) == :(-1//3*d*b^2*c^2*x^-1+-1//3*d*x^-3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+2//3*d*c^2*x^-1*(a+b*arcsin(c*x))^2+-5//3*im*d*b^2*c^3*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+5//3*im*d*b^2*c^3*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+10//3*b*d*c^3*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//3*b*c*d*x^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-526//165375*b^2*d^2*x^5+8//315*d^2*x^5*(a+b*arcsin(c*x))^2+-4208//99225*x*b^2*c^-4*d^2+-2104//297675*b^2*c^-2*d^2*x^3+-2//729*b^2*c^4*d^2*x^9+1//9*d^2*x^5*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+4//63*d^2*x^5*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+212//27783*b^2*c^2*d^2*x^7+-20//441*b*c^-5*d^2*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+-2//315*b*c^-5*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+2//81*b*c^-5*d^2*(1+-1*c^2*x^2)^9//2*(a+b*arcsin(c*x))+8//189*b*c^-5*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+128//4725*b*c^-5*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+16//1575*b*c^-1*d^2*x^4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+64//4725*b*c^-3*d^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-73//3072*c^-4*d^2*(a+b*arcsin(c*x))^2+-73//9216*b^2*d^2*x^4+1//24*d^2*x^4*(a+b*arcsin(c*x))^2+-73//3072*b^2*c^-2*d^2*x^2+-1//256*b^2*c^4*d^2*x^8+1//8*d^2*x^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+1//12*d^2*x^4*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+43//3456*b^2*c^2*d^2*x^6+-25//576*b*c*d^2*x^5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//32*b*c*d^2*x^5*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+73//1536*b*x*c^-3*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+73//2304*b*c^-1*d^2*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-818//33075*b^2*d^2*x^3+8//105*d^2*x^3*(a+b*arcsin(c*x))^2+-1636//11025*x*b^2*c^-2*d^2+-2//343*b^2*c^4*d^2*x^7+1//7*d^2*x^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+4//35*d^2*x^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+136//6125*b^2*c^2*d^2*x^5+-2//49*b*c^-3*d^2*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+2//175*b*c^-3*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+8//105*b*c^-3*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+32//315*b*c^-3*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+16//315*b*c^-1*d^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-25//288*b^2*d^2*x^2+5//96*c^-2*d^2*(a+b*arcsin(c*x))^2+-1//6*c^-2*d^2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+1//108*b^2*c^-2*d^2*(1+-1*c^2*x^2)^3+5//288*b^2*c^2*d^2*x^4+1//18*b*x*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+5//48*b*x*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//72*b*x*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-298//225*x*b^2*d^2+8//15*x*d^2*(a+b*arcsin(c*x))^2+-2//125*b^2*c^4*d^2*x^5+1//5*x*d^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+4//15*x*d^2*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+76//675*b^2*c^2*d^2*x^3+2//25*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+8//45*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+16//15*b*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-11//32*d^2*(a+b*arcsin(c*x))^2+d^2*(a+b*arcsin(c*x))^2*log(1+-1*exp(2*im*arcsin(c*x)))+(1/2)*b^2*d^2*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+(1/2)*d^2*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+1//4*d^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+-1//3*im*b^-1*d^2*(a+b*arcsin(c*x))^3+-1//32*b^2*c^4*d^2*x^4+13//32*b^2*c^2*d^2*x^2+-1*im*b*d^2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-11//16*b*c*x*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//8*b*c*x*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-1*d^2*x^-1*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+-8//3*x*c^2*d^2*(a+b*arcsin(c*x))^2+-2//27*b^2*c^4*d^2*x^3+32//9*x*b^2*c^2*d^2+-4*b*c*d^2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-2*im*c*b^2*d^2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*c*b^2*d^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-10//3*b*c*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-4//3*x*c^2*d^2*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-2//9*b*c*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x)))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-1//4*c^2*d^2*(a+b*arcsin(c*x))^2+b^2*c^2*d^2*log(x)+-1*b^2*c^2*d^2*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+-1*c^2*d^2*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-2*c^2*d^2*(a+b*arcsin(c*x))^2*log(1+-1*exp(2*im*arcsin(c*x)))+-1//2*d^2*x^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+-1//4*b^2*c^4*d^2*x^2+2//3*im*b^-1*c^2*d^2*(a+b*arcsin(c*x))^3+-1*b*c*d^2*x^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+2*im*b*c^2*d^2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//2*b*x*c^3*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^2, x) == :(-2*x*b^2*c^4*d^2+-1//3*b^2*c^2*d^2*x^-1+-1//3*d^2*x^-3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+8//3*x*c^4*d^2*(a+b*arcsin(c*x))^2+-11//3*im*b^2*c^3*d^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+4//3*c^2*d^2*x^-1*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+5//3*b*c^3*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+11//3*im*b^2*c^3*d^2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+22//3*b*c^3*d^2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//3*b*c*d^2*x^-2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x)))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-12622//6670125*b^2*d^3*x^5+16//1155*d^3*x^5*(a+b*arcsin(c*x))^2+-100976//4002075*x*b^2*c^-4*d^3+-50488//12006225*b^2*c^-2*d^3*x^3+-182//29403*b^2*c^4*d^3*x^9+1//11*d^3*x^5*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+2//33*d^3*x^5*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+2//1331*b^2*c^6*d^3*x^11+8//231*d^3*x^5*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+9410//1120581*b^2*c^2*d^3*x^7+-8//297*b*c^-5*d^3*(1+-1*c^2*x^2)^9//2*(a+b*arcsin(c*x))+-4//1155*b*c^-5*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+2//121*b*c^-5*d^3*(1+-1*c^2*x^2)^11//2*(a+b*arcsin(c*x))+2//1617*b*c^-5*d^3*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+16//693*b*c^-5*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+256//17325*b*c^-5*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+32//5775*b*c^-1*d^3*x^4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+128//17325*b*c^-3*d^3*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-79//5120*c^-4*d^3*(a+b*arcsin(c*x))^2+-79//15360*b^2*d^3*x^4+1//40*d^3*x^4*(a+b*arcsin(c*x))^2+-79//5120*b^2*c^-2*d^3*x^2+-57//6400*b^2*c^4*d^3*x^8+1//10*d^3*x^4*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+1//20*d^3*x^4*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+1//500*b^2*c^6*d^3*x^10+3//40*d^3*x^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+401//28800*b^2*c^2*d^3*x^6+-31//960*b*c*d^3*x^5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//32*b*c*d^3*x^5*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//50*b*c*d^3*x^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+79//2560*b*x*c^-3*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+79//3840*b*c^-1*d^3*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-5258//297675*b^2*d^3*x^3+16//315*d^3*x^3*(a+b*arcsin(c*x))^2+-10516//99225*x*b^2*c^-2*d^3+-374//27783*b^2*c^4*d^3*x^7+1//9*d^3*x^3*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+2//21*d^3*x^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+2//729*b^2*c^6*d^3*x^9+8//105*d^3*x^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+4198//165375*b^2*c^2*d^3*x^5+-2//81*b*c^-3*d^3*(1+-1*c^2*x^2)^9//2*(a+b*arcsin(c*x))+2//441*b*c^-3*d^3*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+4//525*b*c^-3*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+16//315*b*c^-3*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+64//945*b*c^-3*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+32//945*b*c^-1*d^3*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-175//3072*b^2*d^3*x^2+35//1024*c^-2*d^3*(a+b*arcsin(c*x))^2+-1//8*c^-2*d^3*(1+-1*c^2*x^2)^4*(a+b*arcsin(c*x))^2+1//256*b^2*c^-2*d^3*(1+-1*c^2*x^2)^4+7//1152*b^2*c^-2*d^3*(1+-1*c^2*x^2)^3+35//3072*b^2*c^2*d^3*x^4+1//32*b*x*c^-1*d^3*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+7//192*b*x*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+35//512*b*x*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+35//768*b*x*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-4322//3675*x*b^2*d^3+16//35*x*d^3*(a+b*arcsin(c*x))^2+-234//6125*b^2*c^4*d^3*x^5+1//7*x*d^3*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+2//343*b^2*c^6*d^3*x^7+6//35*x*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+8//35*x*d^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+1514//11025*b^2*c^2*d^3*x^3+2//49*b*c^-1*d^3*(1+-1*c^2*x^2)^7//2*(a+b*arcsin(c*x))+12//175*b*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+16//105*b*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+32//35*b*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-19//48*d^3*(a+b*arcsin(c*x))^2+d^3*(a+b*arcsin(c*x))^2*log(1+-1*exp(2*im*arcsin(c*x)))+(1/2)*b^2*d^3*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+(1/2)*d^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-1//108*b^2*d^3*(1+-1*c^2*x^2)^3+1//4*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+1//6*d^3*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+-7//144*b^2*c^4*d^3*x^4+-1//3*im*b^-1*d^3*(a+b*arcsin(c*x))^3+71//144*b^2*c^2*d^3*x^2+-1*im*b*d^3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-19//24*b*c*x*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-7//36*b*c*x*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-1//18*b*c*x*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-1*d^3*x^-1*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+-16//5*x*c^2*d^3*(a+b*arcsin(c*x))^2+-14//75*b^2*c^4*d^3*x^3+2//125*b^2*c^6*d^3*x^5+122//25*x*b^2*c^2*d^3+-4*b*c*d^3*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-2*im*c*b^2*d^3*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*c*b^2*d^3*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-22//5*b*c*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-8//5*x*c^2*d^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-6//5*x*c^2*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+-2//5*b*c*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+-2//25*b*c*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x)))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(3//32*c^2*d^3*(a+b*arcsin(c*x))^2+b^2*c^2*d^3*log(x)+-3*c^2*d^3*(a+b*arcsin(c*x))^2*log(1+-1*exp(2*im*arcsin(c*x)))+-21//32*b^2*c^4*d^3*x^2+-3//2*b^2*c^2*d^3*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+-3//2*c^2*d^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+-3//4*c^2*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+-1//2*d^3*x^-2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+1//32*b^2*c^6*d^3*x^4+im*b^-1*c^2*d^3*(a+b*arcsin(c*x))^3+-1*b*c*d^3*x^-1*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))+3*im*b*c^2*d^3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-7//8*b*x*c^3*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+3//16*b*x*c^3*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3, x) == :(-50//9*x*b^2*c^4*d^3+-1//3*b^2*c^2*d^3*x^-1+-1//3*d^3*x^-3*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2+2//27*b^2*c^6*d^3*x^3+16//3*x*c^4*d^3*(a+b*arcsin(c*x))^2+2*c^2*d^3*x^-1*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2+5*b*c^3*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-17//3*im*b^2*c^3*d^3*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1//9*b*c^3*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))+8//3*x*c^4*d^3*(a+b*arcsin(c*x))^2*(1+-1*c^2*x^2)+17//3*im*b^2*c^3*d^3*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+34//3*b*c^3*d^3*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-1//3*b*c*d^3*x^-2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x)))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-1*x*c^-4*d^-1*(a+b*arcsin(c*x))^2+-2*b^2*c^-5*d^-1*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+2*b^2*c^-5*d^-1*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-1//3*c^-2*d^-1*x^3*(a+b*arcsin(c*x))^2+2//27*b^2*c^-2*d^-1*x^3+22//9*x*b^2*c^-4*d^-1+-2*im*c^-5*d^-1*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-22//9*b*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2*im*b*c^-5*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*im*b*c^-5*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-2//9*b*c^-3*d^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(1//4*c^-4*d^-1*(a+b*arcsin(c*x))^2+-1*c^-4*d^-1*(a+b*arcsin(c*x))^2*log(1+exp(2*im*arcsin(c*x)))+-1//2*b^2*c^-4*d^-1*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+-1//2*c^-2*d^-1*x^2*(a+b*arcsin(c*x))^2+1//4*b^2*c^-2*d^-1*x^2+1//3*im*b^-1*c^-4*d^-1*(a+b*arcsin(c*x))^3+im*b*c^-4*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//2*b*x*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-1*x*c^-2*d^-1*(a+b*arcsin(c*x))^2+-2*b^2*c^-3*d^-1*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+2*x*b^2*c^-2*d^-1+2*b^2*c^-3*d^-1*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-2*im*c^-3*d^-1*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-2*b*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2*im*b*c^-3*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*im*b*c^-3*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-1*c^-2*d^-1*(a+b*arcsin(c*x))^2*log(1+exp(2*im*arcsin(c*x)))+-1//2*b^2*c^-2*d^-1*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+1//3*im*b^-1*c^-2*d^-1*(a+b*arcsin(c*x))^3+im*b*c^-2*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-2*b^2*c^-1*d^-1*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+2*b^2*c^-1*d^-1*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-2*im*c^-1*d^-1*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-2*im*b*c^-1*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*im*b*c^-1*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :((1/2)*b^2*d^-1*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+-2*d^-1*(a+b*arcsin(c*x))^2*arctanh(exp(2*im*arcsin(c*x)))+-1//2*b^2*d^-1*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+im*b*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*b*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-1*d^-1*x^-1*(a+b*arcsin(c*x))^2+-2*c*b^2*d^-1*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+2*c*b^2*d^-1*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-4*b*c*d^-1*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-2*im*c*b^2*d^-1*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*im*c*d^-1*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+2*im*c*b^2*d^-1*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-2*im*b*c*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*im*b*c*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-1//2*d^-1*x^-2*(a+b*arcsin(c*x))^2+b^2*c^2*d^-1*log(x)+(1/2)*b^2*c^2*d^-1*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+-2*c^2*d^-1*(a+b*arcsin(c*x))^2*arctanh(exp(2*im*arcsin(c*x)))+-1//2*b^2*c^2*d^-1*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+im*b*c^2*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*b*c^2*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1*b*c*d^-1*x^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1, x) == :(-1//3*d^-1*x^-3*(a+b*arcsin(c*x))^2+-1*c^2*d^-1*x^-1*(a+b*arcsin(c*x))^2+-2*b^2*c^3*d^-1*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+2*b^2*c^3*d^-1*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-1//3*b^2*c^2*d^-1*x^-1+-2*im*c^3*d^-1*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-14//3*b*c^3*d^-1*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-7//3*im*b^2*c^3*d^-1*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+7//3*im*b^2*c^3*d^-1*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-2*im*b*c^3*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*im*b*c^3*d^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1//3*b*c*d^-1*x^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :(b^2*c^-5*d^-2*arctanh(c*x)+-3*b^2*c^-5*d^-2*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-2*x*b^2*c^-4*d^-2+3*b^2*c^-5*d^-2*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+3//2*x*c^-4*d^-2*(a+b*arcsin(c*x))^2+(1/2)*c^-2*d^-2*x^3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1*b*c^-5*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+2*b*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3*im*c^-5*d^-2*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-3*im*b*c^-5*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+3*im*b*c^-5*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :((1/2)*c^-4*d^-2*(a+b*arcsin(c*x))^2+c^-4*d^-2*(a+b*arcsin(c*x))^2*log(1+exp(2*im*arcsin(c*x)))+(1/2)*b^2*c^-4*d^-2*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+-1//2*b^2*c^-4*d^-2*log(1+-1*c^2*x^2)+(1/2)*c^-2*d^-2*x^2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1//3*im*b^-1*c^-4*d^-2*(a+b*arcsin(c*x))^3+-1*im*b*c^-4*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*b*x*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :(b^2*c^-3*d^-2*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+b^2*c^-3*d^-2*arctanh(c*x)+-1*b^2*c^-3*d^-2*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+im*c^-3*d^-2*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+(1/2)*x*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1*b*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+im*b*c^-3*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-1*im*b*c^-3*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :((1/2)*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1//2*b^2*c^-2*d^-2*log(1+-1*c^2*x^2)+-1*b*x*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :(b^2*c^-1*d^-2*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+b^2*c^-1*d^-2*arctanh(c*x)+(1/2)*x*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1*b^2*c^-1*d^-2*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+-1*im*c^-1*d^-2*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-1*b*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+im*b*c^-1*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1*im*b*c^-1*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :((1/2)*b^2*d^-2*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+(1/2)*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-2*d^-2*(a+b*arcsin(c*x))^2*arctanh(exp(2*im*arcsin(c*x)))+-1//2*b^2*d^-2*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+-1//2*b^2*d^-2*log(1+-1*c^2*x^2)+im*b*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*b*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1*b*c*x*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :(c*b^2*d^-2*arctanh(c*x)+-1*d^-2*x^-1*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-3*c*b^2*d^-2*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+3*c*b^2*d^-2*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-1*b*c*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-4*b*c*d^-2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-3*im*c*d^-2*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-2*im*c*b^2*d^-2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*c*b^2*d^-2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+3//2*x*c^2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-3*im*b*c*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+3*im*b*c*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :(b^2*c^2*d^-2*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+b^2*c^2*d^-2*log(x)+c^2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1*b^2*c^2*d^-2*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+-4*c^2*d^-2*(a+b*arcsin(c*x))^2*arctanh(exp(2*im*arcsin(c*x)))+-1//2*b^2*c^2*d^-2*log(1+-1*c^2*x^2)+-1//2*d^-2*x^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1*b*c*d^-2*x^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-2*im*b*c^2*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*im*b*c^2*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-2, x) == :(b^2*c^3*d^-2*arctanh(c*x)+-5*b^2*c^3*d^-2*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+5*b^2*c^3*d^-2*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-1//3*b^2*c^2*d^-2*x^-1+-1//3*d^-2*x^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-5*im*c^3*d^-2*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-26//3*b*c^3*d^-2*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-13//3*im*b^2*c^3*d^-2*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-5//3*c^2*d^-2*x^-1*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-2//3*b*c^3*d^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+5//2*x*c^4*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+13//3*im*b^2*c^3*d^-2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-5*im*b*c^3*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+5*im*b*c^3*d^-2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1//3*b*c*d^-2*x^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x)))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-7//6*b^2*c^-5*d^-3*arctanh(c*x)+-3//4*b^2*c^-5*d^-3*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+3//4*b^2*c^-5*d^-3*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-3//4*im*c^-5*d^-3*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-3//8*x*c^-4*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-1//6*b*c^-5*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+1//4*c^-2*d^-3*x^3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*x*b^2*c^-4*d^-3*(1+-1*c^2*x^2)^-1+5//4*b*c^-5*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-3//4*im*b*c^-5*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+3//4*im*b*c^-5*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-1//4*c^-4*d^-3*(a+b*arcsin(c*x))^2+1//3*b^2*c^-4*d^-3*log(1+-1*c^2*x^2)+1//4*d^-3*x^4*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*b^2*c^-4*d^-3*(1+-1*c^2*x^2)^-1+(1/2)*b*x*c^-3*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c^-1*d^-3*x^3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-1//4*b^2*c^-3*d^-3*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-1//6*b^2*c^-3*d^-3*arctanh(c*x)+1//4*b^2*c^-3*d^-3*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+-1//6*b*c^-3*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-1//8*x*c^-2*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+1//4*im*c^-3*d^-3*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+1//4*b*c^-3*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+1//4*x*c^-2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*x*b^2*c^-2*d^-3*(1+-1*c^2*x^2)^-1+-1//4*im*b*c^-3*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+1//4*im*b*c^-3*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-1//6*b^2*c^-2*d^-3*log(1+-1*c^2*x^2)+1//4*c^-2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*b^2*c^-2*d^-3*(1+-1*c^2*x^2)^-1+-1//3*b*x*c^-1*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*x*c^-1*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-3//4*b^2*c^-1*d^-3*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+1//4*x*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*x*b^2*d^-3*(1+-1*c^2*x^2)^-1+3//4*b^2*c^-1*d^-3*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+3//8*x*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+5//6*b^2*c^-1*d^-3*arctanh(c*x)+-3//4*im*c^-1*d^-3*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-3//4*b*c^-1*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c^-1*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-3//4*im*b*c^-1*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+3//4*im*b*c^-1*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :((1/2)*b^2*d^-3*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+(1/2)*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-2*d^-3*(a+b*arcsin(c*x))^2*arctanh(exp(2*im*arcsin(c*x)))+-2//3*b^2*d^-3*log(1+-1*c^2*x^2)+-1//2*b^2*d^-3*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+1//4*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*b^2*d^-3*(1+-1*c^2*x^2)^-1+im*b*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*b*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-4//3*b*c*x*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c*x*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-1*d^-3*x^-1*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+-15//4*c*b^2*d^-3*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+11//6*c*b^2*d^-3*arctanh(c*x)+15//4*c*b^2*d^-3*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-4*b*c*d^-3*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-2*im*c*b^2*d^-3*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*c*b^2*d^-3*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-15//4*im*c*d^-3*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-7//4*b*c*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//6*b*c*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+1//12*x*b^2*c^2*d^-3*(1+-1*c^2*x^2)^-1+5//4*x*c^2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+15//8*x*c^2*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+-15//4*im*b*c*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+15//4*im*b*c*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(b^2*c^2*d^-3*log(x)+-6*c^2*d^-3*(a+b*arcsin(c*x))^2*arctanh(exp(2*im*arcsin(c*x)))+-7//6*b^2*c^2*d^-3*log(1+-1*c^2*x^2)+-3//2*b^2*c^2*d^-3*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(c*x)))+-1//2*d^-3*x^-2*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+1//12*b^2*c^2*d^-3*(1+-1*c^2*x^2)^-1+3//2*b^2*c^2*d^-3*Polylogarithms.polylog(3,exp(2*im*arcsin(c*x)))+3//2*c^2*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+3//4*c^2*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+-1*b*c*d^-3*x^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+-3*im*b*c^2*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+3*im*b*c^2*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-4//3*b*x*c^3*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+5//6*b*x*c^3*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x)))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3, x) == :(-35//4*b^2*c^3*d^-3*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(c*x)))+-1//2*b^2*c^2*d^-3*x^-1+-1//3*d^-3*x^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+17//6*b^2*c^3*d^-3*arctanh(c*x)+35//4*b^2*c^3*d^-3*Polylogarithms.polylog(3,im*exp(im*arcsin(c*x)))+-38//3*b*c^3*d^-3*(a+b*arcsin(c*x))*arctanh(exp(im*arcsin(c*x)))+-35//4*im*c^3*d^-3*(a+b*arcsin(c*x))^2*arctan(exp(im*arcsin(c*x)))+-29//12*b*c^3*d^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-19//3*im*b^2*c^3*d^-3*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-7//3*c^2*d^-3*x^-1*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+-1//12*x*b^2*c^4*d^-3*(1+-1*c^2*x^2)^-1+1//6*b*c^3*d^-3*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+1//6*b^2*c^2*d^-3*x^-1*(1+-1*c^2*x^2)^-1+19//3*im*b^2*c^3*d^-3*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+35//8*x*c^4*d^-3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2+35//12*x*c^4*d^-3*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2+-35//4*im*b*c^3*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-1//3*b*c*d^-3*x^-2*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))+35//4*im*b*c^3*d^-3*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x))))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :(-2//15*c^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//5*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+52//225*b^2*c^-4*(d+-1*d*c^2*x^2)^(1/2)+-2//125*b^2*c^-4*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+-1//15*c^-2*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+26//675*b^2*c^-4*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2//25*b*c*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//45*b*c^-1*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//15*a*b*x*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//15*x*b^2*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :(-1//32*b^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+1//4*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//8*x*c^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//64*x*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-1//64*b^2*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+1//24*b^-1*c^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+-1//8*b*c*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//8*b*c^-1*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :(4//9*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-1//3*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+2//27*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2//9*b*c*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//3*b*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :((1/2)*x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//4*x*b^2*(d+-1*d*c^2*x^2)^(1/2)+1//4*b^2*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+1//6*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+-1//2*b*c*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-2*b^2*(d+-1*d*c^2*x^2)^(1/2)+-2*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*arctanh(exp(im*arcsin(c*x)))+2*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*a*b*c*x*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2*c*x*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+2*im*b*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :(-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1*im*c*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//3*c*b^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+-1*im*c*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :(-1//2*x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+b^2*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+c^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*arctanh(exp(im*arcsin(c*x)))+-1*b^2*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-1*b^2*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arctanh((1+-1*c^2*x^2)^(1/2))+-1*b*c*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+im*b*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-1*im*b*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2), x) == :(-1//3*b^2*c^2*x^-1*(d+-1*d*c^2*x^2)^(1/2)+-1//3*d^-1*x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-1//3*b^2*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+1//3*im*c^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-2//3*b*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+-1//3*b*c*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//3*im*b^2*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x))))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(1//7*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-2//35*d*c^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+3//35*d*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+304//3675*d*b^2*c^-4*(d+-1*d*c^2*x^2)^(1/2)+-2//343*d*b^2*c^-4*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+-1//35*d*c^-2*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+38//6125*d*b^2*c^-4*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+152//11025*d*b^2*c^-4*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-16//175*b*c*d*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//49*b*d*c^3*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//105*b*d*c^-1*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//35*a*b*d*x*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//35*d*x*b^2*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(1//6*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-43//1728*d*b^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+1//8*d*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-7//1152*d*x*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-1//16*d*x*c^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//108*d*b^2*c^2*x^5*(d+-1*d*c^2*x^2)^(1/2)+1//48*d*b^-1*c^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+7//1152*d*b^2*c^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-7//48*b*c*d*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//16*b*d*c^-1*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//18*b*d*c^3*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(-1//5*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+16//75*d*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+2//125*d*b^2*c^-2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+8//225*d*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-4//15*b*c*d*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//5*b*d*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//25*b*d*c^3*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(1//3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+d*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-22//9*d*b^2*(d+-1*d*c^2*x^2)^(1/2)+-2//27*d*b^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2*d*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*d*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*arctanh(exp(im*arcsin(c*x)))+2*d*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*a*b*c*d*x*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2*c*d*x*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+2*im*b*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-2//3*b*c*d*x*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//9*b*d*c^3*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-3//2*d*x*c^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//4*d*x*b^2*c^2*(d+-1*d*c^2*x^2)^(1/2)+b*c*d*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*im*c*d*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-5//4*c*d*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-1//2*c*d*b^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+-1*im*c*d*b^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*d*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+3//2*b*d*c^3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(-1//2*x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+2*d*b^2*c^2*(d+-1*d*c^2*x^2)^(1/2)+-3//2*d*c^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1*d*b^2*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arctanh((1+-1*c^2*x^2)^(1/2))+-3*d*b^2*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+3*d*b^2*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+3*d*c^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*arctanh(exp(im*arcsin(c*x)))+-1*b*c*d*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*b*d*x*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3*a*b*d*x*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3*d*x*b^2*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-3*im*b*d*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+3*im*b*d*c^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2, x) == :(-1//3*x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+d*c^2*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//3*d*b^2*c^2*x^-1*(d+-1*d*c^2*x^2)^(1/2)+-1//3*d*b^2*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+1//3*d*b^-1*c^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+4//3*im*d*c^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-8//3*b*d*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+-1//3*b*c*d*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//3*im*d*b^2*c^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x))))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(1//9*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+-2//63*c^-4*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//21*d^2*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//63*d*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+160//3969*b^2*c^-4*d^2*(d+-1*d*c^2*x^2)^(1/2)+-2//729*b^2*c^-4*d^2*(1+-1*c^2*x^2)^4*(d+-1*d*c^2*x^2)^(1/2)+-1//63*c^-2*d^2*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+4//1323*b^2*c^-4*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+50//27783*b^2*c^-4*d^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+80//11907*b^2*c^-4*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2//21*b*c*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2//81*b*c^5*d^2*x^9*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//189*b*c^-1*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//63*a*b*x*c^-3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//63*x*b^2*c^-3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+38//441*b*c^3*d^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(1//8*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+-1079//55296*b^2*d^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+5//48*d*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+5//64*d^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-359//36864*x*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)+-5//128*x*c^-2*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//256*b^2*c^4*d^2*x^7*(d+-1*d*c^2*x^2)^(1/2)+209//13824*b^2*c^2*d^2*x^5*(d+-1*d*c^2*x^2)^(1/2)+5//384*b^-1*c^-3*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+359//36864*b^2*c^-3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-59//384*b*c*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//32*b*c^5*d^2*x^8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//128*b*c^-1*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+17//144*b*c^3*d^2*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(-1//7*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^7//2+32//245*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)+2//343*b^2*c^-2*d^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+12//1225*b^2*c^-2*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+16//735*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2//7*b*c*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2//49*b*c^5*d^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//7*b*x*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+6//35*b*c^3*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(1//6*x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+-245//1152*x*b^2*d^2*(d+-1*d*c^2*x^2)^(1/2)+5//16*x*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//24*d*x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-65//1728*x*b^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1//108*x*b^2*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+1//18*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//48*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//48*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+115//1152*b^2*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-5//16*b*c*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(1//5*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-598//225*b^2*d^2*(d+-1*d*c^2*x^2)^(1/2)+1//3*d*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-74//675*b^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2//125*b^2*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+-2*b^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*arctanh(exp(im*arcsin(c*x)))+2*b^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*a*b*c*x*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2*c*x*b^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+2*im*b*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-16//15*b*c*x*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2//25*b*c^5*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+22//45*b*c^3*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+-15//8*x*c^2*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-5//4*d*x*c^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+31//64*x*b^2*c^2*d^2*(d+-1*d*c^2*x^2)^(1/2)+b*c*d^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*im*c*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-89//64*c*b^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-5//8*c*b^-1*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+-1//8*b*c*d^2*(1+-1*c^2*x^2)^3//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//32*x*b^2*c^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1*im*c*b^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+15//8*b*c^3*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(-1//2*x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+-5//2*c^2*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-5//6*d*c^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+40//9*b^2*c^2*d^2*(d+-1*d*c^2*x^2)^(1/2)+2//27*b^2*c^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1*b^2*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arctanh((1+-1*c^2*x^2)^(1/2))+-5*b^2*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+5*b^2*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+5*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*arctanh(exp(im*arcsin(c*x)))+-1*b*c*d^2*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5*a*b*x*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5*x*b^2*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-2//9*b*c^5*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//3*b*x*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5*im*b*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+5*im*b*c^2*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2, x) == :(-1//3*x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2+-7//12*x*b^2*c^4*d^2*(d+-1*d*c^2*x^2)^(1/2)+5//2*x*c^4*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//3*d*c^2*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2+-7//3*b*c^3*d^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//3*b^2*c^2*d^2*x^-1*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+5//6*b^-1*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+7//3*im*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+23//12*b^2*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-14//3*b*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+-5//2*b*c^5*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//3*b*c*d^2*x^-2*(1+-1*c^2*x^2)^3//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+7//3*im*b^2*c^3*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x))))
@test integrate(x^5*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-76//675*b^2*c^-6*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^-1//2+-8//15*c^-6*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+2//125*b^2*c^-6*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^-1//2+298//225*b^2*c^-6*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-4//15*c^-4*d^-1*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//5*c^-2*d^-1*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+2//25*b*c^-1*x^5*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+8//45*b*c^-3*x^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+16//15*a*b*x*c^-5*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+16//15*x*b^2*c^-5*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-15//64*b^2*c^-5*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+-3//8*x*c^-4*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//4*c^-2*d^-1*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//8*b^-1*c^-5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+1//32*b^2*c^-2*x^3*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+15//64*x*b^2*c^-4*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+1//8*b*c^-1*x^4*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+3//8*b*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-2//3*c^-4*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-2//27*b^2*c^-4*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^-1//2+14//9*b^2*c^-4*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-1//3*c^-2*d^-1*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+2//9*b*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+4//3*a*b*x*c^-3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+4//3*x*b^2*c^-3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-1*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+2*b^2*c^-2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+2*a*b*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+2*x*b^2*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(1//3*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2)
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-2*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*arctanh(exp(im*arcsin(c*x)))+2*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-1*d^-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1*im*c*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*im*c*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-1//2*d^-1*x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+b^2*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-1*b^2*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-1*b^2*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh((1+-1*c^2*x^2)^(1/2))+-1*c^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*arctanh(exp(im*arcsin(c*x)))+-1*b*c*x^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+im*b*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1*im*b*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2, x) == :(-1//3*d^-1*x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-2//3*im*c^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2//3*c^2*d^-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//3*b^2*c^2*x^-1*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-2//3*im*b^2*c^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//3*b*c*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+4//3*b*c^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x))))
@test integrate(x^5*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(8//3*c^-6*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+c^-2*d^-1*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-32//9*b^2*c^-6*d^-1*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+2//27*b^2*c^-6*d^-1*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^-1//2+4//3*c^-4*d^-2*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-2*im*b^2*c^-6*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*c^-6*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*b*x*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-16//3*a*b*x*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-16//3*x*b^2*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+-2//9*b*c^-3*d^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+4*im*b*c^-6*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(c^-2*d^-1*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+3//2*x*c^-4*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1*im*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1//2*b^-1*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+-1//4*x*b^2*c^-4*d^-1*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+1//4*b^2*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+-1*im*b^2*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+2*b*c^-5*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-1//2*b*c^-3*d^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x)))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(2*c^-4*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+c^-2*d^-1*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2*b^2*c^-4*d^-1*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-4*a*b*x*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-4*x*b^2*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+-2*im*b^2*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*b*x*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+4*im*b*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(x*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*im*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1//3*b^-1*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+-1*im*b^2*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+2*b*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2*im*b^2*c^-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*c^-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+4*im*b*c^-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(x*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*im*c^-1*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*im*b^2*c^-1*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+2*b*c^-1*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*arctanh(exp(im*arcsin(c*x)))+2*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+4*im*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(-1*d^-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+2*x*c^2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2*im*c*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*im*c*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*c*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-4*b*c*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+4*b*c*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(-1//2*d^-1*x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+3//2*c^2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*b^2*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh((1+-1*c^2*x^2)^(1/2))+-3*b^2*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-3*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*arctanh(exp(im*arcsin(c*x)))+3*b^2*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-1*b*c*d^-1*x^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-2*im*b^2*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-3*im*b*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+3*im*b*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+4*im*b*c^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2, x) == :(-1//3*d^-1*x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-4//3*c^2*d^-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+8//3*x*c^4*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-8//3*im*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1//3*b^2*c^2*d^-1*x^-1*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-1*im*b^2*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-20//3*b*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+-5//3*im*b^2*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//3*b*c*d^-1*x^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+16//3*b*c^3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^5*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(-8//3*c^-6*d^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//3*b^2*c^-6*d^-2*(d+-1*d*c^2*x^2)^-1//2+2*b^2*c^-6*d^-2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-4//3*c^-4*d^-2*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-11//3*im*b^2*c^-6*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-11//3*b*x*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1//3*b*c^-3*d^-2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+11//3*im*b^2*c^-6*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+16//3*a*b*x*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+16//3*x*b^2*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+-22//3*im*b*c^-6*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(-1*x*c^-4*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*x*b^2*c^-4*d^-2*(d+-1*d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-1//3*b^2*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+1//3*b^-1*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+4//3*im*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-8//3*b*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-1//3*b*c^-3*d^-2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+4//3*im*b^2*c^-5*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x))))
@test integrate(x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(-2//3*c^-4*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*b^2*c^-4*d^-2*(d+-1*d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-5//3*im*b^2*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-1//3*b*x*c^-3*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+5//3*im*b^2*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-10//3*im*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(1//3*d^-1*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+1//3*x*b^2*c^-2*d^-2*(d+-1*d*c^2*x^2)^-1//2+-1//3*b^2*c^-3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+1//3*im*c^-3*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2//3*b*c^-3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-1//3*b*c^-1*d^-2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+1//3*im*b^2*c^-3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x))))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(1//3*b^2*c^-2*d^-2*(d+-1*d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-1//3*im*b^2*c^-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1//3*b*x*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+1//3*im*b^2*c^-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2//3*im*b*c^-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(1//3*x*b^2*d^-2*(d+-1*d*c^2*x^2)^-1//2+1//3*x*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+2//3*x*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2//3*im*c^-1*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1//3*b*c^-1*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-2//3*im*b^2*c^-1*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+4//3*b*c^-1*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*b^2*d^-2*(d+-1*d*c^2*x^2)^-1//2+1//3*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-2*b^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*arctanh(exp(im*arcsin(c*x)))+2*b^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-7//3*im*b^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+7//3*im*b^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*b*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*b*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-1//3*b*c*x*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+14//3*im*b*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(-1*d^-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+1//3*x*b^2*c^2*d^-2*(d+-1*d*c^2*x^2)^-1//2+4//3*x*c^2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+8//3*x*c^2*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-8//3*im*c*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1//3*b*c*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-1*im*c*b^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-4*b*c*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+-5//3*im*c*b^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+16//3*b*c*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(-1//2*d^-1*x^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+1//3*b^2*c^2*d^-2*(d+-1*d*c^2*x^2)^-1//2+5//2*c^2*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+5//6*c^2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-1*b^2*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh((1+-1*c^2*x^2)^(1/2))+-5*b^2*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-5*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*arctanh(exp(im*arcsin(c*x)))+5*b^2*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-1*b*c*d^-2*x^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+-13//3*im*b^2*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2//3*b*x*c^3*d^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+13//3*im*b^2*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-5*im*b*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+5*im*b*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+26//3*im*b*c^2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2, x) == :(-1//3*d^-1*x^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-2*c^2*d^-1*x^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+-1//3*b^2*c^2*d^-2*x^-1*(d+-1*d*c^2*x^2)^-1//2+2//3*x*b^2*c^4*d^-2*(d+-1*d*c^2*x^2)^-1//2+8//3*x*c^4*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2+16//3*x*c^4*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-16//3*im*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-32//3*b*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+-8//3*im*b^2*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-8//3*im*b^2*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-1//3*b*c*d^-2*x^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+32//3*b*c^3*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^4*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(-15//64*a^-5*arcsin(a*x)+1//8*a^-5*arcsin(a*x)^3+1//8*a^-1*x^4*arcsin(a*x)+1//32*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)+3//8*a^-3*x^2*arcsin(a*x)+15//64*x*a^-4*(1+-1*a^2*x^2)^(1/2)+-3//8*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+-1//4*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2)
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(-2//27*a^-4*(1+-1*a^2*x^2)^3//2+14//9*a^-4*(1+-1*a^2*x^2)^(1/2)+-2//3*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+2//9*a^-1*x^3*arcsin(a*x)+4//3*x*a^-3*arcsin(a*x)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2)
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(-1//4*a^-3*arcsin(a*x)+1//6*a^-3*arcsin(a*x)^3+(1/2)*a^-1*x^2*arcsin(a*x)+1//4*x*a^-2*(1+-1*a^2*x^2)^(1/2)+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2)
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(2*a^-2*(1+-1*a^2*x^2)^(1/2)+-1*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+2*x*a^-1*arcsin(a*x))
@test integrate((1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(1//3*a^-1*arcsin(a*x)^3)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(-2*Polylogarithms.polylog(3,-1*exp(im*arcsin(a*x)))+2*Polylogarithms.polylog(3,exp(im*arcsin(a*x)))+-2*arcsin(a*x)^2*arctanh(exp(im*arcsin(a*x)))+-2*im*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))*arcsin(a*x)+2*im*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x)))*arcsin(a*x))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(-1*im*a*arcsin(a*x)^2+-1*im*a*Polylogarithms.polylog(2,exp(2*im*arcsin(a*x)))+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+2*a*arcsin(a*x)*log(1+-1*exp(2*im*arcsin(a*x))))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(a^2*Polylogarithms.polylog(3,exp(im*arcsin(a*x)))+-1*a^2*Polylogarithms.polylog(3,-1*exp(im*arcsin(a*x)))+-1*a^2*arctanh((1+-1*a^2*x^2)^(1/2))+-1*a*x^-1*arcsin(a*x)+-1*a^2*arcsin(a*x)^2*arctanh(exp(im*arcsin(a*x)))+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+im*a^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x)))*arcsin(a*x)+-1*im*a^2*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2, x) == :(1//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3)
@test integrate((c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)^2, x) == :(x*c^-1*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-1*im*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-1*im*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a*x)))+2*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)*log(1+exp(2*im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^-5//2*arcsin(a*x)^2, x) == :(1//3*x*c^-2*(c+-1*c*a^2*x^2)^-1//2+1//3*x*c^-1*(c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)^2+2//3*x*c^-2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-1//3*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+-2//3*im*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-2//3*im*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a*x)))+4//3*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)*log(1+exp(2*im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^-7//2*arcsin(a*x)^2, x) == :(1//3*x*c^-3*(c+-1*c*a^2*x^2)^-1//2+1//5*x*c^-1*(c+-1*c*a^2*x^2)^-5//2*arcsin(a*x)^2+1//30*x*c^-3*(1+-1*a^2*x^2)^-1*(c+-1*c*a^2*x^2)^-1//2+4//15*x*c^-2*(c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)^2+8//15*x*c^-3*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-4//15*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+-1//10*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+-8//15*im*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-8//15*im*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a*x)))+16//15*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)*log(1+exp(2*im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^3*arcsin(a*x)^3, x) == :(-413312//128625*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)+-30256//385875*a^-1*c^3*(1+-1*a^2*x^2)^3//2+-4322//1225*x*c^3*arcsin(a*x)+-2664//214375*a^-1*c^3*(1+-1*a^2*x^2)^5//2+-6//2401*a^-1*c^3*(1+-1*a^2*x^2)^7//2+16//35*x*c^3*arcsin(a*x)^3+-702//6125*a^4*c^3*x^5*arcsin(a*x)+1//7*x*c^3*(1+-1*a^2*x^2)^3*arcsin(a*x)^3+3//49*a^-1*c^3*(1+-1*a^2*x^2)^7//2*arcsin(a*x)^2+6//35*x*c^3*(1+-1*a^2*x^2)^2*arcsin(a*x)^3+6//343*a^6*c^3*x^7*arcsin(a*x)+8//35*x*c^3*arcsin(a*x)^3*(1+-1*a^2*x^2)+8//35*a^-1*c^3*(1+-1*a^2*x^2)^3//2*arcsin(a*x)^2+18//175*a^-1*c^3*(1+-1*a^2*x^2)^5//2*arcsin(a*x)^2+48//35*a^-1*c^3*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+1514//3675*a^2*c^3*x^3*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)^2*arcsin(a*x)^3, x) == :(-4144//1125*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)+-298//75*x*c^2*arcsin(a*x)+-272//3375*a^-1*c^2*(1+-1*a^2*x^2)^3//2+-6//625*a^-1*c^2*(1+-1*a^2*x^2)^5//2+8//15*x*c^2*arcsin(a*x)^3+-6//125*a^4*c^2*x^5*arcsin(a*x)+1//5*x*c^2*(1+-1*a^2*x^2)^2*arcsin(a*x)^3+3//25*a^-1*c^2*(1+-1*a^2*x^2)^5//2*arcsin(a*x)^2+4//15*x*c^2*arcsin(a*x)^3*(1+-1*a^2*x^2)+4//15*a^-1*c^2*(1+-1*a^2*x^2)^3//2*arcsin(a*x)^2+8//5*a^-1*c^2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+76//225*a^2*c^2*x^3*arcsin(a*x))
@test integrate(arcsin(a*x)^3*(c+-1*c*a^2*x^2), x) == :(-40//9*c*a^-1*(1+-1*a^2*x^2)^(1/2)+-14//3*c*x*arcsin(a*x)+-2//27*c*a^-1*(1+-1*a^2*x^2)^3//2+2//3*c*x*arcsin(a*x)^3+2*c*a^-1*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^2+1//3*c*x*arcsin(a*x)^3*(1+-1*a^2*x^2)+1//3*c*a^-1*(1+-1*a^2*x^2)^3//2*arcsin(a*x)^2+2//9*c*a^2*x^3*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)^-1*arcsin(a*x)^3, x) == :(-6*im*a^-1*c^-1*Polylogarithms.polylog(4,-1*im*exp(im*arcsin(a*x)))+-6*a^-1*c^-1*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(a*x)))*arcsin(a*x)+6*im*a^-1*c^-1*Polylogarithms.polylog(4,im*exp(im*arcsin(a*x)))+6*a^-1*c^-1*Polylogarithms.polylog(3,im*exp(im*arcsin(a*x)))*arcsin(a*x)+-3*im*a^-1*c^-1*arcsin(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arcsin(a*x)))+-2*im*a^-1*c^-1*arcsin(a*x)^3*arctan(exp(im*arcsin(a*x)))+3*im*a^-1*c^-1*arcsin(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^-2*arcsin(a*x)^3, x) == :((1/2)*x*c^-2*(1+-1*a^2*x^2)^-1*arcsin(a*x)^3+-3*im*a^-1*c^-2*Polylogarithms.polylog(2,im*exp(im*arcsin(a*x)))+-3*im*a^-1*c^-2*Polylogarithms.polylog(4,-1*im*exp(im*arcsin(a*x)))+-3*a^-1*c^-2*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(a*x)))*arcsin(a*x)+3*im*a^-1*c^-2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(a*x)))+3*im*a^-1*c^-2*Polylogarithms.polylog(4,im*exp(im*arcsin(a*x)))+3*a^-1*c^-2*Polylogarithms.polylog(3,im*exp(im*arcsin(a*x)))*arcsin(a*x)+-3//2*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2+-1*im*a^-1*c^-2*arcsin(a*x)^3*arctan(exp(im*arcsin(a*x)))+-6*im*a^-1*c^-2*arcsin(a*x)*arctan(exp(im*arcsin(a*x)))+-3//2*im*a^-1*c^-2*arcsin(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arcsin(a*x)))+3//2*im*a^-1*c^-2*arcsin(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^-3*arcsin(a*x)^3, x) == :(-1//4*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2+-9//4*im*a^-1*c^-3*Polylogarithms.polylog(4,-1*im*exp(im*arcsin(a*x)))+-9//4*a^-1*c^-3*Polylogarithms.polylog(3,-1*im*exp(im*arcsin(a*x)))*arcsin(a*x)+-9//8*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^2+-5//2*im*a^-1*c^-3*Polylogarithms.polylog(2,im*exp(im*arcsin(a*x)))+-1//4*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2*arcsin(a*x)^2+1//4*x*c^-3*(1+-1*a^2*x^2)^-1*arcsin(a*x)+1//4*x*c^-3*(1+-1*a^2*x^2)^-2*arcsin(a*x)^3+3//8*x*c^-3*(1+-1*a^2*x^2)^-1*arcsin(a*x)^3+5//2*im*a^-1*c^-3*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(a*x)))+9//4*im*a^-1*c^-3*Polylogarithms.polylog(4,im*exp(im*arcsin(a*x)))+9//4*a^-1*c^-3*Polylogarithms.polylog(3,im*exp(im*arcsin(a*x)))*arcsin(a*x)+-5*im*a^-1*c^-3*arcsin(a*x)*arctan(exp(im*arcsin(a*x)))+-9//8*im*a^-1*c^-3*arcsin(a*x)^2*Polylogarithms.polylog(2,im*exp(im*arcsin(a*x)))+-3//4*im*a^-1*c^-3*arcsin(a*x)^3*arctan(exp(im*arcsin(a*x)))+9//8*im*a^-1*c^-3*arcsin(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^5//2*arcsin(a*x)^3, x) == :(1//6*x*(c+-1*c*a^2*x^2)^5//2*arcsin(a*x)^3+-245//384*x*c^2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)+-1//216*a^-1*c^2*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^2*x^2)^(1/2)+5//16*x*c^2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3+5//24*c*x*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^3+-65//576*x*c^2*(c+-1*c*a^2*x^2)^(1/2)*(1+-1*a^2*x^2)*arcsin(a*x)+-65//2304*a^3*c^2*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//36*x*c^2*(1+-1*a^2*x^2)^2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)+1//12*a^-1*c^2*(1+-1*a^2*x^2)^5//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2+5//32*a^-1*c^2*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2+5//64*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^4+115//768*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2+865//2304*a*c^2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-15//32*a*c^2*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2)
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^3, x) == :(1//4*x*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^3+-45//64*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)+3//8*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3+-3//32*c*x*(c+-1*c*a^2*x^2)^(1/2)*(1+-1*a^2*x^2)*arcsin(a*x)+-3//128*c*a^3*x^4*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//16*c*a^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2+3//32*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^4+27//128*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2+51//128*a*c*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-9//16*a*c*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2)
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3, x) == :((1/2)*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3+-3//4*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)+1//8*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^4+3//8*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//8*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2+-3//4*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^2)
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(1//4*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^4)
@test integrate((c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)^3, x) == :(x*c^-1*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3+3//2*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(a*x)))+-1*im*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3+3*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2*log(1+exp(2*im*arcsin(a*x)))+-3*im*a^-1*c^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a*x)))*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*arcsin(a*x)^3, x) == :(x*c^-2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+1//3*x*c^-1*(c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)^3+2//3*x*c^-2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3+a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(a*x)))+(1/2)*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a^2*x^2)+-1//2*a^-1*c^-2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+2*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2*log(1+exp(2*im*arcsin(a*x)))+-2//3*im*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3+-2*im*a^-1*c^-2*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a*x)))*arcsin(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*arcsin(a*x)^3, x) == :(x*c^-3*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+-1//20*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^-1//2+1//5*x*c^-1*(c+-1*c*a^2*x^2)^-5//2*arcsin(a*x)^3+4//15*x*c^-2*(c+-1*c*a^2*x^2)^-3//2*arcsin(a*x)^3+8//15*x*c^-3*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3+(1/2)*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a^2*x^2)+-3//20*a^-1*c^-3*(1+-1*a^2*x^2)^-3//2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+-2//5*a^-1*c^-3*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2+1//10*x*c^-3*(1+-1*a^2*x^2)^-1*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)+4//5*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(a*x)))+-8//15*im*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3+8//5*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^2*log(1+exp(2*im*arcsin(a*x)))+-8//5*im*a^-1*c^-3*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a*x)))*arcsin(a*x))
@test integrate(x^4*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(-45//128*a^-5*arcsin(a*x)^2+-45//128*a^-3*x^2+-3//128*a^-1*x^4+3//32*a^-5*arcsin(a*x)^4+3//16*a^-1*x^4*arcsin(a*x)^2+9//16*a^-3*x^2*arcsin(a*x)^2+-3//8*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+-1//4*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+3//32*a^-2*x^3*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)+45//64*x*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(-40//9*x*a^-3+-2//27*a^-1*x^3+2*x*a^-3*arcsin(a*x)^2+-2//3*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+1//3*a^-1*x^3*arcsin(a*x)^2+40//9*a^-4*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)+-1//3*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+2//9*a^-2*x^2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(-3//8*a^-1*x^2+-3//8*a^-3*arcsin(a*x)^2+1//8*a^-3*arcsin(a*x)^4+3//4*a^-1*x^2*arcsin(a*x)^2+-1//2*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+3//4*x*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(-6*x*a^-1+-1*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+3*x*a^-1*arcsin(a*x)^2+6*a^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x))
@test integrate((1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(1//4*a^-1*arcsin(a*x)^4)
@test integrate(x^-1*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(-6*im*Polylogarithms.polylog(4,-1*exp(im*arcsin(a*x)))+-6*Polylogarithms.polylog(3,-1*exp(im*arcsin(a*x)))*arcsin(a*x)+-2*arcsin(a*x)^3*arctanh(exp(im*arcsin(a*x)))+6*im*Polylogarithms.polylog(4,exp(im*arcsin(a*x)))+6*Polylogarithms.polylog(3,exp(im*arcsin(a*x)))*arcsin(a*x)+-3*im*arcsin(a*x)^2*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))+3*im*arcsin(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x))))
@test integrate(x^-2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(3//2*a*Polylogarithms.polylog(3,exp(2*im*arcsin(a*x)))+-1*im*a*arcsin(a*x)^3+-1*x^-1*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+3*a*arcsin(a*x)^2*log(1+-1*exp(2*im*arcsin(a*x)))+-3*im*a*Polylogarithms.polylog(2,exp(2*im*arcsin(a*x)))*arcsin(a*x))
@test integrate(x^-3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^3, x) == :(-1*a^2*arcsin(a*x)^3*arctanh(exp(im*arcsin(a*x)))+-6*a^2*arcsin(a*x)*arctanh(exp(im*arcsin(a*x)))+-3*im*a^2*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))+-3*im*a^2*Polylogarithms.polylog(4,-1*exp(im*arcsin(a*x)))+-3*a^2*Polylogarithms.polylog(3,-1*exp(im*arcsin(a*x)))*arcsin(a*x)+3*im*a^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x)))+3*im*a^2*Polylogarithms.polylog(4,exp(im*arcsin(a*x)))+3*a^2*Polylogarithms.polylog(3,exp(im*arcsin(a*x)))*arcsin(a*x)+-3//2*a*x^-1*arcsin(a*x)^2+-1//2*x^-2*(1+-1*a^2*x^2)^(1/2)*arcsin(a*x)^3+-3//2*im*a^2*arcsin(a*x)^2*Polylogarithms.polylog(2,exp(im*arcsin(a*x)))+3//2*im*a^2*arcsin(a*x)^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(a*x))))
@test integrate((c+-1*c*a^2*x^2)^3*arcsin(a*x)^-1, x) == :(1//64*a^-1*c^3*cosintegral(7*arcsin(a*x))+7//64*a^-1*c^3*cosintegral(5*arcsin(a*x))+21//64*a^-1*c^3*cosintegral(3*arcsin(a*x))+35//64*a^-1*c^3*cosintegral(arcsin(a*x)))
@test integrate((c+-1*c*a^2*x^2)^2*arcsin(a*x)^-1, x) == :(1//16*a^-1*c^2*cosintegral(5*arcsin(a*x))+5//8*a^-1*c^2*cosintegral(arcsin(a*x))+5//16*a^-1*c^2*cosintegral(3*arcsin(a*x)))
@test integrate(arcsin(a*x)^-1*(c+-1*c*a^2*x^2), x) == :(1//4*c*a^-1*cosintegral(3*arcsin(a*x))+3//4*c*a^-1*cosintegral(arcsin(a*x)))
@test integrate(x^4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1, x) == :(1//16*b^-1*c^-5*log(a+b*arcsin(c*x))+-1//16*b^-1*c^-5*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+-1//16*b^-1*c^-5*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+-1//32*b^-1*c^-5*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+-1//32*b^-1*c^-5*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+1//32*b^-1*c^-5*cos(6*a*b^-1)*cosintegral(6*arcsin(c*x)+6*a*b^-1)+1//32*b^-1*c^-5*sin(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1, x) == :(-1//8*b^-1*c^-4*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1//16*b^-1*c^-4*cos(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+-1//16*b^-1*c^-4*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+1//8*b^-1*c^-4*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+1//16*b^-1*c^-4*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+1//16*b^-1*c^-4*cosintegral(5*arcsin(c*x)+5*a*b^-1)*sin(5*a*b^-1))
@test integrate(x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1, x) == :(1//8*b^-1*c^-3*log(a+b*arcsin(c*x))+-1//8*b^-1*c^-3*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+-1//8*b^-1*c^-3*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1))
@test integrate(x*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1, x) == :(-1//4*b^-1*c^-2*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+-1//4*b^-1*c^-2*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+1//4*b^-1*c^-2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+1//4*b^-1*c^-2*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1))
@test integrate((1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1, x) == :((1/2)*b^-1*c^-1*log(a+b*arcsin(c*x))+(1/2)*b^-1*c^-1*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+(1/2)*b^-1*c^-1*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1, x) == :(-3//64*b^-1*c^-4*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+-3//64*b^-1*c^-4*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1//64*b^-1*c^-4*cos(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+-1//64*b^-1*c^-4*cos(7*a*b^-1)*sinintegral(7*arcsin(c*x)+7*a*b^-1)+1//64*b^-1*c^-4*cosintegral(5*arcsin(c*x)+5*a*b^-1)*sin(5*a*b^-1)+1//64*b^-1*c^-4*cosintegral(7*arcsin(c*x)+7*a*b^-1)*sin(7*a*b^-1)+3//64*b^-1*c^-4*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+3//64*b^-1*c^-4*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1))
@test integrate(x^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1, x) == :(1//16*b^-1*c^-3*log(a+b*arcsin(c*x))+-1//16*b^-1*c^-3*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+-1//16*b^-1*c^-3*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+-1//32*b^-1*c^-3*cos(6*a*b^-1)*cosintegral(6*arcsin(c*x)+6*a*b^-1)+-1//32*b^-1*c^-3*sin(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1)+1//32*b^-1*c^-3*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+1//32*b^-1*c^-3*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1))
@test integrate(x*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1, x) == :(-3//16*b^-1*c^-2*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+-1//8*b^-1*c^-2*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1//16*b^-1*c^-2*cosintegral(5*arcsin(c*x)+5*a*b^-1)*sin(5*a*b^-1)+1//8*b^-1*c^-2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+1//16*b^-1*c^-2*cos(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+3//16*b^-1*c^-2*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1))
@test integrate((1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1, x) == :(3//8*b^-1*c^-1*log(a+b*arcsin(c*x))+(1/2)*b^-1*c^-1*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+(1/2)*b^-1*c^-1*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+1//8*b^-1*c^-1*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+1//8*b^-1*c^-1*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1, x) == :(-3//128*b^-1*c^-4*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-3//256*b^-1*c^-4*cos(7*a*b^-1)*sinintegral(7*arcsin(c*x)+7*a*b^-1)+-1//32*b^-1*c^-4*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+-1//256*b^-1*c^-4*cos(9*a*b^-1)*sinintegral(9*arcsin(c*x)+9*a*b^-1)+1//32*b^-1*c^-4*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+1//256*b^-1*c^-4*cosintegral(9*arcsin(c*x)+9*a*b^-1)*sin(9*a*b^-1)+3//128*b^-1*c^-4*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+3//256*b^-1*c^-4*cosintegral(7*arcsin(c*x)+7*a*b^-1)*sin(7*a*b^-1))
@test integrate(x^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1, x) == :(5//128*b^-1*c^-3*log(a+b*arcsin(c*x))+-1//32*b^-1*c^-3*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+-1//32*b^-1*c^-3*cos(6*a*b^-1)*cosintegral(6*arcsin(c*x)+6*a*b^-1)+-1//32*b^-1*c^-3*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+-1//32*b^-1*c^-3*sin(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1)+-1//128*b^-1*c^-3*cos(8*a*b^-1)*cosintegral(8*arcsin(c*x)+8*a*b^-1)+-1//128*b^-1*c^-3*sin(8*a*b^-1)*sinintegral(8*arcsin(c*x)+8*a*b^-1)+1//32*b^-1*c^-3*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+1//32*b^-1*c^-3*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1))
@test integrate(x*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1, x) == :(-9//64*b^-1*c^-2*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+-5//64*b^-1*c^-2*cosintegral(5*arcsin(c*x)+5*a*b^-1)*sin(5*a*b^-1)+-5//64*b^-1*c^-2*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1//64*b^-1*c^-2*cosintegral(7*arcsin(c*x)+7*a*b^-1)*sin(7*a*b^-1)+1//64*b^-1*c^-2*cos(7*a*b^-1)*sinintegral(7*arcsin(c*x)+7*a*b^-1)+5//64*b^-1*c^-2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+5//64*b^-1*c^-2*cos(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+9//64*b^-1*c^-2*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1))
@test integrate((1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1, x) == :(5//16*b^-1*c^-1*log(a+b*arcsin(c*x))+1//32*b^-1*c^-1*cos(6*a*b^-1)*cosintegral(6*arcsin(c*x)+6*a*b^-1)+1//32*b^-1*c^-1*sin(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1)+3//16*b^-1*c^-1*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+3//16*b^-1*c^-1*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+15//32*b^-1*c^-1*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+15//32*b^-1*c^-1*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1))
@test integrate(x^4*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-1, x) == :(-1//2*a^-5*cosintegral(2*arcsin(a*x))+1//8*a^-5*cosintegral(4*arcsin(a*x))+3//8*a^-5*log(arcsin(a*x)))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-1, x) == :(-1//4*a^-4*sinintegral(3*arcsin(a*x))+3//4*a^-4*sinintegral(arcsin(a*x)))
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-1, x) == :((1/2)*a^-3*log(arcsin(a*x))+-1//2*a^-3*cosintegral(2*arcsin(a*x)))
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-1, x) == :((1/2)*a^-3*log(arcsin(a*x))+-1//2*a^-3*cosintegral(2*arcsin(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-1, x) == :(a^-2*sinintegral(arcsin(a*x)))
@test integrate((1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-1, x) == :(a^-1*log(arcsin(a*x)))
@test integrate(x^5*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-1, x) == :(-5//8*b^-1*c^-6*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-5//16*b^-1*c^-6*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1//16*b^-1*c^-6*cosintegral(5*arcsin(c*x)+5*a*b^-1)*sin(5*a*b^-1)+1//16*b^-1*c^-6*cos(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+5//8*b^-1*c^-6*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+5//16*b^-1*c^-6*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1))
@test integrate(x^4*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-1, x) == :(3//8*b^-1*c^-5*log(a+b*arcsin(c*x))+-1//2*b^-1*c^-5*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+-1//2*b^-1*c^-5*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+1//8*b^-1*c^-5*cos(4*a*b^-1)*cosintegral(4*arcsin(c*x)+4*a*b^-1)+1//8*b^-1*c^-5*sin(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-1, x) == :(-3//4*b^-1*c^-4*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1//4*b^-1*c^-4*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+1//4*b^-1*c^-4*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+3//4*b^-1*c^-4*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x)))
@test integrate(x^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-1, x) == :((1/2)*b^-1*c^-3*log(a+b*arcsin(c*x))+-1//2*b^-1*c^-3*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+-1//2*b^-1*c^-3*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1))
@test integrate(x*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-1, x) == :(b^-1*c^-2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+-1*b^-1*c^-2*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1))
@test integrate((1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-1, x) == :(b^-1*c^-1*log(a+b*arcsin(c*x)))
@test integrate((c+-1*c*a^2*x^2)^3*arcsin(a*x)^-2, x) == :(-63//64*a^-1*c^3*sinintegral(3*arcsin(a*x))+-35//64*a^-1*c^3*sinintegral(5*arcsin(a*x))+-35//64*a^-1*c^3*sinintegral(arcsin(a*x))+-7//64*a^-1*c^3*sinintegral(7*arcsin(a*x))+-1*a^-1*c^3*(1+-1*a^2*x^2)^7//2*arcsin(a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^2*arcsin(a*x)^-2, x) == :(-15//16*a^-1*c^2*sinintegral(3*arcsin(a*x))+-5//8*a^-1*c^2*sinintegral(arcsin(a*x))+-5//16*a^-1*c^2*sinintegral(5*arcsin(a*x))+-1*a^-1*c^2*(1+-1*a^2*x^2)^5//2*arcsin(a*x)^-1)
@test integrate(arcsin(a*x)^-2*(c+-1*c*a^2*x^2), x) == :(-3//4*c*a^-1*sinintegral(3*arcsin(a*x))+-3//4*c*a^-1*sinintegral(arcsin(a*x))+-1*c*a^-1*(1+-1*a^2*x^2)^3//2*arcsin(a*x)^-1)
@test integrate((1+-1*x^2)^-1*arcsin(x)^-2+-1*x*(1+-1*x^2)^-3//2*arcsin(x)^-1, x) == :(-1*(1+-1*x^2)^-1//2*arcsin(x)^-1)
@test integrate(x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-2, x) == :(-5//16*b^-2*c^-4*cos(5*a*b^-1)*cosintegral(5*arcsin(c*x)+5*a*b^-1)+-5//16*b^-2*c^-4*sin(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+1//8*b^-2*c^-4*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+1//8*b^-2*c^-4*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+3//16*b^-2*c^-4*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+3//16*b^-2*c^-4*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1*b^-1*c^-1*x^3*(a+b*arcsin(c*x))^-1*(1+-1*c^2*x^2))
@test integrate(x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-2, x) == :((1/2)*b^-2*c^-3*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+-1//2*b^-2*c^-3*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+-1*b^-1*c^-1*x^2*(a+b*arcsin(c*x))^-1*(1+-1*c^2*x^2))
@test integrate(x*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-2*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c*x)))+b^-2*c^-2*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c*x)))+-3//4*b^-2*c^-2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+-3//4*b^-2*c^-2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+3//4*b^-2*c^-2*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+3//4*b^-2*c^-2*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1*x*b^-1*c^-1*(a+b*arcsin(c*x))^-1*(1+-1*c^2*x^2))
@test integrate((1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-1*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+-1*b^-1*c^-1*(a+b*arcsin(c*x))^-1*(1+-1*c^2*x^2)+-1*b^-2*c^-1*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-2, x) == :(-7//64*b^-2*c^-4*cos(7*a*b^-1)*cosintegral(7*arcsin(c*x)+7*a*b^-1)+-7//64*b^-2*c^-4*sin(7*a*b^-1)*sinintegral(7*arcsin(c*x)+7*a*b^-1)+-5//64*b^-2*c^-4*cos(5*a*b^-1)*cosintegral(5*arcsin(c*x)+5*a*b^-1)+-5//64*b^-2*c^-4*sin(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+3//64*b^-2*c^-4*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+3//64*b^-2*c^-4*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+9//64*b^-2*c^-4*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+9//64*b^-2*c^-4*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1*b^-1*c^-1*x^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^-1)
@test integrate(x^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-2, x) == :(-3//16*b^-2*c^-3*cosintegral(6*arcsin(c*x)+6*a*b^-1)*sin(6*a*b^-1)+-1//4*b^-2*c^-3*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+-1//16*b^-2*c^-3*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+1//4*b^-2*c^-3*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+1//16*b^-2*c^-3*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+3//16*b^-2*c^-3*cos(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1)+-1*b^-1*c^-1*x^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^-1)
@test integrate(x*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-2, x) == :(1//8*b^-2*c^-2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+1//8*b^-2*c^-2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+5//16*b^-2*c^-2*cos(5*a*b^-1)*cosintegral(5*arcsin(c*x)+5*a*b^-1)+5//16*b^-2*c^-2*sin(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+9//16*b^-2*c^-2*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+9//16*b^-2*c^-2*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1*x*b^-1*c^-1*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^-1)
@test integrate((1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-1*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+(1/2)*b^-2*c^-1*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+-1*b^-1*c^-1*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^-1+-1*b^-2*c^-1*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-1//2*b^-2*c^-1*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-2, x) == :(-21//256*b^-2*c^-4*cos(7*a*b^-1)*cosintegral(7*arcsin(c*x)+7*a*b^-1)+-21//256*b^-2*c^-4*sin(7*a*b^-1)*sinintegral(7*arcsin(c*x)+7*a*b^-1)+-9//256*b^-2*c^-4*cos(9*a*b^-1)*cosintegral(9*arcsin(c*x)+9*a*b^-1)+-9//256*b^-2*c^-4*sin(9*a*b^-1)*sinintegral(9*arcsin(c*x)+9*a*b^-1)+3//32*b^-2*c^-4*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+3//32*b^-2*c^-4*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+3//128*b^-2*c^-4*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+3//128*b^-2*c^-4*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+-1*b^-1*c^-1*x^3*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^-1)
@test integrate(x^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-2, x) == :(-3//16*b^-2*c^-3*cosintegral(6*arcsin(c*x)+6*a*b^-1)*sin(6*a*b^-1)+-1//8*b^-2*c^-3*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+-1//16*b^-2*c^-3*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-1//16*b^-2*c^-3*cosintegral(8*arcsin(c*x)+8*a*b^-1)*sin(8*a*b^-1)+1//8*b^-2*c^-3*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+1//16*b^-2*c^-3*cos(8*a*b^-1)*sinintegral(8*arcsin(c*x)+8*a*b^-1)+1//16*b^-2*c^-3*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+3//16*b^-2*c^-3*cos(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1)+-1*b^-1*c^-1*x^2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^-1)
@test integrate(x*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-2, x) == :(5//64*b^-2*c^-2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+5//64*b^-2*c^-2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+7//64*b^-2*c^-2*cos(7*a*b^-1)*cosintegral(7*arcsin(c*x)+7*a*b^-1)+7//64*b^-2*c^-2*sin(7*a*b^-1)*sinintegral(7*arcsin(c*x)+7*a*b^-1)+25//64*b^-2*c^-2*cos(5*a*b^-1)*cosintegral(5*arcsin(c*x)+5*a*b^-1)+25//64*b^-2*c^-2*sin(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1)+27//64*b^-2*c^-2*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+27//64*b^-2*c^-2*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1*x*b^-1*c^-1*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^-1)
@test integrate((1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-2, x) == :(-1*b^-1*c^-1*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^-1+-15//16*b^-2*c^-1*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-3//4*b^-2*c^-1*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+-3//16*b^-2*c^-1*cos(6*a*b^-1)*sinintegral(6*arcsin(c*x)+6*a*b^-1)+3//4*b^-2*c^-1*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+3//16*b^-2*c^-1*cosintegral(6*arcsin(c*x)+6*a*b^-1)*sin(6*a*b^-1)+15//16*b^-2*c^-1*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1))
@test integrate(x^5*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-2, x) == :(-1*b^-1*c^-1*x^5*(a+b*arcsin(c*x))^-1+-15//16*b^-2*c^-6*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+-15//16*b^-2*c^-6*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+5//8*b^-2*c^-6*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+5//8*b^-2*c^-6*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+5//16*b^-2*c^-6*cos(5*a*b^-1)*cosintegral(5*arcsin(c*x)+5*a*b^-1)+5//16*b^-2*c^-6*sin(5*a*b^-1)*sinintegral(5*arcsin(c*x)+5*a*b^-1))
@test integrate(x^4*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-5*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+(1/2)*b^-2*c^-5*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+-1*b^-1*c^-1*x^4*(a+b*arcsin(c*x))^-1+-1*b^-2*c^-5*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+-1//2*b^-2*c^-5*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1))
@test integrate(x^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-2, x) == :(-1*b^-1*c^-1*x^3*(a+b*arcsin(c*x))^-1+-3//4*b^-2*c^-4*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+-3//4*b^-2*c^-4*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+3//4*b^-2*c^-4*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+3//4*b^-2*c^-4*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x)))
@test integrate(x^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-3*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-1*b^-1*c^-1*x^2*(a+b*arcsin(c*x))^-1+-1*b^-2*c^-3*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1))
@test integrate(x*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-2*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c*x)))+b^-2*c^-2*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c*x)))+-1*x*b^-1*c^-1*(a+b*arcsin(c*x))^-1)
@test integrate((1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^-2, x) == :(-1*b^-1*c^-1*(a+b*arcsin(c*x))^-1)
@test integrate((1+-1*a^2*x^2)^-1//2*arcsin(a*x)^-3, x) == :(-1//2*a^-1*arcsin(a*x)^-2)
@test integrate(x^3*(a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2), x) == :(-2*d*b^-1*c^-1*x^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1//2+3//8*d*pi^(1/2)*b^-3//2*c^-4*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+3//8*d*pi^(1/2)*b^-3//2*c^-4*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(2*a*b^-1)+-1//8*d*3^(1/2)*pi^(1/2)*b^-3//2*c^-4*cos(6*a*b^-1)*fresnelc(2*3^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-1//8*d*3^(1/2)*pi^(1/2)*b^-3//2*c^-4*fresnels(2*3^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(6*a*b^-1))
@test integrate(x^2*(a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2), x) == :(-2*d*b^-1*c^-1*x^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1//2+-1//4*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-3*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-1//8*d*6^(1/2)*pi^(1/2)*b^-3//2*c^-3*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(3*a*b^-1)+-1//8*d*10^(1/2)*pi^(1/2)*b^-3//2*c^-3*fresnelc(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(5*a*b^-1)+1//4*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-3*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(a*b^-1)+1//8*d*6^(1/2)*pi^(1/2)*b^-3//2*c^-3*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+1//8*d*10^(1/2)*pi^(1/2)*b^-3//2*c^-3*cos(5*a*b^-1)*fresnels(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2)))
@test integrate(x*(a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2), x) == :(d*pi^(1/2)*b^-3//2*c^-2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+d*pi^(1/2)*b^-3//2*c^-2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(2*a*b^-1)+-2*d*x*b^-1*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1//2+(1/2)*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+(1/2)*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2), x) == :(-2*d*b^-1*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^-1//2+(1/2)*d*6^(1/2)*pi^(1/2)*b^-3//2*c^-1*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(3*a*b^-1)+-3//2*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-1//2*d*6^(1/2)*pi^(1/2)*b^-3//2*c^-1*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+3//2*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(a*b^-1))
@test integrate(x^3*(a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2)^2, x) == :(-2*b^-1*c^-1*d^2*x^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1//2+-1//16*pi^(1/2)*b^-3//2*c^-4*d^2*cos(8*a*b^-1)*fresnelc(4*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-1//16*pi^(1/2)*b^-3//2*c^-4*d^2*fresnels(4*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(8*a*b^-1)+3//16*pi^(1/2)*b^-3//2*c^-4*d^2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+3//16*pi^(1/2)*b^-3//2*c^-4*d^2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(2*a*b^-1)+-1//16*3^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*cos(6*a*b^-1)*fresnelc(2*3^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-1//16*3^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*fresnels(2*3^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(6*a*b^-1)+1//16*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+1//16*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(4*a*b^-1))
@test integrate(x^2*(a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2)^2, x) == :(-2*b^-1*c^-1*d^2*x^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1//2+-5//32*2^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-3//32*10^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*fresnelc(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(5*a*b^-1)+-1//32*6^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(3*a*b^-1)+-1//32*14^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*fresnelc(14^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(7*a*b^-1)+1//32*6^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+1//32*14^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*cos(7*a*b^-1)*fresnels(14^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+3//32*10^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*cos(5*a*b^-1)*fresnels(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+5//32*2^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(a*b^-1))
@test integrate(x*(a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2)^2, x) == :(-2*x*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1//2+5//8*pi^(1/2)*b^-3//2*c^-2*d^2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+5//8*pi^(1/2)*b^-3//2*c^-2*d^2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(2*a*b^-1)+(1/2)*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+(1/2)*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(4*a*b^-1)+1//8*3^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*cos(6*a*b^-1)*fresnelc(2*3^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+1//8*3^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*fresnels(2*3^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(6*a*b^-1))
@test integrate((a+b*arcsin(c*x))^-3//2*(d+-1*d*c^2*x^2)^2, x) == :(-2*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^-1//2+-5//4*2^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-5//8*6^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+-1//8*10^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*cos(5*a*b^-1)*fresnels(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))+1//8*10^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*fresnelc(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(5*a*b^-1)+5//4*2^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(a*b^-1)+5//8*6^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c*x))^(1/2))*sin(3*a*b^-1))
@test integrate(x*(1+-1*x^2)^-2*arcsin(x)^3//2+-3*x*(8+-8*x^2)^-1*arcsin(x)^-1//2, x) == :((2+-2*x^2)^-1*arcsin(x)^3//2+-3//4*x*(1+-1*x^2)^-1//2*arcsin(x)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^(1/2), x) == :(1//4*x*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^(1/2)+3//8*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+1//4*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+-1//8*c*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2))+-1//128*c*2^(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2), x) == :((1/2)*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+1//3*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+-1//8*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^(1/2), x) == :(2//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^3//2, x) == :(1//4*x*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^3//2+3//8*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+3//20*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^5//2+3//32*c*a^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+27//256*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+-9//32*a*c*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+-3//32*c*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2))+-3//1024*c*2^(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2, x) == :((1/2)*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+1//5*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^5//2+3//16*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+-3//8*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+-3//32*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^3//2, x) == :(2//5*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^5//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^5//2, x) == :(1//4*x*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^5//2+-225//512*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+3//8*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^5//2+-15//256*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)*(1+-1*a^2*x^2)+3//28*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^7//2+5//32*c*a^-1*(1+-1*a^2*x^2)^3//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+45//256*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+-15//32*a*c*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+15//128*c*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2))+15//8192*c*2^(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^5//2, x) == :((1/2)*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^5//2+-15//32*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+1//7*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^7//2+5//16*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+-5//8*a*x^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^3//2+15//128*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^5//2, x) == :(2//7*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^7//2)
@test integrate((a^2+-1*x^2)^3//2*arcsin(x*a^-1)^(1/2), x) == :(1//4*x*(a^2+-1*x^2)^3//2*arcsin(x*a^-1)^(1/2)+1//4*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^3//2+3//8*x*a^2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2)+-1//8*pi^(1/2)*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(x*a^-1)^(1/2))+-1//128*2^(1/2)*pi^(1/2)*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*fresnels(2*2^(1/2)*pi^-1//2*arcsin(x*a^-1)^(1/2)))
@test integrate((a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2), x) == :((1/2)*x*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2)+1//3*a*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^3//2+-1//8*a*pi^(1/2)*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(x*a^-1)^(1/2)))
@test integrate((a^2+-1*x^2)^-1//2*arcsin(x*a^-1)^(1/2), x) == :(2//3*a*(1+-1*a^-2*x^2)^(1/2)*(a^2+-1*x^2)^-1//2*arcsin(x*a^-1)^3//2)
@test integrate((a^2+-1*x^2)^3//2*arcsin(x*a^-1)^3//2, x) == :(1//4*x*(a^2+-1*x^2)^3//2*arcsin(x*a^-1)^3//2+3//8*x*a^2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^3//2+3//20*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^5//2+3//32*a^-1*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^5//2*arcsin(x*a^-1)^(1/2)+27//256*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2)+-9//32*a*x^2*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2)+-3//32*pi^(1/2)*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(x*a^-1)^(1/2))+-3//1024*2^(1/2)*pi^(1/2)*a^3*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*fresnelc(2*2^(1/2)*pi^-1//2*arcsin(x*a^-1)^(1/2)))
@test integrate((a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^3//2, x) == :((1/2)*x*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^3//2+1//5*a*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^5//2+3//16*a*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2)+-3//8*a^-1*x^2*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*arcsin(x*a^-1)^(1/2)+-3//32*a*pi^(1/2)*(1+-1*a^-2*x^2)^-1//2*(a^2+-1*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(x*a^-1)^(1/2)))
@test integrate((a^2+-1*x^2)^-1//2*arcsin(x*a^-1)^3//2, x) == :(2//5*a*(1+-1*a^-2*x^2)^(1/2)*(a^2+-1*x^2)^-1//2*arcsin(x*a^-1)^5//2)
@test integrate(x*(1+-1*x^2)^-1//2*arcsin(x)^-1//2, x) == :(2^(1/2)*pi^(1/2)*fresnels(2^(1/2)*pi^-1//2*arcsin(x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^5//2*arcsin(a*x)^-1//2, x) == :(5//8*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+15//32*pi^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2))+1//96*3^(1/2)*pi^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*3^(1/2)*pi^-1//2*arcsin(a*x)^(1/2))+3//32*2^(1/2)*pi^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^-1//2, x) == :(3//4*c*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+(1/2)*c*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2))+1//16*c*2^(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-1//2, x) == :(a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^(1/2)+(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^-1//2, x) == :(2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^5//2*arcsin(a*x)^-3//2, x) == :(-2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^5//2*arcsin(a*x)^-1//2+-15//8*pi^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2))+-3//4*2^(1/2)*pi^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2))+-1//8*3^(1/2)*pi^(1/2)*a^-1*c^2*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*3^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^-3//2, x) == :(-2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^-1//2+-2*c*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2))+-1//2*c*2^(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-3//2, x) == :(-2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-1//2+-2*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnels(2*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^-3//2, x) == :(-2*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^-5//2, x) == :(-2//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^3//2*arcsin(a*x)^-3//2+16//3*c*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-1//2*(1+-1*a^2*x^2)+-8//3*c*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2))+-4//3*c*2^(1/2)*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*2^(1/2)*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-5//2, x) == :(8//3*x*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-1//2+-2//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^(1/2)*arcsin(a*x)^-3//2+-8//3*pi^(1/2)*a^-1*(1+-1*a^2*x^2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*fresnelc(2*pi^-1//2*arcsin(a*x)^(1/2)))
@test integrate((c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^-5//2, x) == :(-2//3*a^-1*(1+-1*a^2*x^2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*arcsin(a*x)^-3//2)
@test integrate(x^2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2), x) == :(1//8*b^-1*c^-3*(1+n)^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^(1+n)*(d+-1*d*c^2*x^2)^(1/2)+im*2^(-6+-2n)*c^-3*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-4*im*b^-1*(a+b*arcsin(c*x)))*exp(-4*im*a*b^-1)+-1*im*2^(-6+-2n)*c^-3*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,4*im*b^-1*(a+b*arcsin(c*x)))*exp(4*im*a*b^-1))
@test integrate(x*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2), x) == :(-1//8*c^-2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c*x)))*exp(im*a*b^-1)+-1//8*c^-2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c*x)))*exp(-1*im*a*b^-1)+-1//8*3^(-1+-1n)*c^-2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,3*im*b^-1*(a+b*arcsin(c*x)))*exp(3*im*a*b^-1)+-1//8*3^(-1+-1n)*c^-2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-3*im*b^-1*(a+b*arcsin(c*x)))*exp(-3*im*a*b^-1))
@test integrate((a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2), x) == :((1/2)*b^-1*c^-1*(1+n)^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^(1+n)*(d+-1*d*c^2*x^2)^(1/2)+im*2^(-3+-1n)*c^-1*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c*x)))*exp(2*im*a*b^-1)+-1*im*2^(-3+-1n)*c^-1*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c*x)))*exp(-2*im*a*b^-1))
@test integrate(x^2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^3//2, x) == :(1//16*d*b^-1*c^-3*(1+n)^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^(1+n)*(d+-1*d*c^2*x^2)^(1/2)+im*d*2^(-7+-1n)*c^-3*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c*x)))*exp(2*im*a*b^-1)+im*d*2^(-7+-2n)*c^-3*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-4*im*b^-1*(a+b*arcsin(c*x)))*exp(-4*im*a*b^-1)+-1*im*d*2^(-7+-1n)*c^-3*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c*x)))*exp(-2*im*a*b^-1)+-1*im*d*2^(-7+-2n)*c^-3*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,4*im*b^-1*(a+b*arcsin(c*x)))*exp(4*im*a*b^-1)+im*d*2^(-7+-1n)*3^(-1+-1n)*c^-3*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-6*im*b^-1*(a+b*arcsin(c*x)))*exp(-6*im*a*b^-1)+-1*im*d*2^(-7+-1n)*3^(-1+-1n)*c^-3*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,6*im*b^-1*(a+b*arcsin(c*x)))*exp(6*im*a*b^-1))
@test integrate(x*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^3//2, x) == :(-1//16*d*c^-2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c*x)))*exp(im*a*b^-1)+-1//16*d*c^-2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c*x)))*exp(-1*im*a*b^-1)+-1//32*d*3^(-1n)*c^-2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,3*im*b^-1*(a+b*arcsin(c*x)))*exp(3*im*a*b^-1)+-1//32*d*3^(-1n)*c^-2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-3*im*b^-1*(a+b*arcsin(c*x)))*exp(-3*im*a*b^-1)+-1//32*d*5^(-1+-1n)*c^-2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,5*im*b^-1*(a+b*arcsin(c*x)))*exp(5*im*a*b^-1)+-1//32*d*5^(-1+-1n)*c^-2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-5*im*b^-1*(a+b*arcsin(c*x)))*exp(-5*im*a*b^-1))
@test integrate((a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^3//2, x) == :(3//8*d*b^-1*c^-1*(1+n)^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^(1+n)*(d+-1*d*c^2*x^2)^(1/2)+im*d*2^(-6+-2n)*c^-1*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,4*im*b^-1*(a+b*arcsin(c*x)))*exp(4*im*a*b^-1)+im*d*2^(-3+-1n)*c^-1*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c*x)))*exp(2*im*a*b^-1)+-1*im*d*2^(-6+-2n)*c^-1*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-4*im*b^-1*(a+b*arcsin(c*x)))*exp(-4*im*a*b^-1)+-1*im*d*2^(-3+-1n)*c^-1*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c*x)))*exp(-2*im*a*b^-1))
@test integrate(x^2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^5//2, x) == :(5//128*b^-1*c^-3*d^2*(1+n)^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^(1+n)*(d+-1*d*c^2*x^2)^(1/2)+im*2^(-11+-3n)*c^-3*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-8*im*b^-1*(a+b*arcsin(c*x)))*exp(-8*im*a*b^-1)+im*2^(-8+-2n)*c^-3*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-4*im*b^-1*(a+b*arcsin(c*x)))*exp(-4*im*a*b^-1)+im*2^(-7+-1n)*c^-3*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c*x)))*exp(2*im*a*b^-1)+-1*im*2^(-11+-3n)*c^-3*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,8*im*b^-1*(a+b*arcsin(c*x)))*exp(8*im*a*b^-1)+-1*im*2^(-8+-2n)*c^-3*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,4*im*b^-1*(a+b*arcsin(c*x)))*exp(4*im*a*b^-1)+-1*im*2^(-7+-1n)*c^-3*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c*x)))*exp(-2*im*a*b^-1)+im*2^(-7+-1n)*3^(-1+-1n)*c^-3*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-6*im*b^-1*(a+b*arcsin(c*x)))*exp(-6*im*a*b^-1)+-1*im*2^(-7+-1n)*3^(-1+-1n)*c^-3*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,6*im*b^-1*(a+b*arcsin(c*x)))*exp(6*im*a*b^-1))
@test integrate(x*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^5//2, x) == :(-5//128*c^-2*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c*x)))*exp(im*a*b^-1)+-5//128*c^-2*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c*x)))*exp(-1*im*a*b^-1)+-1//128*3^(1+-1n)*c^-2*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,3*im*b^-1*(a+b*arcsin(c*x)))*exp(3*im*a*b^-1)+-1//128*3^(1+-1n)*c^-2*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-3*im*b^-1*(a+b*arcsin(c*x)))*exp(-3*im*a*b^-1)+-1//128*5^(-1n)*c^-2*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,5*im*b^-1*(a+b*arcsin(c*x)))*exp(5*im*a*b^-1)+-1//128*5^(-1n)*c^-2*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-5*im*b^-1*(a+b*arcsin(c*x)))*exp(-5*im*a*b^-1)+-1//128*7^(-1+-1n)*c^-2*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,7*im*b^-1*(a+b*arcsin(c*x)))*exp(7*im*a*b^-1)+-1//128*7^(-1+-1n)*c^-2*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-7*im*b^-1*(a+b*arcsin(c*x)))*exp(-7*im*a*b^-1))
@test integrate((a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^5//2, x) == :(5//16*b^-1*c^-1*d^2*(1+n)^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^(1+n)*(d+-1*d*c^2*x^2)^(1/2)+-15*im*2^(-7+-1n)*c^-1*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c*x)))*exp(-2*im*a*b^-1)+-3*im*2^(-7+-2n)*c^-1*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-4*im*b^-1*(a+b*arcsin(c*x)))*exp(-4*im*a*b^-1)+3*im*2^(-7+-2n)*c^-1*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,4*im*b^-1*(a+b*arcsin(c*x)))*exp(4*im*a*b^-1)+15*im*2^(-7+-1n)*c^-1*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c*x)))*exp(2*im*a*b^-1)+im*2^(-7+-1n)*3^(-1+-1n)*c^-1*d^2*(im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,6*im*b^-1*(a+b*arcsin(c*x)))*exp(6*im*a*b^-1)+-1*im*2^(-7+-1n)*3^(-1+-1n)*c^-1*d^2*(-1*im*b^-1*(a+b*arcsin(c*x)))^(-1n)*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^n*(d+-1*d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-6*im*b^-1*(a+b*arcsin(c*x)))*exp(-6*im*a*b^-1))
@test integrate(x^3*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^n, x) == :(-3//8*a^-4*(im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,im*arcsin(a*x))+-3//8*a^-4*(-1*im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,-1*im*arcsin(a*x))+1//8*3^(-1+-1n)*a^-4*(im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,3*im*arcsin(a*x))+1//8*3^(-1+-1n)*a^-4*(-1*im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,-3*im*arcsin(a*x)))
@test integrate(x^2*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^n, x) == :((1/2)*a^-3*(1+n)^-1*arcsin(a*x)^(1+n)+im*2^(-3+-1n)*a^-3*(-1*im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,-2*im*arcsin(a*x))+-1*im*2^(-3+-1n)*a^-3*(im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,2*im*arcsin(a*x)))
@test integrate(x*(1+-1*a^2*x^2)^-1//2*arcsin(a*x)^n, x) == :(-1//2*a^-2*(im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,im*arcsin(a*x))+-1//2*a^-2*(-1*im*arcsin(a*x))^(-1n)*arcsin(a*x)^n*SpecialFunctions.gamma(1+n,-1*im*arcsin(a*x)))
@test integrate((1+-1*a^2*x^2)^-1//2*arcsin(a*x)^n, x) == :(a^-1*(1+n)^-1*arcsin(a*x)^(1+n))
@test integrate((d+c*d*x)^5//2*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x)), x) == :(3//8*x*d^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+-2//3*c^-1*d^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//4*c^2*d^2*x^3*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+2//3*b*x*d^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+-3//16*b*c*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+-2//9*b*c^2*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+-1//16*b*c^3*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+5//16*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2))
@test integrate((d+c*d*x)^3//2*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x)), x) == :((1/2)*d*x*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+-1//3*d*c^-1*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//3*b*d*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+-1//4*b*c*d*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+-1//9*b*d*c^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+1//4*d*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2))
@test integrate((d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x)), x) == :((1/2)*x*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+-1//4*b*c*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+1//4*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2))
@test integrate((d+c*d*x)^-1//2*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x)), x) == :(f*c^-1*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1*b*f*x*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+(1/2)*f*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^-3//2*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x)), x) == :(-2*c^-1*f^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+2*b*c^-1*f^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+c*x)+-1//2*b^-1*c^-1*f^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2)
@test integrate((d+c*d*x)^-5//2*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x)), x) == :(-2//3*b*c^-1*f^3*(1+c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-1//3*b*c^-1*f^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+c*x)+-1//3*c^-1*f^3*(1+-1*c*x)^3*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^5//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x)), x) == :(1//4*d*x*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x))+3*d*x*(8+-8*c^2*x^2)^-1*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x))+-1//5*d*c^-1*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//5*b*d*x*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+-5//16*b*c*d*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+-2//15*b*d*c^2*x^3*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+1//16*b*d*c^3*x^4*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+1//25*b*d*c^4*x^5*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+3//16*d*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2)
@test integrate((d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x)), x) == :(1//4*x*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x))+3*x*(8+-8*c^2*x^2)^-1*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x))+-5//16*b*c*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+1//16*b*c^3*x^4*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+3//16*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2)
@test integrate((d+c*d*x)^(1/2)*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x)), x) == :((1/2)*f*x*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+-1//3*b*f*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+1//3*f*c^-1*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//4*b*c*f*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+1//4*f*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+1//9*b*f*c^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2))
@test integrate((d+c*d*x)^-1//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x)), x) == :(-2*b*x*f^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+2*c^-1*f^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//2*x*f^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//4*b*c*f^2*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+3//4*b^-1*c^-1*f^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^-3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x)), x) == :(b*x*f^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+-1*c^-1*f^3*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x))+-4*c^-1*f^3*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+4*b*c^-1*f^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+c*x)+-3//2*b^-1*c^-1*f^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2)
@test integrate((d+c*d*x)^-5//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x)), x) == :(c^-1*f^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))*arcsin(c*x)+2*c^-1*f^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c*x)*(a+b*arcsin(c*x))+-8//3*b*c^-1*f^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+c*x)+-4//3*b*c^-1*f^4*(1+c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-2//3*c^-1*f^4*(1+-1*c*x)^3*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//2*b*c^-1*f^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arcsin(c*x)^2)
@test integrate((d+c*d*x)^5//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x)), x) == :(1//6*x*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x))+5*x*(24+-24*c^2*x^2)^-1*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x))+1//36*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2+5//16*x*(1+-1*c^2*x^2)^-2*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x))+-25//96*b*c*x^2*(1+-1*c^2*x^2)^-5//2*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2+5//32*b^-1*c^-1*(1+-1*c^2*x^2)^-5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2+5//96*b*c^3*x^4*(1+-1*c^2*x^2)^-5//2*(d+c*d*x)^5//2*(f+-1*c*f*x)^5//2)
@test integrate((d+c*d*x)^3//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x)), x) == :(1//4*f*x*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x))+3*f*x*(8+-8*c^2*x^2)^-1*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(a+b*arcsin(c*x))+-1//5*b*f*x*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+1//5*f*c^-1*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-5//16*b*c*f*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+-1//25*b*f*c^4*x^5*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+1//16*b*f*c^3*x^4*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+2//15*b*f*c^2*x^3*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2+3//16*f*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(f+-1*c*f*x)^3//2)
@test integrate((d+c*d*x)^(1/2)*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x)), x) == :(3//8*x*f^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+-2//3*b*x*f^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+1//4*c^2*f^2*x^3*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(a+b*arcsin(c*x))+2//3*c^-1*f^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-3//16*b*c*f^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+-1//16*b*c^3*f^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+2//9*b*c^2*f^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2)+5//16*b^-1*c^-1*f^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(f+-1*c*f*x)^(1/2))
@test integrate((d+c*d*x)^-1//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x)), x) == :(-11//3*b*x*f^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+-3//2*x*f^3*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+11//3*c^-1*f^3*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//9*b*c^2*f^3*x^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+1//3*c*f^3*x^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+3//4*b*c*f^3*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+5//4*b^-1*c^-1*f^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^-3//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x)), x) == :(-15//2*c^-1*f^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x))+3//2*b*x*f^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+b*c*f^4*x^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+-2*c^-1*f^4*(1+-1*c*x)^3*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+8*b*c^-1*f^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+c*x)+-15//2*c^-1*f^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x))*arcsin(c*x)+-5//2*c^-1*f^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c*x)*(a+b*arcsin(c*x))+-5//4*b*c^-1*f^4*(1+-1*c*x)^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+15//4*b*c^-1*f^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*arcsin(c*x)^2)
@test integrate((d+c*d*x)^-5//2*(f+-1*c*f*x)^5//2*(a+b*arcsin(c*x)), x) == :(-1*b*x*f^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+5*c^-1*f^5*(1+-1*c^2*x^2)^3*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+5*c^-1*f^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))*arcsin(c*x)+-28//3*b*c^-1*f^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+c*x)+-8//3*b*c^-1*f^5*(1+c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-5//2*b*c^-1*f^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arcsin(c*x)^2+-2//3*c^-1*f^5*(1+-1*c*x)^4*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+10//3*c^-1*f^5*(1+-1*c*x)^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^5//2*(f+-1*c*f*x)^-1//2*(a+b*arcsin(c*x)), x) == :(-11//3*c^-1*d^3*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-3//2*x*d^3*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+11//3*b*x*d^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+-1//3*c*d^3*x^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//9*b*c^2*d^3*x^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+3//4*b*c*d^3*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+5//4*b^-1*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^3//2*(f+-1*c*f*x)^-1//2*(a+b*arcsin(c*x)), x) == :(-2*c^-1*d^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+2*b*x*d^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+-1//2*x*d^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//4*b*c*d^2*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+3//4*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^(1/2)*(f+-1*c*f*x)^-1//2*(a+b*arcsin(c*x)), x) == :(b*d*x*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2+-1*d*c^-1*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+(1/2)*d*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2*(a+b*arcsin(c*x)), x) == :((1/2)*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(f+-1*c*f*x)^-1//2)
@test integrate((d+c*d*x)^-3//2*(f+-1*c*f*x)^-1//2*(a+b*arcsin(c*x)), x) == :(b*f*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+c*x)+-1*f*c^-1*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^-5//2*(f+-1*c*f*x)^-1//2*(a+b*arcsin(c*x)), x) == :(1//3*x*f^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+-2//3*c^-1*f^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//3*b*c^-1*f^2*(1+c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+1//3*b*c^-1*f^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arctanh(c*x)+1//6*b*c^-1*f^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c^2*x^2))
@test integrate((d+c*d*x)^5//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x)), x) == :(-3//2*b*x*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+15//2*c^-1*d^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x))+b*c*d^4*x^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+2*c^-1*d^4*(1+c*x)^3*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+8*b*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+-1*c*x)+-15//2*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x))*arcsin(c*x)+-5//4*b*c^-1*d^4*(1+c*x)^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+5//2*c^-1*d^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+c*x)*(a+b*arcsin(c*x))+15//4*b*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*arcsin(c*x)^2)
@test integrate((d+c*d*x)^3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x)), x) == :(c^-1*d^3*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x))+-1*b*x*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2+4*b*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+-1*c*x)+4*c^-1*d^3*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-3//2*b^-1*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2)
@test integrate((d+c*d*x)^(1/2)*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x)), x) == :(2*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+-1*c*x)+2*c^-1*d^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//2*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2)
@test integrate((d+c*d*x)^-1//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x)), x) == :(b*d*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+-1*c*x)+d*c^-1*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x)), x) == :(x*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+(1/2)*b*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(f+-1*c*f*x)^-3//2*log(1+-1*c^2*x^2))
@test integrate((d+c*d*x)^-5//2*(f+-1*c*f*x)^-3//2*(a+b*arcsin(c*x)), x) == :(2//3*f*x*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+-1//3*f*c^-1*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//6*b*f*c^-1*(1+c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+1//3*b*f*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c^2*x^2)+1//6*b*f*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arctanh(c*x))
@test integrate((d+c*d*x)^5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)), x) == :(b*x*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-5*c^-1*d^5*(1+-1*c^2*x^2)^3*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+5*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))*arcsin(c*x)+-28//3*b*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c*x)+-10//3*c^-1*d^5*(1+c*x)^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+-8//3*b*c^-1*d^5*(1+-1*c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-5//2*b*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arcsin(c*x)^2+2//3*c^-1*d^5*(1+c*x)^4*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^3//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)), x) == :(c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))*arcsin(c*x)+-2*c^-1*d^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+c*x)*(a+b*arcsin(c*x))+-8//3*b*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c*x)+-4//3*b*c^-1*d^4*(1+-1*c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-1//2*b*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arcsin(c*x)^2+2//3*c^-1*d^4*(1+c*x)^3*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^(1/2)*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)), x) == :(-2//3*b*c^-1*d^3*(1+-1*c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-1//3*b*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c*x)+1//3*c^-1*d^3*(1+c*x)^3*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^-1//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)), x) == :(1//3*x*d^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+-1//3*b*c^-1*d^2*(1+-1*c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-1//3*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arctanh(c*x)+1//6*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c^2*x^2)+2//3*c^-1*d^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^-3//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)), x) == :(2//3*d*x*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+-1//6*b*d*c^-1*(1+-1*c*x)^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+-1//6*b*d*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*arctanh(c*x)+1//3*b*d*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c^2*x^2)+1//3*d*c^-1*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+c*x)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x)))
@test integrate((d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x)), x) == :(-1//6*b*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2+1//3*x*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+2//3*x*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*(a+b*arcsin(c*x))+1//3*b*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(f+-1*c*f*x)^-5//2*log(1+-1*c^2*x^2))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^(1/2), x) == :(-15//64*x*b^2*d^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+3//8*x*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+8//9*b^2*c^-1*d^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2//3*c^-1*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-1//32*b^2*c^2*d^2*x^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//4*c^2*d^2*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+4//27*b^2*c^-1*d^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+4//3*b*x*d^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+5//24*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+15//64*b^2*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+-4//9*b*c^2*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+-3//8*b*c*d^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+-1//8*b*c^3*d^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^(1/2), x) == :((1/2)*d*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//4*d*x*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+4//9*d*b^2*c^-1*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//3*d*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+2//27*d*b^2*c^-1*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+1//4*d*b^2*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+1//6*d*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+2//3*b*d*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+-2//9*b*d*c^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+-1//2*b*c*d*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2), x) == :((1/2)*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//4*x*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//4*b^2*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+1//6*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//2*b*c*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^(1/2), x) == :(e*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-2*e*b^2*c^-1*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-2*a*b*e*x*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-2*e*x*b^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+1//3*e*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2)
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^(1/2), x) == :(-2*c^-1*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+2*x*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-2*im*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1//3*b^-1*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-4*im*b^2*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*b^2*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+4*im*b^2*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+4*b*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-8*im*b*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^(1/2), x) == :(-4//3*b^2*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*cot((1/2)*arcsin(c*x)+1//4*pi)+1//3*im*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+1//3*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*cot((1/2)*arcsin(c*x)+1//4*pi)+-4//3*b*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+-1*im*exp(im*arcsin(c*x)))+-2//3*b*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*csc((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+-1//3*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*csc((1/2)*arcsin(c*x)+1//4*pi)^2*cot((1/2)*arcsin(c*x)+1//4*pi)+4//3*im*b^2*c^-1*e^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^3//2, x) == :(-1//32*d*x*b^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//4*d*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+8//225*d*b^2*c^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-15*d*x*b^2*(64+-64*c^2*x^2)^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+3*d*x*(8+-8*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-1//5*d*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(1+-1*c^2*x^2)+2//125*d*b^2*c^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(1+-1*c^2*x^2)+16//75*d*b^2*c^-1*(1+-1*c^2*x^2)^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//8*b*d*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+1//8*d*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+2//5*b*d*x*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+9//64*d*b^2*c^-1*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*arcsin(c*x)+-4//15*b*d*c^2*x^3*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+-3//8*b*c*d*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+2//25*b*d*c^4*x^5*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2, x) == :(-1//32*x*b^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//4*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-15*x*b^2*(64+-64*c^2*x^2)^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+3*x*(8+-8*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//8*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+1//8*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+9//64*b^2*c^-1*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*arcsin(c*x)+-3//8*b*c*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^3//2, x) == :((1/2)*e*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-4//9*e*b^2*c^-1*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//4*e*x*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2//27*e*b^2*c^-1*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+1//3*e*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-2//3*b*e*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+1//4*e*b^2*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+1//6*e*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//2*b*c*e*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+2//9*b*e*c^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^3//2, x) == :(-4*b^2*c^-1*e^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+2*c^-1*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-1//2*x*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+1//4*x*b^2*e^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+(1/2)*b^-1*c^-1*e^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-4*b*x*e^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))+-1//4*b^2*c^-1*e^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+(1/2)*b*c*e^2*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^3//2, x) == :(-1*c^-1*e^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-4*c^-1*e^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+2*b^2*c^-1*e^3*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+4*x*e^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*b^-1*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-4*im*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+2*a*b*x*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+2*x*b^2*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*arcsin(c*x)+-8*im*b^2*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-4*im*b^2*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+8*im*b^2*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+8*b*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-16*im*b*c^-1*e^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^3//2, x) == :(-8//3*b^2*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*cot((1/2)*arcsin(c*x)+1//4*pi)+1//3*b^-1*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+8//3*im*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+8//3*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*cot((1/2)*arcsin(c*x)+1//4*pi)+-32//3*b*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+-1*im*exp(im*arcsin(c*x)))+-4//3*b*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*csc((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+-2//3*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*csc((1/2)*arcsin(c*x)+1//4*pi)^2*cot((1/2)*arcsin(c*x)+1//4*pi)+32//3*im*b^2*c^-1*e^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2, x) == :(-1//108*x*b^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+1//6*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+-65*x*b^2*(1728+-1728*c^2*x^2)^-1*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+5*x*(24+-24*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+-245//1152*x*b^2*(1+-1*c^2*x^2)^-2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+5//16*x*(1+-1*c^2*x^2)^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+1//18*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2*(a+b*arcsin(c*x))+5//48*b*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2*(a+b*arcsin(c*x))+5//48*b^-1*c^-1*(1+-1*c^2*x^2)^-5//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2+115//1152*b^2*c^-1*(1+-1*c^2*x^2)^-5//2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2*arcsin(c*x)+-5//16*b*c*x^2*(1+-1*c^2*x^2)^-5//2*(d+c*d*x)^5//2*(e+-1*c*e*x)^5//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^5//2, x) == :(-8//225*e*b^2*c^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-1//32*e*x*b^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//4*e*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-15*e*x*b^2*(64+-64*c^2*x^2)^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+3*e*x*(8+-8*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-16//75*e*b^2*c^-1*(1+-1*c^2*x^2)^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-2//125*e*b^2*c^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(1+-1*c^2*x^2)+1//5*e*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(1+-1*c^2*x^2)+-2//5*b*e*x*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+1//8*b*e*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+1//8*e*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+9//64*e*b^2*c^-1*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*arcsin(c*x)+-3//8*b*c*e*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+-2//25*b*e*c^4*x^5*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+4//15*b*e*c^2*x^3*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^5//2, x) == :(-15//64*x*b^2*e^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-8//9*b^2*c^-1*e^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+3//8*x*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-4//27*b^2*c^-1*e^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-1//32*b^2*c^2*e^2*x^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//4*c^2*e^2*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+2//3*c^-1*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-4//3*b*x*e^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+5//24*b^-1*c^-1*e^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+15//64*b^2*c^-1*e^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+-3//8*b*c*e^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+-1//8*b*c^3*e^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+4//9*b*c^2*e^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^5//2, x) == :(-68//9*b^2*c^-1*e^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-3//2*x*e^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+2//27*b^2*c^-1*e^3*(1+-1*c^2*x^2)^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+3//4*x*b^2*e^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+11//3*c^-1*e^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-22//3*b*x*e^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))+-3//4*b^2*c^-1*e^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+1//3*c*e^3*x^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+5//6*b^-1*c^-1*e^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-2//9*b*c^2*e^3*x^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))+3//2*b*c*e^3*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^5//2, x) == :((1/2)*x*e^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-8*c^-1*e^4*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-4*c^-1*e^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+8*x*e^4*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+8*b^2*c^-1*e^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1//4*x*b^2*e^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-8*im*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+8*a*b*x*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+8*x*b^2*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*arcsin(c*x)+-5//2*b^-1*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+1//4*b^2*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*arcsin(c*x)+-16*im*b^2*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-8*im*b^2*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+16*im*b^2*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+16*b*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-1//2*b*c*e^4*x^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))+-32*im*b*c^-1*e^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^5//2, x) == :(c^-1*e^5*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2*b^2*c^-1*e^5*(1+-1*c^2*x^2)^3*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2*a*b*x*e^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2*x*b^2*e^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*arcsin(c*x)+-16//3*b^2*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*cot((1/2)*arcsin(c*x)+1//4*pi)+5//3*b^-1*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+28//3*im*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+28//3*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*cot((1/2)*arcsin(c*x)+1//4*pi)+-112//3*b*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+-1*im*exp(im*arcsin(c*x)))+-8//3*b*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*csc((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+-4//3*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*csc((1/2)*arcsin(c*x)+1//4*pi)^2*cot((1/2)*arcsin(c*x)+1//4*pi)+112//3*im*b^2*c^-1*e^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^-1//2, x) == :(-11//3*c^-1*d^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-3//2*x*d^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-2//27*b^2*c^-1*d^3*(1+-1*c^2*x^2)^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+3//4*x*b^2*d^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+68//9*b^2*c^-1*d^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-3//4*b^2*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+-1//3*c*d^3*x^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+5//6*b^-1*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+22//3*b*x*d^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))+2//9*b*c^2*d^3*x^3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))+3//2*b*c*d^3*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^-1//2, x) == :(-2*c^-1*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+4*b^2*c^-1*d^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-1//2*x*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+1//4*x*b^2*d^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+(1/2)*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+4*b*x*d^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))+-1//4*b^2*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+(1/2)*b*c*d^2*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^-1//2, x) == :(-1*d*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+2*d*b^2*c^-1*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+2*a*b*d*x*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+2*d*x*b^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+1//3*d*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2)
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2, x) == :(1//3*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2)
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-1//2, x) == :(e*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*e*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*im*e*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1*im*e*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-2*im*e*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*im*e*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*b*e*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-4*im*b*e*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-1//2, x) == :(-2//3*b^2*c^-1*e^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2//3*c^-1*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+1//3*x*e^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+2//3*x*b^2*e^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2//3*x*e^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*im*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*b*c^-1*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-1//3*b^2*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*arcsin(c*x)+1//3*c^2*e^2*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+2//3*b*x*e^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-2//3*im*b^2*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-1//3*im*b^2*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//3*b*c*e^2*x^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+2//3*im*b^2*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2//3*b*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-4//3*im*b*c^-1*e^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^-3//2, x) == :((1/2)*x*d^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-8*b^2*c^-1*d^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+4*c^-1*d^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+8*x*d^4*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+8*c^-1*d^4*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1//4*x*b^2*d^4*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-8*im*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-8*a*b*x*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-8*x*b^2*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*arcsin(c*x)+-5//2*b^-1*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+1//4*b^2*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*arcsin(c*x)+-16*im*b^2*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-8*im*b^2*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+16*im*b^2*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+16*b*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-1//2*b*c*d^4*x^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))+32*im*b*c^-1*d^4*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^-3//2, x) == :(c^-1*d^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-2*b^2*c^-1*d^3*(1+-1*c^2*x^2)^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+4*x*d^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+4*c^-1*d^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*b^-1*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-4*im*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-2*a*b*x*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-2*x*b^2*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*arcsin(c*x)+-8*im*b^2*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-4*im*b^2*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+8*im*b^2*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+8*b*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+16*im*b*c^-1*d^3*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^-3//2, x) == :(2*x*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+2*c^-1*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-2*im*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1//3*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-4*im*b^2*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-2*im*b^2*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+4*im*b^2*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+4*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+8*im*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-3//2, x) == :(d*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+d*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*im*d*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1*im*d*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-2*im*d*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*d*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*b*d*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+4*im*b*d*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2, x) == :(x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*im*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1*im*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+2*b*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-3//2, x) == :(-1//3*e*b^2*c^-1*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*e*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+1//3*e*x*b^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+1//3*e*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+2//3*e*x*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2//3*im*e*c^-1*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*b*e*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+1//3*b*e*x*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-2//3*im*e*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//3*im*e*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+1//3*im*e*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+4//3*b*e*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+-2//3*im*b*e*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^5//2*(e+-1*c*e*x)^-5//2, x) == :(-1*c^-1*d^5*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2*b^2*c^-1*d^5*(1+-1*c^2*x^2)^3*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2*a*b*x*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2*x*b^2*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*arcsin(c*x)+-28//3*im*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-28//3*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*tan((1/2)*arcsin(c*x)+1//4*pi)+5//3*b^-1*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+16//3*b^2*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*tan((1/2)*arcsin(c*x)+1//4*pi)+-112//3*im*b^2*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(-1*im*arcsin(c*x)))+-112//3*b*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+-1*im*exp(-1*im*arcsin(c*x)))+-8//3*b*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*sec((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+4//3*c^-1*d^5*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*sec((1/2)*arcsin(c*x)+1//4*pi)^2*tan((1/2)*arcsin(c*x)+1//4*pi))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^-5//2, x) == :(-8//3*im*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-8//3*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*tan((1/2)*arcsin(c*x)+1//4*pi)+1//3*b^-1*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+8//3*b^2*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*tan((1/2)*arcsin(c*x)+1//4*pi)+-32//3*im*b^2*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(-1*im*arcsin(c*x)))+-32//3*b*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+-1*im*exp(-1*im*arcsin(c*x)))+-4//3*b*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*sec((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+2//3*c^-1*d^4*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*sec((1/2)*arcsin(c*x)+1//4*pi)^2*tan((1/2)*arcsin(c*x)+1//4*pi))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^-5//2, x) == :(-1//3*im*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*tan((1/2)*arcsin(c*x)+1//4*pi)+4//3*b^2*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*tan((1/2)*arcsin(c*x)+1//4*pi)+-4//3*im*b^2*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(-1*im*arcsin(c*x)))+-4//3*b*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+-1*im*exp(-1*im*arcsin(c*x)))+-2//3*b*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*sec((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+1//3*c^-1*d^3*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*sec((1/2)*arcsin(c*x)+1//4*pi)^2*tan((1/2)*arcsin(c*x)+1//4*pi))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-5//2, x) == :(1//3*x*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+2//3*x*b^2*d^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2//3*x*d^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2//3*b^2*c^-1*d^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+2//3*c^-1*d^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+-2//3*b*x*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-1//3*im*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*b*c^-1*d^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-1//3*b^2*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*arcsin(c*x)+1//3*c^2*d^2*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+-2//3*im*b^2*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+-1//3*im*b^2*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//3*b*c*d^2*x^2*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+2//3*im*b^2*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2//3*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+4//3*im*b*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-5//2, x) == :(1//3*d*x*b^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+1//3*d*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+1//3*d*b^2*c^-1*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+1//3*d*c^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+2//3*d*x*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2//3*im*d*c^-1*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*b*d*x*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-1//3*b*d*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-2//3*im*d*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1//3*im*d*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+1//3*im*d*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+4//3*b*d*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x)))+2//3*im*b*d*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2, x) == :(1//3*x*b^2*(1+-1*c^2*x^2)^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+1//3*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(1+-1*c^2*x^2)+2//3*x*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-2//3*im*c^-1*(1+-1*c^2*x^2)^5//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2+-1//3*b*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))+-2//3*im*b^2*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+4//3*b*c^-1*(1+-1*c^2*x^2)^5//2*(d+c*d*x)^-5//2*(e+-1*c*e*x)^-5//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2), x) == :(-1//32*b^2*x^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//4*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//8*x*c^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//64*x*b^2*c^-2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//64*b^2*c^-3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+1//24*b^-1*c^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//8*b*c*x^4*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+1//8*b*c^-1*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2), x) == :(4//9*b^2*c^-2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//3*c^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+2//27*b^2*c^-2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-2//9*b*c*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+2//3*b*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2), x) == :((1/2)*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//4*x*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//4*b^2*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+1//6*b^-1*c^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//2*b*c*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2), x) == :((a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arctanh(exp(im*arcsin(c*x)))+2*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*a*b*c*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2*c*x*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+2*im*b*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2), x) == :(-1*x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1*im*c*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//3*c*b^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1*im*c*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x))))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2, x) == :(-43//1728*d*e*b^2*x^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//8*d*e*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-7//1152*d*e*x*b^2*c^-2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//16*d*e*x*c^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//6*d*e*x^3*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+1//108*d*e*b^2*c^2*x^5*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//48*d*e*b^-1*c^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+7//1152*d*e*b^2*c^-3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+-7//48*b*c*d*e*x^4*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+1//16*b*d*e*c^-1*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+1//18*b*d*e*c^3*x^6*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2, x) == :(16//75*d*e*b^2*c^-2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1//5*d*e*c^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+2//125*d*e*b^2*c^-2*(1+-1*c^2*x^2)^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+8//225*d*e*b^2*c^-2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-4//15*b*c*d*e*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+2//5*b*d*e*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+2//25*b*d*e*c^3*x^5*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2, x) == :(-1//32*x*b^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//4*x*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+-15*x*b^2*(64+-64*c^2*x^2)^-1*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+3*x*(8+-8*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+1//8*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x))+1//8*b^-1*c^-1*(1+-1*c^2*x^2)^-3//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2+9//64*b^2*c^-1*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*arcsin(c*x)+-3//8*b*c*x^2*(1+-1*c^2*x^2)^-3//2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2*(a+b*arcsin(c*x)))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2, x) == :(d*e*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-22//9*d*e*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2//27*d*e*b^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+1//3*d*e*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-2*d*e*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*d*e*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arctanh(exp(im*arcsin(c*x)))+2*d*e*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*d*e*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+-2*a*b*c*d*e*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-2*c*d*e*x*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+2*im*b*d*e*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+-2//3*b*c*d*e*x*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+2//9*b*d*e*c^3*x^3*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^3//2*(e+-1*c*e*x)^3//2, x) == :(-1*d*e*x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(1+-1*c^2*x^2)+-3//2*d*e*x*c^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+1//4*d*e*x*b^2*c^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+b*c*d*e*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))+-1*im*c*d*e*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-5//4*c*d*e*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*arcsin(c*x)+-1//2*c*d*e*b^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)+-1*im*c*d*e*b^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*d*e*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x)))+3//2*b*d*e*c^3*x^2*(1+-1*c^2*x^2)^-1//2*(d+c*d*x)^(1/2)*(e+-1*c*e*x)^(1/2)*(a+b*arcsin(c*x)))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2, x) == :(-1//2*x*c^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-1//4*b^2*c^-3*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x)+1//4*x*b^2*c^-2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+1//6*b^-1*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+(1/2)*b*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x)))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2, x) == :(-1*c^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+2*b^2*c^-2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+2*a*b*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+2*x*b^2*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arcsin(c*x))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2, x) == :(1//3*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2)
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2, x) == :(-2*b^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arctanh(exp(im*arcsin(c*x)))+2*b^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*b*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2, x) == :(-1*x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(1+-1*c^2*x^2)+-1*im*c*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-1*im*c*b^2*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+2*b*c*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*log(1+-1*exp(2*im*arcsin(c*x))))
@test integrate(x^2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2, x) == :(x*c^-2*d^-1*e^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-1*im*c^-3*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-1//3*b^-1*c^-3*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-1*im*b^2*c^-3*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+2*b*c^-3*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2, x) == :(c^-2*d^-1*e^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-2*im*b^2*c^-2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*c^-2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+4*im*b*c^-2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2, x) == :(x*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(1+-1*c^2*x^2)+-1*im*c^-1*(1+-1*c^2*x^2)^3//2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2+-1*im*b^2*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+2*b*c^-1*(1+-1*c^2*x^2)^3//2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))
@test integrate(x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2, x) == :(d^-1*e^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-2*b^2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c*x)))+-2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*arctanh(exp(im*arcsin(c*x)))+2*b^2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(3,exp(im*arcsin(c*x)))+-2*im*b^2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*b^2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-2*im*b*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,exp(im*arcsin(c*x)))+2*im*b*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c*x)))+4*im*b*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*arctan(exp(im*arcsin(c*x))))
@test integrate(x^-2*(a+b*arcsin(c*x))^2*(d+c*d*x)^-3//2*(e+-1*c*e*x)^-3//2, x) == :(-1*d^-1*e^-1*x^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+2*x*c^2*d^-1*e^-1*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-2*im*c*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2+-1*im*c*b^2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-1*im*c*b^2*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x)))+-4*b*c*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*arctanh(exp(2*im*arcsin(c*x)))+4*b*c*d^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+c*d*x)^-1//2*(e+-1*c*e*x)^-1//2*(a+b*arcsin(c*x))*log(1+exp(2*im*arcsin(c*x))))

max_stars_repo_path: test/5 Inverse trig functions/5.1 Inverse sine/5.1.4a (f x)^m (d-c^2 d x^2)^p (a+b arcsin(c x))^n.jl