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

@test integrate((d+e*x)^3*(a+b*arcsin(c*x)), x) == :(1//4*e^-1*(d+e*x)^4*(a+b*arcsin(c*x))+1//16*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^3+1//96*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(4*d*(16*e^2+19*c^2*d^2)+e*x*(9*e^2+26*c^2*d^2))+-1//32*b*c^-4*e^-1*(3*e^4+8*c^4*d^4+24*c^2*d^2*e^2)*arcsin(c*x)+7//48*b*d*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^2)
@test integrate((d+e*x)^2*(a+b*arcsin(c*x)), x) == :(1//3*e^-1*(d+e*x)^3*(a+b*arcsin(c*x))+1//9*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^2+1//18*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(4*e^2+16*c^2*d^2+5*d*e*x*c^2)+-1//6*b*d*e^-1*(2*d^2+3*c^-2*e^2)*arcsin(c*x))
@test integrate((a+b*arcsin(c*x))*(d+e*x), x) == :((1/2)*e^-1*(d+e*x)^2*(a+b*arcsin(c*x))+-1//4*b*e^-1*(2*d^2+c^-2*e^2)*arcsin(c*x)+1//4*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)+3//4*b*d*c^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate(a+b*arcsin(c*x), x) == :(a*x+b*x*arcsin(c*x)+b*c^-1*(1+-1*c^2*x^2)^(1/2))
@test integrate((d+e*x)^-1*(a+b*arcsin(c*x)), x) == :(e^-1*(a+b*arcsin(c*x))*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+e^-1*(a+b*arcsin(c*x))*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-1*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-1*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1//2*im*b^-1*e^-1*(a+b*arcsin(c*x))^2)
@test integrate((d+e*x)^-2*(a+b*arcsin(c*x)), x) == :(-1*e^-1*(d+e*x)^-1*(a+b*arcsin(c*x))+b*c*e^-1*(-1*e^2+c^2*d^2)^-1//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2)))
@test integrate((d+e*x)^-3*(a+b*arcsin(c*x)), x) == :(-1//2*e^-1*(d+e*x)^-2*(a+b*arcsin(c*x))+b*c*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-2*e^2+2*c^2*d^2)^-1+(1/2)*b*d*c^3*e^-1*(-1*e^2+c^2*d^2)^-3//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2)))
@test integrate((d+e*x)^-4*(a+b*arcsin(c*x)), x) == :(-1//3*e^-1*(d+e*x)^-3*(a+b*arcsin(c*x))+b*c*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-6*e^2+6*c^2*d^2)^-1+(1/2)*b*d*c^3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2+1//6*b*c^3*e^-1*(-1*e^2+c^2*d^2)^-5//2*(e^2+2*c^2*d^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2)))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^3, x) == :(-2*x*b^2*d^3+-3//32*c^-4*e^3*(a+b*arcsin(c*x))^2+-1//4*d^4*e^-1*(a+b*arcsin(c*x))^2+-1//32*b^2*e^3*x^4+1//4*e^-1*(a+b*arcsin(c*x))^2*(d+e*x)^4+-3//4*e*b^2*d^2*x^2+-3//4*e*c^-2*d^2*(a+b*arcsin(c*x))^2+-3//32*b^2*c^-2*e^3*x^2+-2//9*d*b^2*e^2*x^3+2*b*c^-1*d^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-4//3*d*x*b^2*c^-2*e^2+1//8*b*c^-1*e^3*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//16*b*x*c^-3*e^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//3*b*d*c^-3*e^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//3*b*d*c^-1*e^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//2*b*e*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+e*x)^2, x) == :(-2*x*b^2*d^2+-2//27*b^2*e^2*x^3+-1//3*d^3*e^-1*(a+b*arcsin(c*x))^2+1//3*e^-1*(a+b*arcsin(c*x))^2*(d+e*x)^3+-4//9*x*b^2*c^-2*e^2+-1//2*d*e*b^2*x^2+-1//2*d*e*c^-2*(a+b*arcsin(c*x))^2+2*b*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//9*b*c^-3*e^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//9*b*c^-1*e^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*d*e*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+e*x), x) == :((1/2)*e^-1*(a+b*arcsin(c*x))^2*(d+e*x)^2+-2*d*x*b^2+-1//2*d^2*e^-1*(a+b*arcsin(c*x))^2+-1//4*e*b^2*x^2+-1//4*e*c^-2*(a+b*arcsin(c*x))^2+2*b*d*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+(1/2)*b*e*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2, x) == :(x*(a+b*arcsin(c*x))^2+-2*x*b^2+2*b*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-1, x) == :(e^-1*(a+b*arcsin(c*x))^2*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+e^-1*(a+b*arcsin(c*x))^2*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*b^2*e^-1*Polylogarithms.polylog(3,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*b^2*e^-1*Polylogarithms.polylog(3,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1//3*im*b^-1*e^-1*(a+b*arcsin(c*x))^3+-2*im*b*e^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-2*im*b*e^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-2, x) == :(-1*e^-1*(a+b*arcsin(c*x))^2*(d+e*x)^-1+-2*c*b^2*e^-1*(-1*e^2+c^2*d^2)^-1//2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*c*b^2*e^-1*(-1*e^2+c^2*d^2)^-1//2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-2*im*b*c*e^-1*(-1*e^2+c^2*d^2)^-1//2*(a+b*arcsin(c*x))*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*im*b*c*e^-1*(-1*e^2+c^2*d^2)^-1//2*(a+b*arcsin(c*x))*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-3, x) == :(-1//2*e^-1*(a+b*arcsin(c*x))^2*(d+e*x)^-2+-1*b^2*c^2*e^-1*(-1*e^2+c^2*d^2)^-1*log(d+e*x)+b*c*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(a+b*arcsin(c*x))+d*b^2*c^3*e^-1*(-1*e^2+c^2*d^2)^-3//2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*d*b^2*c^3*e^-1*(-1*e^2+c^2*d^2)^-3//2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+im*b*d*c^3*e^-1*(-1*e^2+c^2*d^2)^-3//2*(a+b*arcsin(c*x))*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*d*c^3*e^-1*(-1*e^2+c^2*d^2)^-3//2*(a+b*arcsin(c*x))*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^-1*(d+e*x)^3, x) == :(b^-1*c^-1*d^3*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+b^-1*c^-1*d^3*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+-1//4*b^-1*c^-4*e^3*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+-1//8*b^-1*c^-4*e^3*cos(4*a*b^-1)*sinintegral(4*arcsin(c*x)+4*a*b^-1)+1//4*b^-1*c^-4*e^3*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+1//8*b^-1*c^-4*e^3*cosintegral(4*arcsin(c*x)+4*a*b^-1)*sin(4*a*b^-1)+-3//2*e*b^-1*c^-2*d^2*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1)+-3//4*d*b^-1*c^-3*e^2*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+-3//4*d*b^-1*c^-3*e^2*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+3//2*e*b^-1*c^-2*d^2*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+3//4*d*b^-1*c^-3*e^2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+3//4*d*b^-1*c^-3*e^2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^-1*(d+e*x)^2, x) == :(b^-1*c^-1*d^2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+b^-1*c^-1*d^2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+-1//4*b^-1*c^-3*e^2*cos(3*a*b^-1)*cosintegral(3*arcsin(c*x)+3*a*b^-1)+-1//4*b^-1*c^-3*e^2*sin(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+1//4*b^-1*c^-3*e^2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+1//4*b^-1*c^-3*e^2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+d*e*b^-1*c^-2*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-1*d*e*b^-1*c^-2*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c*x))^-1*(d+e*x), x) == :(d*b^-1*c^-1*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c*x))+d*b^-1*c^-1*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+(1/2)*e*b^-1*c^-2*cos(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-1//2*e*b^-1*c^-2*cosintegral(2*arcsin(c*x)+2*a*b^-1)*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c*x))^-1, x) == :(b^-1*c^-1*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c*x)))+b^-1*c^-1*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^-2*(d+e*x)^2, x) == :(b^-2*c^-1*d^2*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1*b^-1*c^-1*d^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1+-1*b^-2*c^-1*d^2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+-3//4*b^-2*c^-3*e^2*cosintegral(3*arcsin(c*x)+3*a*b^-1)*sin(3*a*b^-1)+-1//4*b^-2*c^-3*e^2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+1//4*b^-2*c^-3*e^2*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+3//4*b^-2*c^-3*e^2*cos(3*a*b^-1)*sinintegral(3*arcsin(c*x)+3*a*b^-1)+-1*b^-1*c^-1*e^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1+2*d*e*b^-2*c^-2*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+2*d*e*b^-2*c^-2*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-2*d*e*x*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1)
@test integrate((a+b*arcsin(c*x))^-2*(d+e*x), x) == :(d*b^-2*c^-1*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+e*b^-2*c^-2*cos(2*a*b^-1)*cosintegral(2*arcsin(c*x)+2*a*b^-1)+e*b^-2*c^-2*sin(2*a*b^-1)*sinintegral(2*arcsin(c*x)+2*a*b^-1)+-1*d*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1+-1*d*b^-2*c^-1*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x))+-1*e*x*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1)
@test integrate((a+b*arcsin(c*x))^-2, x) == :(b^-2*c^-1*cosintegral(a*b^-1+arcsin(c*x))*sin(a*b^-1)+-1*b^-1*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^-1+-1*b^-2*c^-1*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c*x)))
@test integrate((d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^3*(a+b*arcsin(c*x)), x) == :((1/2)*x*f^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//3*c^-4*g^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//5*c^-4*g^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//4*f*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*g*c^-2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-3//8*f*x*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//4*b*c*f^3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//25*b*c*g^3*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//4*b^-1*c^-1*f^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//45*b*c^-1*g^3*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*g^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+b*g*x*c^-1*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//16*b*c*f*g^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//3*b*c*g*f^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//16*b*f*c^-1*g^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//16*f*b^-1*c^-3*g^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((d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^2*(a+b*arcsin(c*x)), x) == :((1/2)*x*f^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//4*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//8*x*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-2//3*f*g*c^-2*(d+-1*d*c^2*x^2)^(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+-1*d*c^2*x^2)^(1/2)+-1//16*b*c*g^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//4*b^-1*c^-1*f^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^-1*g^2*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*g^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//9*b*c*f*g*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//3*b*f*g*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))*(f+g*x), x) == :((1/2)*f*x*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//3*g*c^-2*(d+-1*d*c^2*x^2)^(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+-1*d*c^2*x^2)^(1/2)+-1//9*b*c*g*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//3*b*g*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//4*f*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((d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(a+b*arcsin(c*x)), x) == :(a*g^-1*(d+-1*d*c^2*x^2)^(1/2)+b*g^-1*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*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)*(f+g*x)^-1+-1*a*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+-1*b*c*x*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+(1/2)*c*x*b^-1*g^-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^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(1+-1*c^2*f^2*g^-2)+im*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-2*(a+b*arcsin(c*x)), x) == :(-1*a*g^-1*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1+-1*b*g^-1*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*arcsin(c*x)+b*c*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*log(f+g*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)*(f+g*x)^-2+a*f*c^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+b*f*c^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*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)*(f+g*x)^-2*(g+f*x*c^2)^2*(-1*g^2+c^2*f^2)^-1+-1*a*c^3*f^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1*arcsin(c*x)+-1*b*f*c^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//2*b*c^3*f^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1*arcsin(c*x)^2+im*b*f*c^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1//2*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*b*f*c^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^-1//2*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((d+-1*d*c^2*x^2)^3//2*(f+g*x)^3*(a+b*arcsin(c*x)), x) == :(3//8*d*x*f^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//5*d*c^-4*g^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//4*d*x*f^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//7*d*c^-4*g^3*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//8*d*f*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+(1/2)*d*f*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-8//175*b*c*d*g^3*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-5//16*b*c*d*f^3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//5*d*g*c^-2*f^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-3//16*d*f*x*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//16*b*d*c^3*f^3*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//49*b*d*c^3*g^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*g^3*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*g^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//16*d*b^-1*c^-1*f^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-7//32*b*c*d*f*g^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2//5*b*c*d*g*f^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//12*b*d*f*c^3*g^2*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//5*b*d*g*x*c^-1*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//25*b*d*g*c^3*f^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//32*b*d*f*c^-1*g^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//32*d*f*b^-1*c^-3*g^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((d+-1*d*c^2*x^2)^3//2*(f+g*x)^2*(a+b*arcsin(c*x)), x) == :(1//8*d*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//8*d*x*f^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//16*d*x*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//4*d*x*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//6*d*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-7//96*b*c*d*g^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-5//16*b*c*d*f^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2//5*d*f*g*c^-2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//16*b*d*c^3*f^2*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*g^2*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*g^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//36*b*d*c^3*g^2*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//16*d*b^-1*c^-1*f^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-4//15*b*c*d*f*g*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//5*b*d*f*g*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//25*b*d*f*g*c^3*x^5*(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))*(f+g*x), x) == :(3//8*d*f*x*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//5*d*g*c^-2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//4*d*f*x*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-5//16*b*c*d*f*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2//15*b*c*d*g*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//5*b*d*g*x*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//16*b*d*f*c^3*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//25*b*d*g*c^3*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//16*d*f*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((d+-1*d*c^2*x^2)^3//2*(f+g*x)^-1*(a+b*arcsin(c*x)), x) == :(1//3*d*g^-1*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1*a*d*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+a*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+(1/2)*d*f*x*c^2*g^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*b*d*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)*arcsin(c*x)+-1//3*b*c*d*x*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//9*b*d*c^3*g^-1*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//4*b*d*f*c^3*g^-2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//4*c*d*f*b^-1*g^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+im*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+b*c*d*x*g^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+-1*im*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//2*d*b^-1*c^-1*g^-4*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(-1*g^2+c^2*f^2)^2+-1//2*c*d*x*b^-1*g^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+-1//2*d*b^-1*c^-1*g^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(g+c*f)*(-1g+c*f))
@test integrate((d+-1*d*c^2*x^2)^5//2*(f+g*x)^3*(a+b*arcsin(c*x)), x) == :(5//16*x*d^2*f^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//7*c^-4*d^2*g^3*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//6*x*d^2*f^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//9*c^-4*d^2*g^3*(1+-1*c^2*x^2)^4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//36*b*c^-1*d^2*f^3*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)+5//24*x*d^2*f^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+15//64*f*d^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-25//96*b*c*d^2*f^3*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-15//128*f*x*c^-2*d^2*g^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-3//7*g*c^-2*d^2*f^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//21*b*c*d^2*g^3*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*g^3*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*g^3*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*g^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//8*f*d^2*g^2*x^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//16*f*d^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+5//32*b^-1*c^-1*d^2*f^3*(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*f^3*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+19//441*b*c^3*d^2*g^3*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-59//256*b*c*f*d^2*g^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//7*b*c*g*d^2*f^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//49*b*g*c^5*d^2*f^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-3//64*b*f*c^5*d^2*g^2*x^8*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+3//7*b*g*x*c^-1*d^2*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+9//35*b*g*c^3*d^2*f^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+15//256*b*f*c^-1*d^2*g^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+15//256*f*b^-1*c^-3*d^2*g^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//96*b*f*c^3*d^2*g^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*(f+g*x)^2*(a+b*arcsin(c*x)), x) == :(5//16*x*d^2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//64*d^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-5//128*x*c^-2*d^2*g^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//6*x*d^2*f^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//8*d^2*g^2*x^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//36*b*c^-1*d^2*f^2*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)+5//24*x*d^2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+5//48*d^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-59//768*b*c*d^2*g^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-25//96*b*c*d^2*f^2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2//7*f*g*c^-2*d^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//64*b*c^5*d^2*g^2*x^8*(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*f^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*f^2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//256*b*c^-1*d^2*g^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*g^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*g^2*x^6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2//7*b*c*f*g*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2//49*b*f*g*c^5*d^2*x^7*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//7*b*f*g*x*c^-1*d^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+6//35*b*f*g*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((d+-1*d*c^2*x^2)^5//2*(a+b*arcsin(c*x))*(f+g*x), x) == :(5//16*f*x*d^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//7*g*c^-2*d^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//6*f*x*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//36*b*f*c^-1*d^2*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)+5//24*f*x*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-25//96*b*c*f*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*g*d^2*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//49*b*g*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*g*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*g*c^3*d^2*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+5//32*f*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*f*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((d+-1*d*c^2*x^2)^5//2*(f+g*x)^-1*(a+b*arcsin(c*x)), x) == :(a*d^2*g^-5*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2+-1//3*d^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//5*d^2*g^-1*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+b*d^2*g^-5*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2*arcsin(c*x)+-1//3*d^2*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))*(-2*g^2+c^2*f^2)+b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*a*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+-1*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//4*f*c^4*d^2*g^-2*x^3*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+-1//25*b*c^5*d^2*g^-1*x^5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+1//8*f*x*c^2*d^2*g^-2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//45*b*c^3*d^2*g^-1*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+2//15*b*c*x*d^2*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1*b*c*x*d^2*g^-5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2+-1//2*f*x*c^2*d^2*g^-4*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(-2*g^2+c^2*f^2)+-1//9*b*c^3*d^2*g^-3*x^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+-1//16*b*f*c^3*d^2*g^-2*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-1//16*c*f*b^-1*d^2*g^-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*x*d^2*g^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+1//16*b*f*c^5*d^2*g^-2*x^4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+im*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+(1/2)*c*x*b^-1*d^2*g^-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*g^2+c^2*f^2)^2+(1/2)*b^-1*c^-1*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(-1*g^2+c^2*f^2)^3+(1/2)*b^-1*c^-1*d^2*g^-4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(-1*g^2+c^2*f^2)^2+-1*im*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//4*c*f*b^-1*d^2*g^-4*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+1//4*b*f*c^3*d^2*g^-4*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2))
@test integrate((d+-1*d*c^2*x^2)^-1//2*(f+g*x)^3*(a+b*arcsin(c*x)), x) == :(-2//3*c^-4*g^3*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+(1/2)*b^-1*c^-1*f^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-3*g*c^-2*f^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//3*c^-2*g^3*x^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//9*b*c^-1*g^3*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*g^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+3*b*g*x*c^-1*f^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-3//2*f*x*c^-2*g^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+3//4*b*f*c^-1*g^2*x^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+3//4*f*b^-1*c^-3*g^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((d+-1*d*c^2*x^2)^-1//2*(f+g*x)^2*(a+b*arcsin(c*x)), x) == :((1/2)*b^-1*c^-1*f^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*f*g*c^-2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1//2*x*c^-2*g^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+1//4*b*c^-1*g^2*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*g^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*b*f*g*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))*(f+g*x), x) == :(-1*g*c^-2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+b*g*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+(1/2)*f*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((d+-1*d*c^2*x^2)^-1//2*(f+g*x)^-1*(a+b*arcsin(c*x)), x) == :(b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(a+b*arcsin(c*x))*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(a+b*arcsin(c*x))*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((d+-1*d*c^2*x^2)^-1//2*(f+g*x)^-2*(a+b*arcsin(c*x)), x) == :(g*(d+-1*d*c^2*x^2)^-1//2*(f+g*x)^-1*(-1*g^2+c^2*f^2)^-1*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+-1*b*c*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1*log(f+g*x)+b*f*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*b*f*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*f*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*f*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((d+-1*d*c^2*x^2)^-3//2*(f+g*x)^3*(a+b*arcsin(c*x)), x) == :(c^-4*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*(g*(g^2+3*c^2*f^2)+f*x*c^2*(3*g^2+c^2*f^2))+c^-4*d^-1*g^3*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)*(a+b*arcsin(c*x))+(1/2)*b*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^3*log(1+-1*c*x)+(1/2)*b*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^3*log(1+c*x)+-1*b*x*c^-3*d^-1*g^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-3//2*f*b^-1*c^-3*d^-1*g^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((d+-1*d*c^2*x^2)^-3//2*(f+g*x)^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))*(x*(g^2+c^2*f^2)+2*f*g)+(1/2)*b*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^2*log(1+-1*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*(-1g+c*f)^2*log(1+c*x)+-1//2*b^-1*c^-3*d^-1*g^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((d+-1*d*c^2*x^2)^-3//2*(a+b*arcsin(c*x))*(f+g*x), x) == :(c^-2*d^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*(g+f*x*c^2)+(1/2)*b*c^-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)*log(1+-1*c*x)+(1/2)*b*c^-2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)*log(1+c*x))
@test integrate((d+-1*d*c^2*x^2)^-3//2*(f+g*x)^-1*(a+b*arcsin(c*x)), x) == :(b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^-1*log(cos((1/2)*arcsin(c*x)+1//4*pi))+b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^-1*log(sin((1/2)*arcsin(c*x)+1//4*pi))+(1/2)*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^-1*(a+b*arcsin(c*x))*tan((1/2)*arcsin(c*x)+1//4*pi)+-1//2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^-1*(a+b*arcsin(c*x))*cot((1/2)*arcsin(c*x)+1//4*pi)+b*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*b*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((d+-1*d*c^2*x^2)^-5//2*(f+g*x)^3*(a+b*arcsin(c*x)), 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*(f+g*x)*(g^2+c^2*f^2+2*f*g*x*c^2)+1//3*c^-4*d^-2*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*(g+c*f)*(g+f*x*c^2)*(-2g+2*c*f)+1//3*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(d+-1*d*c^2*x^2)^-1//2*(f+g*x)^2*(a+b*arcsin(c*x))*(g+f*x*c^2)+-1//12*b*g*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^2*log(1+-1*c*x)+1//3*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^2*(-1g+c*f)*log(1+-1*c*x)+1//3*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^2*(g+c*f)*log(1+c*x)+1//12*b*g*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^2*log(1+c*x))
@test integrate((d+-1*d*c^2*x^2)^-5//2*(a+b*arcsin(c*x))*(f+g*x), x) == :(2//3*f*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*(f+g*x)+1//3*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*(g+f*x*c^2)+-1//6*b*g*c^-2*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arctanh(c*x)+1//3*b*f*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((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^3, x) == :((1/2)*x*f^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-2//15*c^-4*g^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//4*x*b^2*f^3*(d+-1*d*c^2*x^2)^(1/2)+1//5*g^3*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+52//225*b^2*c^-4*g^3*(d+-1*d*c^2*x^2)^(1/2)+-3//32*f*b^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+-2//125*b^2*c^-4*g^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+-1//15*c^-2*g^3*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+3//4*f*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+4//3*g*b^2*c^-2*f^2*(d+-1*d*c^2*x^2)^(1/2)+26//675*b^2*c^-4*g^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1*g*c^-2*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-3//8*f*x*c^-2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//4*b^2*c^-1*f^3*(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*f^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+2//9*g*b^2*c^-2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+3//64*f*x*b^2*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)+-3//64*f*b^2*c^-3*g^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-2//25*b*c*g^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))+-1//2*b*c*f^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))+1//8*f*b^-1*c^-3*g^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+2//45*b*c^-1*g^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))+4//15*a*b*x*c^-3*g^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*g^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+2*b*g*x*c^-1*f^2*(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*f*g^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))+-2//3*b*c*g*f^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))+3//8*b*f*c^-1*g^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((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^2, x) == :((1/2)*x*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//4*x*b^2*f^2*(d+-1*d*c^2*x^2)^(1/2)+-1//32*b^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+1//4*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//8*x*c^-2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//64*x*b^2*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)+8//9*f*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-2//3*f*g*c^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1//64*b^2*c^-3*g^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+1//4*b^2*c^-1*f^2*(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*f^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//24*b^-1*c^-3*g^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//27*f*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1//2*b*c*f^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//8*b*c*g^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//8*b*c^-1*g^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//9*b*c*f*g*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*b*f*g*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)*(f+g*x), x) == :((1/2)*f*x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//4*f*x*b^2*(d+-1*d*c^2*x^2)^(1/2)+4//9*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-1//3*g*c^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+2//27*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//4*f*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*f*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)+-2//9*b*c*g*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//2*b*c*f*x^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*b*g*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)*(f+g*x)^-1, x) == :(a^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)+-2*b^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)+b^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)^2+2*a*b*g^-1*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-1*a^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+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)*(f+g*x)^-1+-2*im*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*a*b*c*x*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+-2*a*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*c*x*b^2*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-2*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+2*im*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*a*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))*arcsin(c*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)*(f+g*x)^-1*(1+-1*c^2*f^2*g^-2)+1//3*c*x*b^-1*g^-1*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+im*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arcsin(c*x)^2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arcsin(c*x)^2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*im*a*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*a*b*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^(1/2)*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2*(f+g*x)^3, x) == :(-15//64*d*x*b^2*f^3*(d+-1*d*c^2*x^2)^(1/2)+-2//35*d*c^-4*g^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+3//8*d*x*f^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+3//35*d*g^3*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+304//3675*d*b^2*c^-4*g^3*(d+-1*d*c^2*x^2)^(1/2)+-43//576*d*f*b^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+-2//343*d*b^2*c^-4*g^3*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+-1//32*d*x*b^2*f^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1//35*d*c^-2*g^3*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//4*d*x*f^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//7*d*g^3*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+3//8*d*f*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+16//25*d*g*b^2*c^-2*f^2*(d+-1*d*c^2*x^2)^(1/2)+38//6125*d*b^2*c^-4*g^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+152//11025*d*b^2*c^-4*g^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+(1/2)*d*f*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-7//384*d*f*x*b^2*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)+-3//5*d*g*c^-2*f^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-3//16*d*f*x*c^-2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//8*b*d*c^-1*f^3*(1+-1*c^2*x^2)^3//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//8*d*b^-1*c^-1*f^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//36*d*f*b^2*c^2*g^2*x^5*(d+-1*d*c^2*x^2)^(1/2)+6//125*d*g*b^2*c^-2*f^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+8//75*d*g*b^2*c^-2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+9//64*d*b^2*c^-1*f^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-16//175*b*c*d*g^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))+-3//8*b*c*d*f^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))+1//16*d*f*b^-1*c^-3*g^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+2//49*b*d*c^3*g^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*g^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))+4//35*a*b*d*x*c^-3*g^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*g^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+7//384*d*f*b^2*c^-3*g^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-7//16*b*c*d*f*g^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))+-4//5*b*c*d*g*f^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//6*b*d*f*c^3*g^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))+3//16*b*d*f*c^-1*g^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))+6//5*b*d*g*x*c^-1*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+6//25*b*d*g*c^3*f^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)^3//2*(f+g*x)^2, x) == :(-43//1728*d*b^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+-15//64*d*x*b^2*f^2*(d+-1*d*c^2*x^2)^(1/2)+1//8*d*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+3//8*d*x*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-7//1152*d*x*b^2*c^-2*g^2*(d+-1*d*c^2*x^2)^(1/2)+-1//16*d*x*c^-2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//32*d*x*b^2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//4*d*x*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//6*d*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//108*d*b^2*c^2*g^2*x^5*(d+-1*d*c^2*x^2)^(1/2)+32//75*d*f*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-2//5*d*f*g*c^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//8*b*d*c^-1*f^2*(1+-1*c^2*x^2)^3//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//8*d*b^-1*c^-1*f^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//48*d*b^-1*c^-3*g^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//125*d*f*g*b^2*c^-2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+7//1152*d*b^2*c^-3*g^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+9//64*d*b^2*c^-1*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+16//225*d*f*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-7//48*b*c*d*g^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))+-3//8*b*c*d*f^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//16*b*d*c^-1*g^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//18*b*d*c^3*g^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))+-8//15*b*c*d*f*g*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//5*b*d*f*g*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))+4//25*b*d*f*g*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((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2*(f+g*x), x) == :(-15//64*d*f*x*b^2*(d+-1*d*c^2*x^2)^(1/2)+3//8*d*f*x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+16//75*d*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)+-1//5*d*g*c^-2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//32*d*f*x*b^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//4*d*f*x*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+2//125*d*g*b^2*c^-2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+8//225*d*g*b^2*c^-2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//8*b*d*f*c^-1*(1+-1*c^2*x^2)^3//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//8*d*f*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)+9//64*d*f*b^2*c^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-4//15*b*c*d*g*x^3*(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*d*f*x^2*(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*g*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*g*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((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^3//2*(f+g*x)^-1, x) == :(-4//9*d*b^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)+-2//27*d*b^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//3*d*g^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1*d*a^2*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+2*d*b^2*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+d*a^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+(1/2)*d*f*x*c^2*g^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1*d*b^2*g^-3*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)^2*(g+c*f)*(-1g+c*f)+-1//4*d*f*x*b^2*c^2*g^-2*(d+-1*d*c^2*x^2)^(1/2)+-2*im*d*b^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*a*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*a*b*d*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)*arcsin(c*x)+-2*d*b^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+2*im*d*b^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*a*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*d*b^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+-2//3*b*c*d*x*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+1//4*c*d*f*b^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+1//6*c*d*f*b^-1*g^-2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+2//9*b*d*c^3*g^-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))+im*d*b^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arcsin(c*x)^2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*d*b^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arcsin(c*x)^2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//2*b*d*f*c^3*g^-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*d*b^-1*c^-1*g^-4*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(-1*g^2+c^2*f^2)^2+-2*im*a*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*a*b*d*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^3//2*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*a*b*c*d*x*g^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+2*c*d*x*b^2*g^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)*arcsin(c*x)+-1//3*c*d*x*b^-1*g^-3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)*(g+c*f)*(-1g+c*f)+-1//3*d*b^-1*c^-1*g^-2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(g+c*f)*(-1g+c*f))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^5//2*(f+g*x)^3, x) == :(-245//1152*x*b^2*d^2*f^3*(d+-1*d*c^2*x^2)^(1/2)+-2//63*c^-4*d^2*g^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//21*d^2*g^3*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//16*x*d^2*f^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+160//3969*b^2*c^-4*d^2*g^3*(d+-1*d*c^2*x^2)^(1/2)+-1079//18432*f*b^2*d^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+-65//1728*x*b^2*d^2*f^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-2//729*b^2*c^-4*d^2*g^3*(1+-1*c^2*x^2)^4*(d+-1*d*c^2*x^2)^(1/2)+-1//63*c^-2*d^2*g^3*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//108*x*b^2*d^2*f^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+1//6*x*d^2*f^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//9*d^2*g^3*x^4*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+4//1323*b^2*c^-4*d^2*g^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+5//24*x*d^2*f^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+5//63*d^2*g^3*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+15//64*f*d^2*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+50//27783*b^2*c^-4*d^2*g^3*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+80//11907*b^2*c^-4*d^2*g^3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+96//245*g*b^2*c^-2*d^2*f^2*(d+-1*d*c^2*x^2)^(1/2)+-359//12288*f*x*b^2*c^-2*d^2*g^2*(d+-1*d*c^2*x^2)^(1/2)+-15//128*f*x*c^-2*d^2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-3//7*g*c^-2*d^2*f^2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-3//256*f*b^2*c^4*d^2*g^2*x^7*(d+-1*d*c^2*x^2)^(1/2)+1//18*b*c^-1*d^2*f^3*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//8*f*d^2*g^2*x^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//16*f*d^2*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+5//48*b*c^-1*d^2*f^3*(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*f^3*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+6//343*g*b^2*c^-2*d^2*f^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+16//245*g*b^2*c^-2*d^2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+36//1225*g*b^2*c^-2*d^2*f^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+115//1152*b^2*c^-1*d^2*f^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+209//4608*f*b^2*c^2*d^2*g^2*x^5*(d+-1*d*c^2*x^2)^(1/2)+-5//16*b*c*d^2*f^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))+-2//21*b*c*d^2*g^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))+-2//81*b*c^5*d^2*g^3*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*g^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))+4//63*a*b*x*c^-3*d^2*g^3*(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*g^3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+5//128*f*b^-1*c^-3*d^2*g^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+38//441*b*c^3*d^2*g^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))+359//12288*f*b^2*c^-3*d^2*g^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+-59//128*b*c*f*d^2*g^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))+-6//7*b*c*g*d^2*f^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))+-6//49*b*g*c^5*d^2*f^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))+-3//32*b*f*c^5*d^2*g^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))+6//7*b*g*x*c^-1*d^2*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+15//128*b*f*c^-1*d^2*g^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//48*b*f*c^3*d^2*g^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))+18//35*b*g*c^3*d^2*f^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*(f+g*x)^2, x) == :(-1079//55296*b^2*d^2*g^2*x^3*(d+-1*d*c^2*x^2)^(1/2)+-245//1152*x*b^2*d^2*f^2*(d+-1*d*c^2*x^2)^(1/2)+5//16*x*d^2*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//64*d^2*g^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*g^2*(d+-1*d*c^2*x^2)^(1/2)+-65//1728*x*b^2*d^2*f^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-5//128*x*c^-2*d^2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//108*x*b^2*d^2*f^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+-1//256*b^2*c^4*d^2*g^2*x^7*(d+-1*d*c^2*x^2)^(1/2)+1//6*x*d^2*f^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//8*d^2*g^2*x^3*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+5//24*x*d^2*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+5//48*d^2*g^2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+64//245*f*g*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)+209//13824*b^2*c^2*d^2*g^2*x^5*(d+-1*d*c^2*x^2)^(1/2)+-2//7*f*g*c^-2*d^2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//18*b*c^-1*d^2*f^2*(1+-1*c^2*x^2)^5//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//343*f*g*b^2*c^-2*d^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+5//48*b*c^-1*d^2*f^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*f^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+5//384*b^-1*c^-3*d^2*g^2*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)+24//1225*f*g*b^2*c^-2*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+32//735*f*g*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+115//1152*b^2*c^-1*d^2*f^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+359//36864*b^2*c^-3*d^2*g^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*g^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))+-5//16*b*c*d^2*f^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//32*b*c^5*d^2*g^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*g^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*g^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))+-4//7*b*c*f*g*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//49*b*f*g*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))+4//7*b*f*g*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))+12//35*b*f*g*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*(f+g*x), x) == :(-245//1152*f*x*b^2*d^2*(d+-1*d*c^2*x^2)^(1/2)+5//16*f*x*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+32//245*g*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)+-65//1728*f*x*b^2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+-1//7*g*c^-2*d^2*(1+-1*c^2*x^2)^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//108*f*x*b^2*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+1//6*f*x*d^2*(1+-1*c^2*x^2)^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+2//343*g*b^2*c^-2*d^2*(1+-1*c^2*x^2)^3*(d+-1*d*c^2*x^2)^(1/2)+5//24*f*x*d^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+12//1225*g*b^2*c^-2*d^2*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+16//735*g*b^2*c^-2*d^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+1//18*b*f*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*f*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*f*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*f*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*f*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))+-2//7*b*c*g*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*g*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*g*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*g*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*(f+g*x)^-1, x) == :(-2//15*d^2*g^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+52//225*b^2*d^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)+a^2*d^2*g^-5*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2+-2*b^2*d^2*g^-5*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2+-2//125*b^2*d^2*g^-1*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^(1/2)+4//9*b^2*d^2*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+26//675*b^2*d^2*g^-1*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)+b^2*d^2*g^-5*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2*arcsin(c*x)^2+-1//3*d^2*g^-3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(-2*g^2+c^2*f^2)+-1//15*c^2*d^2*g^-1*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//5*c^4*d^2*g^-1*x^4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+2//27*b^2*d^2*g^-3*(d+-1*d*c^2*x^2)^(1/2)*(1+-1*c^2*x^2)*(-2*g^2+c^2*f^2)+-1*a^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(g+f*x*c^2))+2*a*b*d^2*g^-5*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2*arcsin(c*x)+-1//4*f*c^4*d^2*g^-2*x^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+-1//64*f*x*b^2*c^2*d^2*g^-2*(d+-1*d*c^2*x^2)^(1/2)+1//8*f*x*c^2*d^2*g^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)+1//32*f*b^2*c^4*d^2*g^-2*x^3*(d+-1*d*c^2*x^2)^(1/2)+-2*im*b^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*a*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+2*im*b^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*a*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*b^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+-2//25*b*c^5*d^2*g^-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))+-1//2*f*x*c^2*d^2*g^-4*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+-1//24*c*f*b^-1*d^2*g^-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//4*f*x*b^2*c^2*d^2*g^-4*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+1//64*c*f*b^2*d^2*g^-2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+2//45*b*c^3*d^2*g^-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*c*x*d^2*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)+4//15*c*x*b^2*d^2*g^-1*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*arcsin(c*x)+im*b^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arcsin(c*x)^2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*b^2*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arcsin(c*x)^2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*a*b*c*x*d^2*g^-5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2+-2*c*x*b^2*d^2*g^-5*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^2*arcsin(c*x)+-2//9*b*c^3*d^2*g^-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))*(-2*g^2+c^2*f^2)+-1//4*c*f*b^2*d^2*g^-4*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)*arcsin(c*x)+-1//6*c*f*b^-1*d^2*g^-4*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)*(-2*g^2+c^2*f^2)+-1//8*b*f*c^3*d^2*g^-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*c*x*b^-1*d^2*g^-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*g^2+c^2*f^2)^2+1//3*b^-1*c^-1*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(-1*g^2+c^2*f^2)^3+1//3*b^-1*c^-1*d^2*g^-4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^(1/2)*(f+g*x)^-1*(-1*g^2+c^2*f^2)^2+1//8*b*f*c^5*d^2*g^-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))+2//3*b*c*x*d^2*g^-3*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(-2*g^2+c^2*f^2)+(1/2)*b*f*c^3*d^2*g^-4*x^2*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(-2*g^2+c^2*f^2)+-2*im*a*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*a*b*d^2*g^-6*(1+-1*c^2*x^2)^-1//2*(d+-1*d*c^2*x^2)^(1/2)*(-1*g^2+c^2*f^2)^5//2*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(f+g*x)^3, x) == :(-2//3*c^-4*g^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-2//27*b^2*c^-4*g^3*(1+-1*c^2*x^2)^2*(d+-1*d*c^2*x^2)^-1//2+14//9*b^2*c^-4*g^3*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-3*g*c^-2*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+6*g*b^2*c^-2*f^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-1//3*c^-2*g^3*x^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+1//3*b^-1*c^-1*f^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+(1/2)*f*b^-1*c^-3*g^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+-3//2*f*x*c^-2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-3//4*f*b^2*c^-3*g^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^-1*g^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))+3//4*f*x*b^2*c^-2*g^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+4//3*b*x*c^-3*g^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+6*b*g*x*c^-1*f^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(a+b*arcsin(c*x))+3//2*b*f*c^-1*g^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((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(f+g*x)^2, x) == :(-2*f*g*c^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+4*f*g*b^2*c^-2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-1//2*x*c^-2*g^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-1//4*b^2*c^-3*g^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^-1*f^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//4*x*b^2*c^-2*g^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+1//6*b^-1*c^-3*g^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+(1/2)*b*c^-1*g^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*b*f*g*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*(f+g*x)^-1, x) == :(im*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*im*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*b*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(f+g*x)^-2, x) == :(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*g^2+c^2*f^2)^-1+g*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(f+g*x)^-1*(-1*g^2+c^2*f^2)^-1*(1+-1*c^2*x^2)+-2*b*c*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1*(a+b*arcsin(c*x))*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b*c*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1*(a+b*arcsin(c*x))*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*c*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*c*b^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-1*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*f*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*(-1*g^2+c^2*f^2)^-3//2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*f*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*(-1*g^2+c^2*f^2)^-3//2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*im*f*b^2*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b*f*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*f*b^2*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*b*f*c^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2*(f+g*x)^3, x) == :(f*x*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(f^2+3*c^-2*g^2)+g*c^-4*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(g^2+3*c^2*f^2)+c^-4*d^-1*g^3*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-2*b^2*c^-4*d^-1*g^3*(d+-1*d*c^2*x^2)^-1//2*(1+-1*c^2*x^2)+-1*im*f*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*(3*g^2+c^2*f^2)+-1*f*b^-1*c^-3*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))^3*(d+-1*d*c^2*x^2)^-1//2+-2*a*b*x*c^-3*d^-1*g^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2+-2*x*b^2*c^-3*d^-1*g^3*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*arcsin(c*x)+-1*im*f*b^2*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(3*g^2+c^2*f^2)*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(c*x)))+-2*im*g*b^2*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g^2+3*c^2*f^2)*Polylogarithms.polylog(2,-1*im*exp(im*arcsin(c*x)))+2*im*g*b^2*c^-4*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g^2+3*c^2*f^2)*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+2*b*f*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))*(3*g^2+c^2*f^2)*log(1+exp(2*im*arcsin(c*x)))+4*im*b*g*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))*(g^2+3*c^2*f^2)*arctan(exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-3//2*(f+g*x)^2, x) == :(x*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2*(g^2+c^2*f^2)+2*f*g*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*(g^2+c^2*f^2)+-1//3*b^-1*c^-3*d^-1*g^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*im*b^2*c^-3*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g^2+c^2*f^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))*(g^2+c^2*f^2)*log(1+exp(2*im*arcsin(c*x)))+-4*im*f*g*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)))+4*im*f*g*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)))+8*im*b*f*g*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*(f+g*x), x) == :(f*x*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+g*c^-2*d^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-1*im*f*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*f*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*im*g*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*g*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)))+2*b*f*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)))+4*im*b*g*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*(f+g*x)^-1, x) == :((1/2)*im*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*(g+c*f)^-1+(1/2)*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*(g+c*f)^-1*tan((1/2)*arcsin(c*x)+1//4*pi)+-1//2*im*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*(-1g+c*f)^-1+-1//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*(-1g+c*f)^-1*cot((1/2)*arcsin(c*x)+1//4*pi)+-2*im*b^2*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^-1*Polylogarithms.polylog(2,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*(g+c*f)^-1*Polylogarithms.polylog(2,im*exp(-1*im*arcsin(c*x)))+2*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^-1*(a+b*arcsin(c*x))*log(1+-1*im*exp(-1*im*arcsin(c*x)))+2*b*d^-1*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^-1*(a+b*arcsin(c*x))*log(1+-1*im*exp(im*arcsin(c*x)))+im*d^-1*g^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*g^2+c^2*f^2)^-3//2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*im*d^-1*g^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*g^2+c^2*f^2)^-3//2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*im*b^2*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*im*b^2*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+2*b*d^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1*g^2+c^2*f^2)^-3//2*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2*(f+g*x)^3, x) == :(-1//6*b^2*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^3*cot((1/2)*arcsin(c*x)+1//4*pi)+-1//12*im*c^-4*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*(-1g+c*f)^3+-1//12*c^-4*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*(-1g+c*f)^3*cot((1/2)*arcsin(c*x)+1//4*pi)+1//6*b^2*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^3*tan((1/2)*arcsin(c*x)+1//4*pi)+1//12*im*c^-4*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*(g+c*f)^3+1//12*c^-4*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*(g+c*f)^3*tan((1/2)*arcsin(c*x)+1//4*pi)+-1//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*(-1g+c*f)^3*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x)))+-1//4*im*c^-4*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*(-1g+c*f)^2*(2g+c*f)+-1//4*c^-4*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*(-1g+c*f)^2*(2g+c*f)*cot((1/2)*arcsin(c*x)+1//4*pi)+-1//12*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^3*sec((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+-1//12*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^3*csc((1/2)*arcsin(c*x)+1//4*pi)^2*(a+b*arcsin(c*x))+-1//24*c^-4*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*(-1g+c*f)^3*csc((1/2)*arcsin(c*x)+1//4*pi)^2*cot((1/2)*arcsin(c*x)+1//4*pi)+1//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*(g+c*f)^3*Polylogarithms.polylog(2,im*exp(-1*im*arcsin(c*x)))+1//3*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^3*(a+b*arcsin(c*x))*log(1+-1*im*exp(-1*im*arcsin(c*x)))+1//3*b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^3*(a+b*arcsin(c*x))*log(1+-1*im*exp(im*arcsin(c*x)))+1//4*im*c^-4*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*(g+c*f)^2*(-2g+c*f)+1//4*c^-4*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*(g+c*f)^2*(-2g+c*f)*tan((1/2)*arcsin(c*x)+1//4*pi)+1//24*c^-4*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*(g+c*f)^3*sec((1/2)*arcsin(c*x)+1//4*pi)^2*tan((1/2)*arcsin(c*x)+1//4*pi)+im*b^2*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^2*(-2g+c*f)*Polylogarithms.polylog(2,im*exp(-1*im*arcsin(c*x)))+b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(g+c*f)^2*(a+b*arcsin(c*x))*(-2g+c*f)*log(1+-1*im*exp(-1*im*arcsin(c*x)))+b*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^2*(a+b*arcsin(c*x))*(2g+c*f)*log(1+-1*im*exp(im*arcsin(c*x)))+-1*im*b^2*c^-4*d^-2*(1+-1*c^2*x^2)^(1/2)*(d+-1*d*c^2*x^2)^-1//2*(-1g+c*f)^2*(2g+c*f)*Polylogarithms.polylog(2,im*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-5//2*(f+g*x)^2, x) == :(1//3*x*b^2*d^-2*f^2*(d+-1*d*c^2*x^2)^-1//2+2//3*x*d^-2*f^2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*x*b^2*c^-2*d^-2*g^2*(d+-1*d*c^2*x^2)^-1//2+1//3*x*d^-2*f^2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*d^-2*g^2*x^3*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+2//3*f*g*b^2*c^-2*d^-2*(d+-1*d*c^2*x^2)^-1//2+-2//3*im*c^-1*d^-2*f^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*f^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^-3*d^-2*g^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*g^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*f*g*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2//3*im*b^2*c^-1*d^-2*f^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)))+-2//3*b*c^-3*d^-2*g^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*g^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*g^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*f^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)))+-2//3*im*f*g*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*f*g*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))+2//3*im*f*g*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)))+4//3*im*b*f*g*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*(f+g*x), x) == :(1//3*f*x*b^2*d^-2*(d+-1*d*c^2*x^2)^-1//2+1//3*g*b^2*c^-2*d^-2*(d+-1*d*c^2*x^2)^-1//2+2//3*f*x*d^-2*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*f*x*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+1//3*g*c^-2*d^-2*(1+-1*c^2*x^2)^-1*(a+b*arcsin(c*x))^2*(d+-1*d*c^2*x^2)^-1//2+-2//3*im*f*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*f*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*f*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)))+-1//3*im*g*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*g*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*g*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)))+4//3*b*f*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)))+2//3*im*b*g*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((1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^3*log(h*(f+g*x)^m), x) == :(6*m*b^3*c^-1*Polylogarithms.polylog(5,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+6*m*b^3*c^-1*Polylogarithms.polylog(5,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+1//4*b^-1*c^-1*(a+b*arcsin(c*x))^4*log(h*(f+g*x)^m)+im*m*c^-1*(a+b*arcsin(c*x))^3*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*m*c^-1*(a+b*arcsin(c*x))^3*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-3*b*m*c^-1*(a+b*arcsin(c*x))^2*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-3*b*m*c^-1*(a+b*arcsin(c*x))^2*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//4*m*b^-1*c^-1*(a+b*arcsin(c*x))^4*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//4*m*b^-1*c^-1*(a+b*arcsin(c*x))^4*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+1//20*im*m*b^-2*c^-1*(a+b*arcsin(c*x))^5+-6*im*m*b^2*c^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(4,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-6*im*m*b^2*c^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(4,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))^2*log(h*(f+g*x)^m), x) == :(1//3*b^-1*c^-1*(a+b*arcsin(c*x))^3*log(h*(f+g*x)^m)+im*m*c^-1*(a+b*arcsin(c*x))^2*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*m*c^-1*(a+b*arcsin(c*x))^2*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*im*m*b^2*c^-1*Polylogarithms.polylog(4,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*im*m*b^2*c^-1*Polylogarithms.polylog(4,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b*m*c^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-2*b*m*c^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//3*m*b^-1*c^-1*(a+b*arcsin(c*x))^3*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//3*m*b^-1*c^-1*(a+b*arcsin(c*x))^3*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+1//12*im*m*b^-2*c^-1*(a+b*arcsin(c*x))^4)
@test integrate((1+-1*c^2*x^2)^-1//2*(a+b*arcsin(c*x))*log(h*(f+g*x)^m), x) == :((1/2)*b^-1*c^-1*(a+b*arcsin(c*x))^2*log(h*(f+g*x)^m)+-1*b*m*c^-1*Polylogarithms.polylog(3,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*b*m*c^-1*Polylogarithms.polylog(3,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*m*c^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*m*c^-1*(a+b*arcsin(c*x))*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//2*m*b^-1*c^-1*(a+b*arcsin(c*x))^2*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1//2*m*b^-1*c^-1*(a+b*arcsin(c*x))^2*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+1//6*im*m*b^-2*c^-1*(a+b*arcsin(c*x))^3)
@test integrate((1+-1*c^2*x^2)^-1//2*log(h*(f+g*x)^m), x) == :(c^-1*arcsin(c*x)*log(h*(f+g*x)^m)+im*m*c^-1*Polylogarithms.polylog(2,im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+im*m*c^-1*Polylogarithms.polylog(2,im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+(1/2)*im*m*c^-1*arcsin(c*x)^2+-1*m*c^-1*arcsin(c*x)*log(1+-1*im*g*((-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x)))+-1*m*c^-1*arcsin(c*x)*log(1+-1*im*g*(-1*(-1*g^2+c^2*f^2)^(1/2)+c*f)^-1*exp(im*arcsin(c*x))))
@test integrate((d+e*x)^3*(a+b*arcsin(c*x))*(f+g*x), x) == :(f*x*d^3*(a+b*arcsin(c*x))+(1/2)*d^2*x^2*(a+b*arcsin(c*x))*(d*g+3*e*f)+-1//32*b*c^-4*(3*e^2*(e*f+3*d*g)+8*c^2*d^2*(d*g+3*e*f))*arcsin(c*x)+1//4*e^2*x^4*(a+b*arcsin(c*x))*(e*f+3*d*g)+1//5*g*e^3*x^5*(a+b*arcsin(c*x))+1//2400*b*c^-5*(1+-1*c^2*x^2)^(1/2)*(256*g*e^3+75*x*c^2*(3*e^2*(e*f+3*d*g)+8*c^2*d^2*(d*g+3*e*f))+2400*f*c^4*d^3+1600*d*e*c^2*(d*g+e*f))+d*e*x^3*(a+b*arcsin(c*x))*(d*g+e*f)+1//16*b*c^-1*e^2*x^3*(1+-1*c^2*x^2)^(1/2)*(e*f+3*d*g)+1//25*b*g*c^-1*e^3*x^4*(1+-1*c^2*x^2)^(1/2)+1//75*b*e*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(4*g*e^2+25*d*c^2*(d*g+e*f)))
@test integrate((d+e*x)^2*(a+b*arcsin(c*x))*(f+g*x), x) == :(f*x*d^2*(a+b*arcsin(c*x))+(1/2)*d*x^2*(a+b*arcsin(c*x))*(d*g+2*e*f)+-1//32*b*c^-4*(3*g*e^2+8*d*c^2*(d*g+2*e*f))*arcsin(c*x)+1//3*e*x^3*(a+b*arcsin(c*x))*(e*f+2*d*g)+1//4*g*e^2*x^4*(a+b*arcsin(c*x))+1//288*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(x*(27*g*e^2+72*d*c^2*(d*g+2*e*f))+64*e*(e*f+2*d*g)+288*f*c^2*d^2)+1//9*b*e*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(e*f+2*d*g)+1//16*b*g*c^-1*e^2*x^3*(1+-1*c^2*x^2)^(1/2))
@test integrate((a+b*arcsin(c*x))*(d+e*x)*(f+g*x), x) == :(x^2*(a+b*arcsin(c*x))*((1/2)*d*g+(1/2)*e*f)+d*f*x*(a+b*arcsin(c*x))+-1//4*b*c^-2*(d*g+e*f)*arcsin(c*x)+1//3*e*g*x^3*(a+b*arcsin(c*x))+1//36*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(8*e*g+9*x*c^2*(d*g+e*f)+36*d*f*c^2)+1//9*b*e*g*c^-1*x^2*(1+-1*c^2*x^2)^(1/2))
@test integrate((d+e*x)^-1*(a+b*arcsin(c*x))*(f+g*x), x) == :(g*x*e^-1*(a+b*arcsin(c*x))+e^-2*(a+b*arcsin(c*x))*(e*f+-1*d*g)*log(d+e*x)+b*g*c^-1*e^-1*(1+-1*c^2*x^2)^(1/2)+b*e^-2*(e*f+-1*d*g)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*e^-2*(e*f+-1*d*g)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-2*(e*f+-1*d*g)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-2*(e*f+-1*d*g)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*e^-2*(e*f+-1*d*g)*arcsin(c*x)*log(d+e*x)+-1//2*im*b*e^-2*arcsin(c*x)^2*(e*f+-1*d*g))
@test integrate((d+e*x)^-2*(a+b*arcsin(c*x))*(f+g*x), x) == :(g*e^-2*(a+b*arcsin(c*x))*log(d+e*x)+-1*e^-2*(d+e*x)^-1*(a+b*arcsin(c*x))*(e*f+-1*d*g)+b*g*e^-2*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*g*e^-2*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*g*e^-2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*g*e^-2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*g*e^-2*arcsin(c*x)*log(d+e*x)+-1//2*im*b*g*e^-2*arcsin(c*x)^2+b*c*e^-2*(-1*e^2+c^2*d^2)^-1//2*(e*f+-1*d*g)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2)))
@test integrate((d+e*x)^-3*(a+b*arcsin(c*x))*(f+g*x), x) == :(-1*(d+e*x)^-2*(f+g*x)^2*(-2*d*g+2*e*f)^-1*(a+b*arcsin(c*x))+(1/2)*b*e^-2*g^2*(e*f+-1*d*g)^-1*arcsin(c*x)+-1//2*b*c*e^-2*(-1*e^2+c^2*d^2)^-3//2*(2*g*e^2+-1*d*c^2*(d*g+e*f))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+(1/2)*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g))
@test integrate((d+e*x)^-4*(a+b*arcsin(c*x))*(f+g*x), x) == :(-1//2*g*e^-2*(d+e*x)^-2*(a+b*arcsin(c*x))+-1//3*e^-2*(d+e*x)^-3*(a+b*arcsin(c*x))*(e*f+-1*d*g)+(1/2)*b*c*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2*(-1*e*g+d*f*c^2)+1//6*b*c^3*e^-2*(-1*e^2+c^2*d^2)^-5//2*(e^2*(e*f+-4*d*g)+c^2*d^2*(d*g+2*e*f))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+1//6*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g))
@test integrate((d+e*x)^-5*(a+b*arcsin(c*x))*(f+g*x), x) == :(-1//3*g*e^-2*(d+e*x)^-3*(a+b*arcsin(c*x))+-1//4*e^-2*(d+e*x)^-4*(a+b*arcsin(c*x))*(e*f+-1*d*g)+-1//24*b*c^3*e^-2*(-1*e^2+c^2*d^2)^-7//2*(4*g*e^4+-2*c^4*d^3*(d*g+3*e*f)+-1*d*c^2*e^2*(-13*d*g+9*e*f))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//24*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-2*(4*g*e^2+-1*d*c^2*(-1*d*g+5*e*f))+1//12*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-3*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)+1//24*b*c^3*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-3*(4*e^2*(e*f+-4*d*g)+c^2*d^2*(d*g+11*e*f)))
@test integrate((d+e*x)^-6*(a+b*arcsin(c*x))*(f+g*x), x) == :(-1//4*g*e^-2*(d+e*x)^-4*(a+b*arcsin(c*x))+-1//5*e^-2*(d+e*x)^-5*(a+b*arcsin(c*x))*(e*f+-1*d*g)+1//40*b*c^5*e^-2*(-1*e^2+c^2*d^2)^-9//2*(3*e^4*(e*f+-6*d*g)+2*c^4*d^4*(d*g+4*e*f)+c^2*d^2*e^2*(-19*d*g+24*e*f))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//24*b*c^3*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-4*(4*g*e^4+-1*c^4*d^3*(d*g+10*e*f)+-1*d*c^2*e^2*(-18*d*g+11*e*f))+-1//60*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-3*(-1*e^2+c^2*d^2)^-2*(5*g*e^2+-1*d*c^2*(-2*d*g+7*e*f))+1//20*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-4*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)+1//120*b*c^3*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-3*(e^2*(-34*d*g+9*e*f)+c^2*d^2*(-1*d*g+26*e*f)))
@test integrate((d+e*x)^3*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(f*x*d^3*(a+b*arcsin(c*x))+(1/2)*d^2*x^2*(a+b*arcsin(c*x))*(d*g+3*e*f)+-1//96*b*c^-6*(5*h*e^3+9*e*c^2*(f*e^2+3*h*d^2+3*d*e*g)+24*c^4*d^2*(d*g+3*e*f))*arcsin(c*x)+1//3*d*x^3*(a+b*arcsin(c*x))*(h*d^2+3*f*e^2+3*d*e*g)+1//4*e*x^4*(a+b*arcsin(c*x))*(f*e^2+3*h*d^2+3*d*e*g)+1//5*e^2*x^5*(a+b*arcsin(c*x))*(e*g+3*d*h)+1//6*h*e^3*x^6*(a+b*arcsin(c*x))+1//7200*b*c^-5*(1+-1*c^2*x^2)^(1/2)*(x*(375*h*e^3+675*e*c^2*(f*e^2+3*h*d^2+3*d*e*g)+1800*c^4*d^2*(d*g+3*e*f))+768*e^2*(e*g+3*d*h)+1600*d*c^2*(h*d^2+3*f*e^2+3*d*e*g)+7200*f*c^4*d^3)+1//225*b*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(12*e^2*(e*g+3*d*h)+25*d*c^2*(h*d^2+3*f*e^2+3*d*e*g))+1//25*b*c^-1*e^2*x^4*(1+-1*c^2*x^2)^(1/2)*(e*g+3*d*h)+1//36*b*h*c^-1*e^3*x^5*(1+-1*c^2*x^2)^(1/2)+1//144*b*e*c^-3*x^3*(1+-1*c^2*x^2)^(1/2)*(5*h*e^2+9*c^2*(f*e^2+3*h*d^2+3*d*e*g)))
@test integrate((d+e*x)^2*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(x^3*(a+b*arcsin(c*x))*(1//3*f*e^2+1//3*h*d^2+2//3*d*e*g)+f*x*d^2*(a+b*arcsin(c*x))+(1/2)*d*x^2*(a+b*arcsin(c*x))*(d*g+2*e*f)+-1//32*b*c^-4*(3*e*(e*g+2*d*h)+8*d*c^2*(d*g+2*e*f))*arcsin(c*x)+1//4*e*x^4*(a+b*arcsin(c*x))*(e*g+2*d*h)+1//5*h*e^2*x^5*(a+b*arcsin(c*x))+1//7200*b*c^-5*(1+-1*c^2*x^2)^(1/2)*(768*h*e^2+1600*c^2*(f*e^2+h*d^2+2*d*e*g)+225*x*c^2*(3*e*(e*g+2*d*h)+8*d*c^2*(d*g+2*e*f))+7200*f*c^4*d^2)+1//225*b*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(12*h*e^2+25*c^2*(f*e^2+h*d^2+2*d*e*g))+1//16*b*e*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(e*g+2*d*h)+1//25*b*h*c^-1*e^2*x^4*(1+-1*c^2*x^2)^(1/2))
@test integrate((a+b*arcsin(c*x))*(d+e*x)*(f+g*x+h*x^2), x) == :(x^2*(a+b*arcsin(c*x))*((1/2)*d*g+(1/2)*e*f)+x^3*(a+b*arcsin(c*x))*(1//3*d*h+1//3*e*g)+d*f*x*(a+b*arcsin(c*x))+-1//32*b*c^-4*(3*e*h+8*c^2*(d*g+e*f))*arcsin(c*x)+1//4*e*h*x^4*(a+b*arcsin(c*x))+1//288*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(x*(27*e*h+72*c^2*(d*g+e*f))+64*d*h+64*e*g+288*d*f*c^2)+1//9*b*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(d*h+e*g)+1//16*b*e*h*c^-1*x^3*(1+-1*c^2*x^2)^(1/2))
@test integrate((d+e*x)^-1*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(x*e^-2*(a+b*arcsin(c*x))*(e*g+-1*d*h)+e^-3*(a+b*arcsin(c*x))*(f*e^2+h*d^2+-1*d*e*g)*log(d+e*x)+(1/2)*h*e^-1*x^2*(a+b*arcsin(c*x))+b*e^-3*(f*e^2+h*d^2+-1*d*e*g)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*e^-3*(f*e^2+h*d^2+-1*d*e*g)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-3*(f*e^2+h*d^2+-1*d*e*g)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-3*(f*e^2+h*d^2+-1*d*e*g)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*e^-3*(f*e^2+h*d^2+-1*d*e*g)*arcsin(c*x)*log(d+e*x)+-1//2*im*b*e^-3*arcsin(c*x)^2*(f*e^2+h*d^2+-1*d*e*g)+-1//4*b*h*c^-2*e^-1*arcsin(c*x)+1//4*b*c^-1*e^-2*(1+-1*c^2*x^2)^(1/2)*(-4*d*h+4*e*g+e*h*x))
@test integrate((d+e*x)^-2*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(h*x*e^-2*(a+b*arcsin(c*x))+e^-3*(a+b*arcsin(c*x))*(e*g+-2*d*h)*log(d+e*x)+-1*e^-3*(d+e*x)^-1*(a+b*arcsin(c*x))*(f*e^2+h*d^2+-1*d*e*g)+b*h*c^-1*e^-2*(1+-1*c^2*x^2)^(1/2)+b*e^-3*(e*g+-2*d*h)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*e^-3*(e*g+-2*d*h)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-3*(e*g+-2*d*h)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-3*(e*g+-2*d*h)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*e^-3*(e*g+-2*d*h)*arcsin(c*x)*log(d+e*x)+-1//2*im*b*e^-3*arcsin(c*x)^2*(e*g+-2*d*h)+b*c*e^-3*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+h*d^2+-1*d*e*g)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2)))
@test integrate((d+e*x)^-3*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(h*e^-3*(a+b*arcsin(c*x))*log(d+e*x)+-1*e^-3*(d+e*x)^-1*(a+b*arcsin(c*x))*(e*g+-2*d*h)+-1//2*e^-3*(d+e*x)^-2*(a+b*arcsin(c*x))*(f*e^2+h*d^2+-1*d*e*g)+b*h*e^-3*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*h*e^-3*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*h*e^-3*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*h*e^-3*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*h*e^-3*arcsin(c*x)*log(d+e*x)+-1//2*im*b*h*e^-3*arcsin(c*x)^2+-1//2*b*c*e^-3*(-1*e^2+c^2*d^2)^-3//2*(2*e^2*(e*g+-2*d*h)+-1*d*c^2*(f*e^2+-3*h*d^2+d*e*g))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+(1/2)*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(f*e^2+h*d^2+-1*d*e*g))
@test integrate((d+e*x)^-4*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(-1*h*e^-3*(d+e*x)^-1*(a+b*arcsin(c*x))+-1//2*e^-3*(d+e*x)^-2*(a+b*arcsin(c*x))*(e*g+-2*d*h)+-1//3*e^-3*(d+e*x)^-3*(a+b*arcsin(c*x))*(f*e^2+h*d^2+-1*d*e*g)+1//6*b*c*e^-3*(-1*e^2+c^2*d^2)^-5//2*(6*h*e^4+c^2*e^2*(f*e^2+-5*h*d^2+-4*d*e*g)+c^4*d^2*(2*f*e^2+2*h*d^2+d*e*g))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//2*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2*(e^2*(e*g+-2*d*h)+-1*c^2*(-1*h*d^3+d*f*e^2))+1//6*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-1*(f*e^2+h*d^2+-1*d*e*g))
@test integrate((d+e*x)^-5*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(-1//2*h*e^-3*(d+e*x)^-2*(a+b*arcsin(c*x))+-1//3*e^-3*(d+e*x)^-3*(a+b*arcsin(c*x))*(e*g+-2*d*h)+-1//4*e^-3*(d+e*x)^-4*(a+b*arcsin(c*x))*(f*e^2+h*d^2+-1*d*e*g)+-1//24*b*c^3*e^-3*(-1*e^2+c^2*d^2)^-7//2*(4*e^4*(e*g+-5*d*h)+-2*c^4*d^3*(h*d^2+3*f*e^2+d*e*g)+-1*d*c^2*e^2*(-7*h*d^2+9*f*e^2+-13*d*e*g))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//24*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-2*(4*e^2*(e*g+-2*d*h)+-1*d*c^2*(-3*h*d^2+5*f*e^2+-1*d*e*g))+1//12*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-3*(-1*e^2+c^2*d^2)^-1*(f*e^2+h*d^2+-1*d*e*g)+1//24*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-3*(12*h*e^4+c^4*d^2*(-1*h*d^2+11*f*e^2+d*e*g)+4*c^2*e^2*(f*e^2+h*d^2+-4*d*e*g)))
@test integrate((d+e*x)^-6*(a+b*arcsin(c*x))*(f+g*x+h*x^2), x) == :(-1//3*h*e^-3*(d+e*x)^-3*(a+b*arcsin(c*x))+-1//4*e^-3*(d+e*x)^-4*(a+b*arcsin(c*x))*(e*g+-2*d*h)+-1//5*e^-3*(d+e*x)^-5*(a+b*arcsin(c*x))*(f*e^2+h*d^2+-1*d*e*g)+1//120*b*c^3*e^-3*(-1*e^2+c^2*d^2)^-9//2*(20*h*e^6+2*c^6*d^4*(2*h*d^2+12*f*e^2+3*d*e*g)+9*c^2*e^4*(f*e^2+11*h*d^2+-6*d*e*g)+3*c^4*d^2*e^2*(-6*h*d^2+24*f*e^2+-19*d*e*g))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//60*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-3*(-1*e^2+c^2*d^2)^-2*(5*e^2*(e*g+-2*d*h)+-1*d*c^2*(-3*h*d^2+7*f*e^2+-2*d*e*g))+1//20*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-4*(-1*e^2+c^2*d^2)^-1*(f*e^2+h*d^2+-1*d*e*g)+1//24*b*c^3*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-4*(-4*e^3*(e*g+-5*d*h)+c^4*d^3*(d*g+10*e*f)+d*e*c^2*(h*d^2+11*f*e^2+-18*d*e*g))+1//120*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-3*(20*h*e^4+c^2*e^2*(9*f*e^2+19*h*d^2+-34*d*e*g)+c^4*d^2*(-4*h*d^2+26*f*e^2+-1*d*e*g)))
@test integrate((d+e*x)^3*(a+b*arcsin(c*x))*(f+g*x+h*x^2+i*x^3), x) == :(x^4*(a+b*arcsin(c*x))*(1//4*f*e^3+1//4*i*d^3+3//4*d*g*e^2+3//4*e*h*d^2)+f*x*d^3*(a+b*arcsin(c*x))+(1/2)*d^2*x^2*(a+b*arcsin(c*x))*(d*g+3*e*f)+-1//96*b*c^-6*(5*e^2*(e*h+3*d*i)+9*c^2*(f*e^3+i*d^3+3*d*g*e^2+3*e*h*d^2)+24*c^4*d^2*(d*g+3*e*f))*arcsin(c*x)+1//3*d*x^3*(a+b*arcsin(c*x))*(h*d^2+3*f*e^2+3*d*e*g)+1//5*e*x^5*(a+b*arcsin(c*x))*(g*e^2+3*i*d^2+3*d*e*h)+1//6*e^2*x^6*(a+b*arcsin(c*x))*(e*h+3*d*i)+1//7*i*e^3*x^7*(a+b*arcsin(c*x))+1//352800*b*c^-7*(1+-1*c^2*x^2)^(1/2)*(23040*i*e^3+3675*x*c^2*(5*e^2*(e*h+3*d*i)+9*c^2*(f*e^3+i*d^3+3*d*g*e^2+3*e*h*d^2)+24*c^4*d^2*(d*g+3*e*f))+37632*e*c^2*(g*e^2+3*i*d^2+3*d*e*h)+78400*d*c^4*(h*d^2+3*f*e^2+3*d*e*g)+352800*f*c^6*d^3)+1//144*b*c^-3*x^3*(1+-1*c^2*x^2)^(1/2)*(5*e^2*(e*h+3*d*i)+9*c^2*(f*e^3+i*d^3+3*d*g*e^2+3*e*h*d^2))+1//11025*b*c^-5*x^2*(1+-1*c^2*x^2)^(1/2)*(360*i*e^3+588*e*c^2*(g*e^2+3*i*d^2+3*d*e*h)+1225*d*c^4*(h*d^2+3*f*e^2+3*d*e*g))+1//36*b*c^-1*e^2*x^5*(1+-1*c^2*x^2)^(1/2)*(e*h+3*d*i)+1//49*b*i*c^-1*e^3*x^6*(1+-1*c^2*x^2)^(1/2)+1//1225*b*e*c^-3*x^4*(1+-1*c^2*x^2)^(1/2)*(30*i*e^2+49*c^2*(g*e^2+3*i*d^2+3*d*e*h)))
@test integrate((d+e*x)^2*(a+b*arcsin(c*x))*(f+g*x+h*x^2+i*x^3), x) == :(x^3*(a+b*arcsin(c*x))*(1//3*f*e^2+1//3*h*d^2+2//3*d*e*g)+x^4*(a+b*arcsin(c*x))*(1//4*g*e^2+1//4*i*d^2+(1/2)*d*e*h)+f*x*d^2*(a+b*arcsin(c*x))+(1/2)*d*x^2*(a+b*arcsin(c*x))*(d*g+2*e*f)+-1//96*b*c^-6*(5*i*e^2+9*c^2*(g*e^2+i*d^2+2*d*e*h)+24*d*c^4*(d*g+2*e*f))*arcsin(c*x)+1//5*e*x^5*(a+b*arcsin(c*x))*(e*h+2*d*i)+1//6*i*e^2*x^6*(a+b*arcsin(c*x))+1//7200*b*c^-5*(1+-1*c^2*x^2)^(1/2)*(x*(375*i*e^2+675*c^2*(g*e^2+i*d^2+2*d*e*h)+1800*d*c^4*(d*g+2*e*f))+768*e*(e*h+2*d*i)+1600*c^2*(f*e^2+h*d^2+2*d*e*g)+7200*f*c^4*d^2)+1//144*b*c^-3*x^3*(1+-1*c^2*x^2)^(1/2)*(5*i*e^2+9*c^2*(g*e^2+i*d^2+2*d*e*h))+1//225*b*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(12*e*(e*h+2*d*i)+25*c^2*(f*e^2+h*d^2+2*d*e*g))+1//25*b*e*c^-1*x^4*(1+-1*c^2*x^2)^(1/2)*(e*h+2*d*i)+1//36*b*i*c^-1*e^2*x^5*(1+-1*c^2*x^2)^(1/2))
@test integrate((a+b*arcsin(c*x))*(d+e*x)*(f+g*x+h*x^2+i*x^3), x) == :(x^2*(a+b*arcsin(c*x))*((1/2)*d*g+(1/2)*e*f)+x^3*(a+b*arcsin(c*x))*(1//3*d*h+1//3*e*g)+x^4*(a+b*arcsin(c*x))*(1//4*d*i+1//4*e*h)+d*f*x*(a+b*arcsin(c*x))+-1//32*b*c^-4*(3*d*i+3*e*h+8*c^2*(d*g+e*f))*arcsin(c*x)+1//5*e*i*x^5*(a+b*arcsin(c*x))+1//7200*b*c^-5*(1+-1*c^2*x^2)^(1/2)*(768*e*i+1600*c^2*(d*h+e*g)+225*x*c^2*(3*d*i+3*e*h+8*c^2*(d*g+e*f))+7200*d*f*c^4)+1//16*b*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(d*i+e*h)+1//225*b*c^-3*x^2*(1+-1*c^2*x^2)^(1/2)*(12*e*i+25*c^2*(d*h+e*g))+1//25*b*e*i*c^-1*x^4*(1+-1*c^2*x^2)^(1/2))
@test integrate((d+e*x)^-1*(a+b*arcsin(c*x))*(f+g*x+h*x^2+i*x^3), x) == :(x*e^-3*(a+b*arcsin(c*x))*(g*e^2+i*d^2+-1*d*e*h)+e^-4*(a+b*arcsin(c*x))*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*log(d+e*x)+(1/2)*e^-2*x^2*(a+b*arcsin(c*x))*(e*h+-1*d*i)+1//3*i*e^-1*x^3*(a+b*arcsin(c*x))+b*e^-4*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*e^-4*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-4*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-4*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*e^-4*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*arcsin(c*x)*log(d+e*x)+-1//2*im*b*e^-4*arcsin(c*x)^2*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)+-1//4*b*c^-2*e^-2*(e*h+-1*d*i)*arcsin(c*x)+1//36*b*c^-3*e^-3*(1+-1*c^2*x^2)^(1/2)*(8*i*e^2+36*c^2*(g*e^2+i*d^2+-1*d*e*h)+9*e*x*c^2*(e*h+-1*d*i))+1//9*b*i*c^-1*e^-1*x^2*(1+-1*c^2*x^2)^(1/2))
@test integrate((d+e*x)^-2*(a+b*arcsin(c*x))*(f+g*x+h*x^2+i*x^3), x) == :(x*e^-3*(a+b*arcsin(c*x))*(e*h+-2*d*i)+e^-4*(a+b*arcsin(c*x))*(g*e^2+3*i*d^2+-2*d*e*h)*log(d+e*x)+(1/2)*i*e^-2*x^2*(a+b*arcsin(c*x))+-1*e^-4*(d+e*x)^-1*(a+b*arcsin(c*x))*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)+b*c^-1*e^-3*(1+-1*c^2*x^2)^(1/2)*(e*h+-2*d*i)+b*e^-4*(g*e^2+3*i*d^2+-2*d*e*h)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*e^-4*(g*e^2+3*i*d^2+-2*d*e*h)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-4*(g*e^2+3*i*d^2+-2*d*e*h)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-4*(g*e^2+3*i*d^2+-2*d*e*h)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*e^-4*(g*e^2+3*i*d^2+-2*d*e*h)*arcsin(c*x)*log(d+e*x)+-1//2*im*b*e^-4*arcsin(c*x)^2*(g*e^2+3*i*d^2+-2*d*e*h)+-1//4*b*i*c^-2*e^-2*arcsin(c*x)+b*c*e^-4*(-1*e^2+c^2*d^2)^-1//2*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+1//4*b*i*x*c^-1*e^-2*(1+-1*c^2*x^2)^(1/2))
@test integrate((d+e*x)^-3*(a+b*arcsin(c*x))*(f+g*x+h*x^2+i*x^3), x) == :(i*x*e^-3*(a+b*arcsin(c*x))+e^-4*(a+b*arcsin(c*x))*(e*h+-3*d*i)*log(d+e*x)+-1*e^-4*(d+e*x)^-1*(a+b*arcsin(c*x))*(g*e^2+3*i*d^2+-2*d*e*h)+-1//2*e^-4*(d+e*x)^-2*(a+b*arcsin(c*x))*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)+b*i*c^-1*e^-3*(1+-1*c^2*x^2)^(1/2)+b*e^-4*(e*h+-3*d*i)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*e^-4*(e*h+-3*d*i)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-4*(e*h+-3*d*i)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*e^-4*(e*h+-3*d*i)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*e^-4*(e*h+-3*d*i)*arcsin(c*x)*log(d+e*x)+-1//2*im*b*e^-4*arcsin(c*x)^2*(e*h+-3*d*i)+-1//2*b*c*e^-4*(-1*e^2+c^2*d^2)^-3//2*(-1*c^2*(-4*i*d^4+d*f*e^3)+2*g*e^4+-6*i*d^2*e^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+(1/2)*b*c*d*e^-4*(-1*e^2+c^2*d^2)^-3//2*(c^2*(4*i*d^3+d*g*e^2)+4*e^2*(e*h+-2*d*i))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+(1/2)*b*c*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(f*e^3+2*i*d^3+-2*d*g*e^2)+-1//2*b*c*d^2*e^-3*(-1*e^2+c^2*d^2)^-3//2*(4*e*i+3*d*h*c^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+5//2*b*i*c^3*d^4*e^-4*(-1*e^2+c^2*d^2)^-3//2*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+(1/2)*b*c*d*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(g*e^2+-4*i*d^2+4*d*e*h)+-1//2*b*c*d^2*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(3*e*h+4*d*i)+5//2*b*c*i*d^3*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1)
@test integrate((d+e*x)^-4*(a+b*arcsin(c*x))*(f+g*x+h*x^2+i*x^3), x) == :(i*e^-4*(a+b*arcsin(c*x))*log(d+e*x)+-1*e^-4*(d+e*x)^-1*(a+b*arcsin(c*x))*(e*h+-3*d*i)+-1//2*e^-4*(d+e*x)^-2*(a+b*arcsin(c*x))*(g*e^2+3*i*d^2+-2*d*e*h)+-1//3*e^-4*(d+e*x)^-3*(a+b*arcsin(c*x))*(f*e^3+-1*i*d^3+e*h*d^2+-1*d*g*e^2)+b*i*e^-4*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b*i*e^-4*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*i*e^-4*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*b*i*e^-4*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*b*i*e^-4*arcsin(c*x)*log(d+e*x)+-1//2*im*b*i*e^-4*arcsin(c*x)^2+1//12*b*c*e^-1*(-1*e^2+c^2*d^2)^-5//2*(c^2*(2*f*e^2+6*h*d^2+-9*d*e*g)+12*h*e^2+4*f*c^4*d^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//4*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2*(2*e^2*(e*g+-4*d*h)+-1*d*c^2*(-2*h*d^2+2*f*e^2+-1*d*e*g))+1//12*b*c*d*e^-2*(-1*e^2+c^2*d^2)^-5//2*(c^2*(g*e^2+-18*i*d^2+-18*d*e*h)+-36*i*e^2+2*g*c^4*d^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+1//12*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-1*(2*f*e^2+6*h*d^2+-3*d*e*g)+1//12*b*c^3*d^2*e^-3*(-1*e^2+c^2*d^2)^-5//2*(e*(2*e*h+81*d*i)+4*h*c^2*d^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-11//4*b*i*c^3*d^4*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2+-11//12*b*c*i*d^3*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-1+-11//12*b*i*c^3*d^3*e^-4*(-1*e^2+c^2*d^2)^-5//2*(e^2+2*c^2*d^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1//4*b*c*d*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2*(4*e^2*(e*h+6*d*i)+-1*d*c^2*(g*e^2+6*i*d^2+-2*d*e*h))+1//4*b*c*d^2*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-2*(18*i*e^2+d*c^2*(2*e*h+9*d*i))+1//12*b*c*d*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-1*(g*e^2+-18*i*d^2+-6*d*e*h)+1//12*b*c*d^2*e^-3*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-2*(-1*e^2+c^2*d^2)^-1*(2*e*h+27*d*i))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-3*(f+g*x), x) == :(-1*(a+b*arcsin(c*x))^2*(d+e*x)^-2*(f+g*x)^2*(-2*d*g+2*e*f)^-1+(1/2)*b^2*e^-2*g^2*(e*f+-1*d*g)^-1*arcsin(c*x)^2+a*b*e^-2*g^2*(e*f+-1*d*g)^-1*arcsin(c*x)+-1*b^2*c^2*e^-2*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)*log(d+e*x)+-2*c*g*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*c*g*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+d*b^2*c^3*e^-2*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*a*b*c*e^-2*(-1*e^2+c^2*d^2)^-3//2*(2*g*e^2+-1*d*c^2*(d*g+e*f))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-1*d*b^2*c^3*e^-2*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+a*b*c*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)+c*b^2*e^-1*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)*arcsin(c*x)+-2*im*c*g*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*im*c*g*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+im*d*b^2*c^3*e^-2*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*d*b^2*c^3*e^-2*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-3*(f+g*x)^2, x) == :(a^2*e^-3*g^2*log(d+e*x)+2*b^2*e^-3*g^2*Polylogarithms.polylog(3,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*b^2*e^-3*g^2*Polylogarithms.polylog(3,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1//2*a^2*e^-3*(d+e*x)^-2*(e*f+-1*d*g)^2+b^2*e^-3*g^2*arcsin(c*x)^2*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+b^2*e^-3*g^2*arcsin(c*x)^2*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-2*g*a^2*e^-3*(d+e*x)^-1*(e*f+-1*d*g)+-1//2*b^2*e^-3*(d+e*x)^-2*(e*f+-1*d*g)^2*arcsin(c*x)^2+-1//3*im*b^2*e^-3*g^2*arcsin(c*x)^3+-1*im*a*b*e^-3*g^2*arcsin(c*x)^2+-1*a*b*e^-3*(d+e*x)^-2*(e*f+-1*d*g)^2*arcsin(c*x)+-1*b^2*c^2*e^-3*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)^2*log(d+e*x)+-2*im*a*b*e^-3*g^2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-2*im*a*b*e^-3*g^2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-2*im*b^2*e^-3*g^2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+-2*im*b^2*e^-3*g^2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+-2*g*b^2*e^-3*(d+e*x)^-1*arcsin(c*x)^2*(e*f+-1*d*g)+2*a*b*e^-3*g^2*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*a*b*e^-3*g^2*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+d*b^2*c^3*e^-3*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)^2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*d*b^2*c^3*e^-3*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)^2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-4*a*b*g*e^-3*(d+e*x)^-1*(e*f+-1*d*g)*arcsin(c*x)+-4*c*g*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(e*f+-1*d*g)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+4*c*g*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(e*f+-1*d*g)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+a*b*c*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)^2+c*b^2*e^-2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^-1*(-1*e^2+c^2*d^2)^-1*(e*f+-1*d*g)^2*arcsin(c*x)+-1*a*b*c*e^-3*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)*(4*g*e^2+-1*d*c^2*(e*f+3*d*g))*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+im*d*b^2*c^3*e^-3*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)^2*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1*im*d*b^2*c^3*e^-3*(-1*e^2+c^2*d^2)^-3//2*(e*f+-1*d*g)^2*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-4*im*c*g*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(e*f+-1*d*g)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+4*im*c*g*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(e*f+-1*d*g)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(g+h*x)^3*(d+e*x+f*x^2), x) == :(d*x*g^3*(a+b*arcsin(c*x))^2+(1/2)*g^2*x^2*(a+b*arcsin(c*x))^2*(e*g+3*d*h)+-2*d*x*b^2*g^3+-5//96*f*c^-6*h^3*(a+b*arcsin(c*x))^2+-3//32*h*c^-4*(a+b*arcsin(c*x))^2*(h*(d*h+3*e*g)+3*f*g^2)+-2//27*g*b^2*x^3*(f*g^2+3*h*(d*h+e*g))+-2//125*b^2*h^2*x^5*(e*h+3*f*g)+-1//4*b^2*g^2*x^2*(e*g+3*d*h)+-1//4*c^-2*g^2*(a+b*arcsin(c*x))^2*(e*g+3*d*h)+-1//32*h*b^2*x^4*(h*(d*h+3*e*g)+3*f*g^2)+-1//108*f*b^2*h^3*x^6+1//3*g*x^3*(a+b*arcsin(c*x))^2*(f*g^2+3*h*(d*h+e*g))+1//4*h*x^4*(a+b*arcsin(c*x))^2*(h*(d*h+3*e*g)+3*f*g^2)+1//5*h^2*x^5*(a+b*arcsin(c*x))^2*(e*h+3*f*g)+1//6*f*h^3*x^6*(a+b*arcsin(c*x))^2+-16//75*x*b^2*c^-4*h^2*(e*h+3*f*g)+-8//225*b^2*c^-2*h^2*x^3*(e*h+3*f*g)+-5//96*f*b^2*c^-4*h^3*x^2+-5//288*f*b^2*c^-2*h^3*x^4+-4//9*g*x*b^2*c^-2*(f*g^2+3*h*(d*h+e*g))+-3//32*h*b^2*c^-2*x^2*(h*(d*h+3*e*g)+3*f*g^2)+2*b*d*c^-1*g^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+4//9*b*g*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(f*g^2+3*h*(d*h+e*g))+16//75*b*c^-5*h^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+3*f*g)+(1/2)*b*x*c^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*g+3*d*h)+1//8*b*h*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(h*(d*h+3*e*g)+3*f*g^2)+1//18*b*f*c^-1*h^3*x^5*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//9*b*g*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(f*g^2+3*h*(d*h+e*g))+2//25*b*c^-1*h^2*x^4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+3*f*g)+3//16*b*h*x*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(h*(d*h+3*e*g)+3*f*g^2)+5//48*b*f*x*c^-5*h^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+5//72*b*f*c^-3*h^3*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+8//75*b*c^-3*h^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+3*f*g))
@test integrate((a+b*arcsin(c*x))^2*(g+h*x)^2*(d+e*x+f*x^2), x) == :(x^3*(a+b*arcsin(c*x))^2*(1//3*f*g^2+1//3*h*(d*h+2*e*g))+-2//27*b^2*x^3*(f*g^2+h*(d*h+2*e*g))+d*x*g^2*(a+b*arcsin(c*x))^2+(1/2)*g*x^2*(a+b*arcsin(c*x))^2*(e*g+2*d*h)+-2*d*x*b^2*g^2+-4//9*x*b^2*c^-2*(f*g^2+h*(d*h+2*e*g))+-3//32*h*c^-4*(a+b*arcsin(c*x))^2*(e*h+2*f*g)+-2//125*f*b^2*h^2*x^5+-1//4*g*b^2*x^2*(e*g+2*d*h)+-1//4*g*c^-2*(a+b*arcsin(c*x))^2*(e*g+2*d*h)+-1//32*h*b^2*x^4*(e*h+2*f*g)+1//4*h*x^4*(a+b*arcsin(c*x))^2*(e*h+2*f*g)+1//5*f*h^2*x^5*(a+b*arcsin(c*x))^2+-16//75*f*x*b^2*c^-4*h^2+-8//225*f*b^2*c^-2*h^2*x^3+-3//32*h*b^2*c^-2*x^2*(e*h+2*f*g)+4//9*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(f*g^2+h*(d*h+2*e*g))+2*b*d*c^-1*g^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//9*b*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(f*g^2+h*(d*h+2*e*g))+16//75*b*f*c^-5*h^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+(1/2)*b*g*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*g+2*d*h)+1//8*b*h*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+2*f*g)+2//25*b*f*c^-1*h^2*x^4*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//16*b*h*x*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+2*f*g)+8//75*b*f*c^-3*h^2*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(g+h*x)*(d+e*x+f*x^2), x) == :(x^2*(a+b*arcsin(c*x))^2*((1/2)*d*h+(1/2)*e*g)+x^3*(a+b*arcsin(c*x))^2*(1//3*e*h+1//3*f*g)+-2//27*b^2*x^3*(e*h+f*g)+-1//4*b^2*x^2*(d*h+e*g)+-1//4*c^-2*(a+b*arcsin(c*x))^2*(d*h+e*g)+d*g*x*(a+b*arcsin(c*x))^2+-2*d*g*x*b^2+-4//9*x*b^2*c^-2*(e*h+f*g)+-3//32*f*h*c^-4*(a+b*arcsin(c*x))^2+-1//32*f*h*b^2*x^4+1//4*f*h*x^4*(a+b*arcsin(c*x))^2+-3//32*f*h*b^2*c^-2*x^2+4//9*b*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+f*g)+(1/2)*b*x*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(d*h+e*g)+2*b*d*g*c^-1*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+2//9*b*c^-1*x^2*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))*(e*h+f*g)+1//8*b*f*h*c^-1*x^3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x))+3//16*b*f*h*x*c^-3*(1+-1*c^2*x^2)^(1/2)*(a+b*arcsin(c*x)))
@test integrate((a+b*arcsin(c*x))^2*(g+h*x)^-1*(d+e*x+f*x^2), x) == :(a^2*h^-3*(d*h^2+f*g^2+-1*e*g*h)*log(g+h*x)+(1/2)*f*a^2*h^-1*x^2+-1*x*a^2*h^-2*(f*g+-1*e*h)+2*x*b^2*h^-2*(f*g+-1*e*h)+2*b^2*h^-3*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(3,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*b^2*h^-3*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(3,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-1//4*f*b^2*h^-1*x^2+b^2*h^-3*arcsin(c*x)^2*(d*h^2+f*g^2+-1*e*g*h)*log(1+-1*im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+b^2*h^-3*arcsin(c*x)^2*(d*h^2+f*g^2+-1*e*g*h)*log(1+-1*im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+(1/2)*f*b^2*h^-1*x^2*arcsin(c*x)^2+-1*x*b^2*h^-2*arcsin(c*x)^2*(f*g+-1*e*h)+-1//3*im*b^2*h^-3*arcsin(c*x)^3*(d*h^2+f*g^2+-1*e*g*h)+-1//4*f*b^2*c^-2*h^-1*arcsin(c*x)^2+a*b*f*h^-1*x^2*arcsin(c*x)+-1*im*a*b*h^-3*arcsin(c*x)^2*(d*h^2+f*g^2+-1*e*g*h)+-2*im*a*b*h^-3*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(2,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-2*im*a*b*h^-3*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(2,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-2*im*b^2*h^-3*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(2,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+-2*im*b^2*h^-3*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(2,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+-2*a*b*x*h^-2*(f*g+-1*e*h)*arcsin(c*x)+-2*b^2*c^-1*h^-2*(1+-1*c^2*x^2)^(1/2)*(f*g+-1*e*h)*arcsin(c*x)+2*a*b*h^-3*(d*h^2+f*g^2+-1*e*g*h)*arcsin(c*x)*log(1+-1*im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*a*b*h^-3*(d*h^2+f*g^2+-1*e*g*h)*arcsin(c*x)*log(1+-1*im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-1//2*a*b*f*c^-2*h^-1*arcsin(c*x)+-1//2*a*b*c^-1*h^-2*(1+-1*c^2*x^2)^(1/2)*(-4*e*h+4*f*g+-1*f*h*x)+(1/2)*f*x*b^2*c^-1*h^-1*(1+-1*c^2*x^2)^(1/2)*arcsin(c*x))
@test integrate((a+b*arcsin(c*x))^2*(g+h*x)^-2*(d+e*x+f*x^2), x) == :(f*x*a^2*h^-2+-1*a^2*h^-3*(g+h*x)^-1*(d*h^2+f*g^2+-1*e*g*h)+-1*a^2*h^-3*(-1*e*h+2*f*g)*log(g+h*x)+-2*f*x*b^2*h^-2+-2*b^2*h^-3*(-1*e*h+2*f*g)*Polylogarithms.polylog(3,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-2*b^2*h^-3*(-1*e*h+2*f*g)*Polylogarithms.polylog(3,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+f*x*b^2*h^-2*arcsin(c*x)^2+-1*b^2*h^-3*(g+h*x)^-1*arcsin(c*x)^2*(d*h^2+f*g^2+-1*e*g*h)+-1*b^2*h^-3*arcsin(c*x)^2*(-1*e*h+2*f*g)*log(1+-1*im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-1*b^2*h^-3*arcsin(c*x)^2*(-1*e*h+2*f*g)*log(1+-1*im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+1//3*im*b^2*h^-3*arcsin(c*x)^3*(-1*e*h+2*f*g)+im*a*b*h^-3*arcsin(c*x)^2*(-1*e*h+2*f*g)+-2*a*b*h^-3*(g+h*x)^-1*(d*h^2+f*g^2+-1*e*g*h)*arcsin(c*x)+-2*a*b*h^-3*(-1*e*h+2*f*g)*arcsin(c*x)*log(1+-1*im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-2*a*b*h^-3*(-1*e*h+2*f*g)*arcsin(c*x)*log(1+-1*im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+-2*c*b^2*h^-3*(-1*h^2+c^2*g^2)^-1//2*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(2,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*im*a*b*h^-3*(-1*e*h+2*f*g)*Polylogarithms.polylog(2,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*im*a*b*h^-3*(-1*e*h+2*f*g)*Polylogarithms.polylog(2,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*im*b^2*h^-3*(-1*e*h+2*f*g)*Polylogarithms.polylog(2,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+2*im*b^2*h^-3*(-1*e*h+2*f*g)*Polylogarithms.polylog(2,im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))*arcsin(c*x)+2*a*b*f*x*h^-2*arcsin(c*x)+2*a*b*f*c^-1*h^-2*(1+-1*c^2*x^2)^(1/2)+2*c*b^2*h^-3*(-1*h^2+c^2*g^2)^-1//2*(d*h^2+f*g^2+-1*e*g*h)*Polylogarithms.polylog(2,im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*f*b^2*c^-1*h^-2*(1+-1*c^2*x^2)^(1/2)*arcsin(c*x)+2*a*b*c*h^-3*(-1*h^2+c^2*g^2)^-1//2*(d*h^2+f*g^2+-1*e*g*h)*arctan((1+-1*c^2*x^2)^-1//2*(-1*h^2+c^2*g^2)^-1//2*(h+g*x*c^2))+-2*im*c*b^2*h^-3*(-1*h^2+c^2*g^2)^-1//2*(d*h^2+f*g^2+-1*e*g*h)*arcsin(c*x)*log(1+-1*im*h*(-1*(-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x)))+2*im*c*b^2*h^-3*(-1*h^2+c^2*g^2)^-1//2*(d*h^2+f*g^2+-1*e*g*h)*arcsin(c*x)*log(1+-1*im*h*((-1*h^2+c^2*g^2)^(1/2)+c*g)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-2*(e*f+e*h*x^2+2*d*h*x), x) == :(-1*(a+b*arcsin(c*x))^2*(d+e*x)^-1*(f+-1*h*d^2*e^-2)+h*x*e^-1*(a+b*arcsin(c*x))^2+-2*h*x*b^2*e^-1+-2*c*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*a*b*h*c^-1*e^-1*(1+-1*c^2*x^2)^(1/2)+2*c*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*h*b^2*c^-1*e^-1*(1+-1*c^2*x^2)^(1/2)*arcsin(c*x)+2*a*b*c*e^-2*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+-2*im*c*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*im*c*b^2*e^-2*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x))))
@test integrate((a+b*arcsin(c*x))^2*(d+e*x)^-2*(e*f+e*h*x^2+2*d*h*x)^2, x) == :(-2//27*b^2*h^2*x^3+-1*e^-3*(a+b*arcsin(c*x))^2*(d+e*x)^-1*(f*e^2+-1*h*d^2)^2+-4//9*x*b^2*c^-2*h^2+1//3*e^-3*h^2*(a+b*arcsin(c*x))^2*(d+e*x)^3+-2*h*x*b^2*e^-2*(-1*h*d^2+2*f*e^2)+2*h*x*e^-2*(a+b*arcsin(c*x))^2*(f*e^2+-1*h*d^2)+-1//2*d*b^2*e^-1*h^2*x^2+-1//3*b^2*d^3*e^-3*h^2*arcsin(c*x)^2+4//9*b^2*c^-3*h^2*(1+-1*c^2*x^2)^(1/2)*arcsin(c*x)+-2*c*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)^2*Polylogarithms.polylog(2,im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*c*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)^2*Polylogarithms.polylog(2,im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1//2*d*b^2*c^-2*e^-1*h^2*arcsin(c*x)^2+2//9*b^2*c^-1*h^2*x^2*(1+-1*c^2*x^2)^(1/2)*arcsin(c*x)+2*a*b*c*e^-3*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)^2*arctan((1+-1*c^2*x^2)^-1//2*(-1*e^2+c^2*d^2)^-1//2*(e+d*x*c^2))+2*h*b^2*c^-1*e^-2*(1+-1*c^2*x^2)^(1/2)*(-1*h*d^2+2*f*e^2)*arcsin(c*x)+1//9*a*b*h*c^-3*e^-2*(1+-1*c^2*x^2)^(1/2)*(c^2*(-25*h*d^2+36*f*e^2)+4*h*e^2)+2//9*a*b*c^-1*e^-2*h^2*(1+-1*c^2*x^2)^(1/2)*(d+e*x)^2+d*x*b^2*c^-1*e^-1*h^2*(1+-1*c^2*x^2)^(1/2)*arcsin(c*x)+-2*im*c*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)^2*arcsin(c*x)*log(1+-1*im*e*(-1*(-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+2*im*c*b^2*e^-3*(-1*e^2+c^2*d^2)^-1//2*(f*e^2+-1*h*d^2)^2*arcsin(c*x)*log(1+-1*im*e*((-1*e^2+c^2*d^2)^(1/2)+c*d)^-1*exp(im*arcsin(c*x)))+-1//3*a*b*d*c^-2*e^-3*h^2*(3*e^2+2*c^2*d^2)*arcsin(c*x)+5//9*a*b*d*c^-1*e^-2*h^2*(1+-1*c^2*x^2)^(1/2)*(d+e*x))
@test integrate(x^3*arcsin(a+b*x), x) == :(1//4*x^4*arcsin(a+b*x)+-1//32*b^-4*(3+8*a^4+24*a^2)*arcsin(a+b*x)+-1//96*b^-4*(1+-1*(a+b*x)^2)^(1/2)*(-1*(9+26*a^2)*(a+b*x)+4*a*(16+19*a^2))+1//16*b^-1*x^3*(1+-1*(a+b*x)^2)^(1/2)+-7//48*a*b^-2*x^2*(1+-1*(a+b*x)^2)^(1/2))
@test integrate(x^2*arcsin(a+b*x), x) == :(1//3*x^3*arcsin(a+b*x)+1//9*b^-1*x^2*(1+-1*(a+b*x)^2)^(1/2)+1//18*b^-3*(1+-1*(a+b*x)^2)^(1/2)*(4+11*a^2+-5*a*b*x)+1//6*a*b^-3*(3+2*a^2)*arcsin(a+b*x))
@test integrate(x*arcsin(a+b*x), x) == :((1/2)*x^2*arcsin(a+b*x)+-3//4*a*b^-2*(1+-1*(a+b*x)^2)^(1/2)+-1//4*b^-2*(1+2*a^2)*arcsin(a+b*x)+1//4*x*b^-1*(1+-1*(a+b*x)^2)^(1/2))
@test integrate(arcsin(a+b*x), x) == :(b^-1*(1+-1*(a+b*x)^2)^(1/2)+b^-1*(a+b*x)*arcsin(a+b*x))
@test integrate(x^-1*arcsin(a+b*x), x) == :(arcsin(a+b*x)*log(1+-1*((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+arcsin(a+b*x)*log(1+-1*(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+-1*im*Polylogarithms.polylog(2,((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+-1*im*Polylogarithms.polylog(2,(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+-1//2*im*arcsin(a+b*x)^2)
@test integrate(x^-2*arcsin(a+b*x), x) == :(-1*x^-1*arcsin(a+b*x)+-1*b*(1+-1*a^2)^-1//2*arctanh((1+-1*a^2)^-1//2*(1+-1*(a+b*x)^2)^-1//2*(1+-1*a*(a+b*x))))
@test integrate(x^-3*arcsin(a+b*x), x) == :(-1//2*x^-2*arcsin(a+b*x)+-1*b*x^-1*(1+-1*(a+b*x)^2)^(1/2)*(2+-2*a^2)^-1+-1//2*a*b^2*(1+-1*a^2)^-3//2*arctanh((1+-1*a^2)^-1//2*(1+-1*(a+b*x)^2)^-1//2*(1+-1*a*(a+b*x))))
@test integrate(x^-4*arcsin(a+b*x), x) == :(-1//3*x^-3*arcsin(a+b*x)+-1*b*x^-2*(1+-1*(a+b*x)^2)^(1/2)*(6+-6*a^2)^-1+-1//6*b^3*(1+-1*a^2)^-5//2*(1+2*a^2)*arctanh((1+-1*a^2)^-1//2*(1+-1*(a+b*x)^2)^-1//2*(1+-1*a*(a+b*x)))+-1//2*a*b^2*x^-1*(1+-1*a^2)^-2*(1+-1*(a+b*x)^2)^(1/2))
@test integrate(x^-5*arcsin(a+b*x), x) == :(-1//4*x^-4*arcsin(a+b*x)+-1*b*x^-3*(1+-1*(a+b*x)^2)^(1/2)*(12+-12*a^2)^-1+-5//24*a*b^2*x^-2*(1+-1*a^2)^-2*(1+-1*(a+b*x)^2)^(1/2)+-1//8*a*b^4*(1+-1*a^2)^-7//2*(3+2*a^2)*arctanh((1+-1*a^2)^-1//2*(1+-1*(a+b*x)^2)^-1//2*(1+-1*a*(a+b*x)))+-1//24*b^3*x^-1*(1+-1*a^2)^-3*(1+-1*(a+b*x)^2)^(1/2)*(4+11*a^2))
@test integrate(x^3*arcsin(a+b*x)^2, x) == :(-3//32*b^-4*(a+b*x)^2+-3//32*b^-4*arcsin(a+b*x)^2+-1//32*b^-4*(a+b*x)^4+1//4*x^4*arcsin(a+b*x)^2+2*x*a^3*b^-3+-3//4*a^2*b^-4*(a+b*x)^2+-3//4*a^2*b^-4*arcsin(a+b*x)^2+-1//4*a^4*b^-4*arcsin(a+b*x)^2+2//9*a*b^-4*(a+b*x)^3+4//3*a*x*b^-3+-2*a^3*b^-4*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)+-4//3*a*b^-4*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)+1//8*b^-4*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)^3*arcsin(a+b*x)+1//16*b^-4*(1+-1*(a+b*x)^2)^(1/2)*(3a+3*b*x)*arcsin(a+b*x)+-2//3*a*b^-4*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)^2*arcsin(a+b*x)+3//2*a^2*b^-4*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)*arcsin(a+b*x))
@test integrate(x^2*arcsin(a+b*x)^2, x) == :(-4//9*x*b^-2+-2//27*b^-3*(a+b*x)^3+1//3*x^3*arcsin(a+b*x)^2+(1/2)*a*b^-3*(a+b*x)^2+(1/2)*a*b^-3*arcsin(a+b*x)^2+-2*x*a^2*b^-2+1//3*a^3*b^-3*arcsin(a+b*x)^2+4//9*b^-3*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)+2*a^2*b^-3*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)+2//9*b^-3*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)^2*arcsin(a+b*x)+-1*a*b^-3*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)*arcsin(a+b*x))
@test integrate(x*arcsin(a+b*x)^2, x) == :((1/2)*x^2*arcsin(a+b*x)^2+-1//4*b^-2*(a+b*x)^2+-1//4*b^-2*arcsin(a+b*x)^2+2*a*x*b^-1+-1//2*a^2*b^-2*arcsin(a+b*x)^2+(1/2)*b^-2*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)*arcsin(a+b*x)+-2*a*b^-2*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x))
@test integrate(arcsin(a+b*x)^2, x) == :(-2x+b^-1*arcsin(a+b*x)^2*(a+b*x)+2*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x))
@test integrate(x^-1*arcsin(a+b*x)^2, x) == :(2*Polylogarithms.polylog(3,((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+2*Polylogarithms.polylog(3,(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+arcsin(a+b*x)^2*log(1+-1*((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+arcsin(a+b*x)^2*log(1+-1*(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+-1//3*im*arcsin(a+b*x)^3+-2*im*Polylogarithms.polylog(2,((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))*arcsin(a+b*x)+-2*im*Polylogarithms.polylog(2,(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))*arcsin(a+b*x))
@test integrate(x^-3*arcsin(a+b*x)^2, x) == :(-1//2*x^-2*arcsin(a+b*x)^2+b^2*(1+-1*a^2)^-1*log(x)+a*b^2*(-1+a^2)^-3//2*Polylogarithms.polylog(2,-1*im*(a+(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))+-1*a*b^2*(-1+a^2)^-3//2*Polylogarithms.polylog(2,-1*im*(a+-1*(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))+-1*b*x^-1*(1+-1*a^2)^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)+im*a*b^2*(-1+a^2)^-3//2*arcsin(a+b*x)*log(1+im*(a+(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))+-1*im*a*b^2*(-1+a^2)^-3//2*arcsin(a+b*x)*log(1+im*(a+-1*(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x))))
@test integrate(x^2*arcsin(a+b*x)^3, x) == :(-14//9*b^-3*(1+-1*(a+b*x)^2)^(1/2)+1//3*x^3*arcsin(a+b*x)^3+2//27*b^-3*(1+-1*(a+b*x)^2)^3//2+(1/2)*a*b^-3*arcsin(a+b*x)^3+-6*a^2*b^-3*(1+-1*(a+b*x)^2)^(1/2)+-3//4*a*b^-3*arcsin(a+b*x)+-2//9*b^-3*(a+b*x)^3*arcsin(a+b*x)+-1//3*b^-3*(4a+4*b*x)*arcsin(a+b*x)+1//3*a^3*b^-3*arcsin(a+b*x)^3+2//3*b^-3*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2+-6*a^2*b^-3*(a+b*x)*arcsin(a+b*x)+3*a^2*b^-3*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2+1//3*b^-3*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)^2*arcsin(a+b*x)^2+3//2*a*b^-3*(a+b*x)^2*arcsin(a+b*x)+3//4*a*b^-3*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)+-3//2*a*b^-3*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2*(a+b*x))
@test integrate(x*arcsin(a+b*x)^3, x) == :((1/2)*x^2*arcsin(a+b*x)^3+-1//4*b^-2*arcsin(a+b*x)^3+3//8*b^-2*arcsin(a+b*x)+6*a*b^-2*(1+-1*(a+b*x)^2)^(1/2)+-3//4*b^-2*(a+b*x)^2*arcsin(a+b*x)+-1//2*a^2*b^-2*arcsin(a+b*x)^3+-1//8*b^-2*(1+-1*(a+b*x)^2)^(1/2)*(3a+3*b*x)+-3*a*b^-2*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2+6*a*b^-2*(a+b*x)*arcsin(a+b*x)+1//4*b^-2*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2*(3a+3*b*x))
@test integrate(arcsin(a+b*x)^3, x) == :(-6*b^-1*(1+-1*(a+b*x)^2)^(1/2)+b^-1*arcsin(a+b*x)^3*(a+b*x)+-1*b^-1*(6a+6*b*x)*arcsin(a+b*x)+3*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2)
@test integrate(x^-1*arcsin(a+b*x)^3, x) == :(arcsin(a+b*x)^3*log(1+-1*((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+arcsin(a+b*x)^3*log(1+-1*(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+6*im*Polylogarithms.polylog(4,((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+6*im*Polylogarithms.polylog(4,(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+6*Polylogarithms.polylog(3,((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))*arcsin(a+b*x)+6*Polylogarithms.polylog(3,(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))*arcsin(a+b*x)+-1//4*im*arcsin(a+b*x)^4+-3*im*arcsin(a+b*x)^2*Polylogarithms.polylog(2,((1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x)))+-3*im*arcsin(a+b*x)^2*Polylogarithms.polylog(2,(-1*(1+-1*a^2)^(1/2)+im*a)^-1*exp(im*arcsin(a+b*x))))
@test integrate(x^-2*arcsin(a+b*x)^3, x) == :(-1*x^-1*arcsin(a+b*x)^3+-6*im*b*(-1+a^2)^-1//2*Polylogarithms.polylog(3,-1*im*(a+(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))+-6*b*(-1+a^2)^-1//2*Polylogarithms.polylog(2,-1*im*(a+(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))*arcsin(a+b*x)+6*im*b*(-1+a^2)^-1//2*Polylogarithms.polylog(3,-1*im*(a+-1*(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))+6*b*(-1+a^2)^-1//2*Polylogarithms.polylog(2,-1*im*(a+-1*(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))*arcsin(a+b*x)+-3*im*b*(-1+a^2)^-1//2*arcsin(a+b*x)^2*log(1+im*(a+(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x)))+3*im*b*(-1+a^2)^-1//2*arcsin(a+b*x)^2*log(1+im*(a+-1*(-1+a^2)^(1/2))^-1*exp(im*arcsin(a+b*x))))
@test integrate(x^2*arcsin(a+b*x)^-1, x) == :(-1//4*b^-3*cosintegral(3*arcsin(a+b*x))+1//4*b^-3*cosintegral(arcsin(a+b*x))+a^2*b^-3*cosintegral(arcsin(a+b*x))+-1*a*b^-3*sinintegral(2*arcsin(a+b*x)))
@test integrate(x*arcsin(a+b*x)^-1, x) == :((1/2)*b^-2*sinintegral(2*arcsin(a+b*x))+-1*a*b^-2*cosintegral(arcsin(a+b*x)))
@test integrate(arcsin(a+b*x)^-1, x) == :(b^-1*cosintegral(arcsin(a+b*x)))
@test integrate(arcsin(a+b*x)^-2, x) == :(-1*b^-1*sinintegral(arcsin(a+b*x))+-1*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^-1)
@test integrate(arcsin(a+b*x)^-3, x) == :(-1//2*b^-1*cosintegral(arcsin(a+b*x))+(1/2)*b^-1*arcsin(a+b*x)^-1*(a+b*x)+-1//2*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^-2)
@test integrate(x^2*(a+b*arcsin(c+d*x))^(1/2), x) == :(1//3*d^-3*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^3+c^2*d^-3*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+(1/2)*c*d^-3*(a+b*arcsin(c+d*x))^(1/2)*cos(2*arcsin(c+d*x))+-1//4*c*pi^(1/2)*b^(1/2)*d^-3*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//4*c*pi^(1/2)*b^(1/2)*d^-3*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-1//8*2^(1/2)*pi^(1/2)*b^(1/2)*d^-3*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//72*6^(1/2)*pi^(1/2)*b^(1/2)*d^-3*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+1//8*2^(1/2)*pi^(1/2)*b^(1/2)*d^-3*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+1//72*6^(1/2)*pi^(1/2)*b^(1/2)*d^-3*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+(1/2)*2^(1/2)*pi^(1/2)*b^(1/2)*c^2*d^-3*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+-1//2*2^(1/2)*pi^(1/2)*b^(1/2)*c^2*d^-3*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate(x*(a+b*arcsin(c+d*x))^(1/2), x) == :(-1//4*d^-2*(a+b*arcsin(c+d*x))^(1/2)*cos(2*arcsin(c+d*x))+-1*c*d^-2*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+1//8*pi^(1/2)*b^(1/2)*d^-2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//8*pi^(1/2)*b^(1/2)*d^-2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+(1/2)*c*2^(1/2)*pi^(1/2)*b^(1/2)*d^-2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//2*c*2^(1/2)*pi^(1/2)*b^(1/2)*d^-2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^(1/2), x) == :(d^-1*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+(1/2)*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+-1//2*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate(x*(a+b*arcsin(c+d*x))^3//2, x) == :(-1//4*d^-2*(a+b*arcsin(c+d*x))^3//2*cos(2*arcsin(c+d*x))+-1*c*d^-2*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+3//16*b*d^-2*(a+b*arcsin(c+d*x))^(1/2)*sin(2*arcsin(c+d*x))+-3//2*b*c*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+-3//32*pi^(1/2)*b^3//2*d^-2*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+3//32*pi^(1/2)*b^3//2*d^-2*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+3//4*c*2^(1/2)*pi^(1/2)*b^3//2*d^-2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+3//4*c*2^(1/2)*pi^(1/2)*b^3//2*d^-2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^3//2, x) == :(d^-1*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+3//2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+-3//4*2^(1/2)*pi^(1/2)*b^3//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-3//4*2^(1/2)*pi^(1/2)*b^3//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate(x*(a+b*arcsin(c+d*x))^5//2, x) == :(-1//4*d^-2*(a+b*arcsin(c+d*x))^5//2*cos(2*arcsin(c+d*x))+-1*c*d^-2*(a+b*arcsin(c+d*x))^5//2*(c+d*x)+5//16*b*d^-2*(a+b*arcsin(c+d*x))^3//2*sin(2*arcsin(c+d*x))+15//64*b^2*d^-2*(a+b*arcsin(c+d*x))^(1/2)*cos(2*arcsin(c+d*x))+-15//128*pi^(1/2)*b^5//2*d^-2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-15//128*pi^(1/2)*b^5//2*d^-2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-5//2*b*c*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2+15//4*c*b^2*d^-2*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+-15//8*c*2^(1/2)*pi^(1/2)*b^5//2*d^-2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+15//8*c*2^(1/2)*pi^(1/2)*b^5//2*d^-2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^5//2, x) == :(d^-1*(a+b*arcsin(c+d*x))^5//2*(c+d*x)+-15//4*b^2*d^-1*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+5//2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2+-15//8*2^(1/2)*pi^(1/2)*b^5//2*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+15//8*2^(1/2)*pi^(1/2)*b^5//2*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^7//2, x) == :(d^-1*(a+b*arcsin(c+d*x))^7//2*(c+d*x)+-105//8*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+-35//4*b^2*d^-1*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+7//2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^5//2+105//16*2^(1/2)*pi^(1/2)*b^7//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+105//16*2^(1/2)*pi^(1/2)*b^7//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate(x^2*(a+b*arcsin(c+d*x))^-1//2, x) == :(c*pi^(1/2)*b^-1//2*d^-3*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-1*c*pi^(1/2)*b^-1//2*d^-3*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//12*6^(1/2)*pi^(1/2)*b^-1//2*d^-3*cos(3*a*b^-1)*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//12*6^(1/2)*pi^(1/2)*b^-1//2*d^-3*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+1//4*2^(1/2)*pi^(1/2)*b^-1//2*d^-3*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//4*2^(1/2)*pi^(1/2)*b^-1//2*d^-3*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+2^(1/2)*pi^(1/2)*b^-1//2*c^2*d^-3*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2^(1/2)*pi^(1/2)*b^-1//2*c^2*d^-3*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate(x*(a+b*arcsin(c+d*x))^-1//2, x) == :((1/2)*pi^(1/2)*b^-1//2*d^-2*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//2*pi^(1/2)*b^-1//2*d^-2*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-1*c*2^(1/2)*pi^(1/2)*b^-1//2*d^-2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1*c*2^(1/2)*pi^(1/2)*b^-1//2*d^-2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1//2, x) == :(2^(1/2)*pi^(1/2)*b^-1//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2^(1/2)*pi^(1/2)*b^-1//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate(x*(a+b*arcsin(c+d*x))^-3//2, x) == :(-1*b^-1*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(2c+2*d*x)+2*c*b^-1*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+2*pi^(1/2)*b^-3//2*d^-2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2*pi^(1/2)*b^-3//2*d^-2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-2*c*2^(1/2)*pi^(1/2)*b^-3//2*d^-2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+2*c*2^(1/2)*pi^(1/2)*b^-3//2*d^-2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^-3//2, x) == :(-2*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+-2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate(x*(a+b*arcsin(c+d*x))^-5//2, x) == :(-4//3*b^-2*d^-2*(a+b*arcsin(c+d*x))^-1//2+8//3*b^-2*d^-2*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^2+-8//3*pi^(1/2)*b^-5//2*d^-2*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-4//3*c*b^-2*d^-2*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)+-1//3*b^-1*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2*(2c+2*d*x)+2//3*c*b^-1*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2+8//3*pi^(1/2)*b^-5//2*d^-2*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+4//3*c*2^(1/2)*pi^(1/2)*b^-5//2*d^-2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+4//3*c*2^(1/2)*pi^(1/2)*b^-5//2*d^-2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-5//2, x) == :(-2//3*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2+1//3*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1//2*(4c+4*d*x)+-4//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-4//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate(x*(a+b*arcsin(c+d*x))^-7//2, x) == :(-4//15*b^-2*d^-2*(a+b*arcsin(c+d*x))^-3//2+8//15*b^-2*d^-2*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^2+-32//15*pi^(1/2)*b^-7//2*d^-2*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-32//15*pi^(1/2)*b^-7//2*d^-2*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-8//15*c*b^-3*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+-4//15*c*b^-2*d^-2*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)+-1//5*b^-1*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2*(2c+2*d*x)+1//15*b^-3*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(32c+32*d*x)+2//5*c*b^-1*d^-2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2+-8//15*c*2^(1/2)*pi^(1/2)*b^-7//2*d^-2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+8//15*c*2^(1/2)*pi^(1/2)*b^-7//2*d^-2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-7//2, x) == :(-2//5*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2+1//15*b^-2*d^-1*(a+b*arcsin(c+d*x))^-3//2*(4c+4*d*x)+8//15*b^-3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+-8//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+8//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate(x^2*(a+b*arcsin(c+d*x))^n, x) == :(-1//8*im*d^-3*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-1*im*a*b^-1)+1//8*im*d^-3*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c+d*x)))*exp(im*a*b^-1)+c*2^(-2+-1n)*d^-3*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c+d*x)))*exp(2*im*a*b^-1)+c*2^(-2+-1n)*d^-3*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-2*im*a*b^-1)+(1/2)*im*c^2*d^-3*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c+d*x)))*exp(im*a*b^-1)+-1//2*im*c^2*d^-3*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-1*im*a*b^-1)+-1//8*im*3^(-1+-1n)*d^-3*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,3*im*b^-1*(a+b*arcsin(c+d*x)))*exp(3*im*a*b^-1)+1//8*im*3^(-1+-1n)*d^-3*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-3*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-3*im*a*b^-1))
@test integrate(x*(a+b*arcsin(c+d*x))^n, x) == :(-1*2^(-3+-1n)*d^-2*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,2*im*b^-1*(a+b*arcsin(c+d*x)))*exp(2*im*a*b^-1)+-1*2^(-3+-1n)*d^-2*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-2*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-2*im*a*b^-1)+(1/2)*im*c*d^-2*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-1*im*a*b^-1)+-1//2*im*c*d^-2*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c+d*x)))*exp(im*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^n, x) == :((1/2)*im*d^-1*(im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,im*b^-1*(a+b*arcsin(c+d*x)))*exp(im*a*b^-1)+-1//2*im*d^-1*(-1*im*b^-1*(a+b*arcsin(c+d*x)))^(-1n)*(a+b*arcsin(c+d*x))^n*SpecialFunctions.gamma(1+n,-1*im*b^-1*(a+b*arcsin(c+d*x)))*exp(-1*im*a*b^-1))
@test integrate((c*e+d*e*x)^4*(a+b*arcsin(c+d*x)), x) == :(-2//15*b*d^-1*e^4*(1+-1*(c+d*x)^2)^3//2+1//5*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)+1//5*d^-1*e^4*(c+d*x)^5*(a+b*arcsin(c+d*x))+1//25*b*d^-1*e^4*(1+-1*(c+d*x)^2)^5//2)
@test integrate((c*e+d*e*x)^3*(a+b*arcsin(c+d*x)), x) == :(-3//32*b*d^-1*e^3*arcsin(c+d*x)+1//4*d^-1*e^3*(c+d*x)^4*(a+b*arcsin(c+d*x))+1//16*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^3+3//32*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x))
@test integrate((c*e+d*e*x)^2*(a+b*arcsin(c+d*x)), x) == :(-1//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^3//2+1//3*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)+1//3*d^-1*e^2*(c+d*x)^3*(a+b*arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))*(c*e+d*e*x), x) == :((1/2)*e*d^-1*(c+d*x)^2*(a+b*arcsin(c+d*x))+-1//4*b*e*d^-1*arcsin(c+d*x)+1//4*b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x))
@test integrate(a+b*arcsin(c+d*x), x) == :(a*x+b*d^-1*(1+-1*(c+d*x)^2)^(1/2)+b*d^-1*(c+d*x)*arcsin(c+d*x))
@test integrate((c*e+d*e*x)^-1*(a+b*arcsin(c+d*x)), x) == :(d^-1*e^-1*(a+b*arcsin(c+d*x))*log(1+-1*exp(2*im*arcsin(c+d*x)))+-1//2*im*b*d^-1*e^-1*Polylogarithms.polylog(2,exp(2*im*arcsin(c+d*x)))+-1//2*im*b^-1*d^-1*e^-1*(a+b*arcsin(c+d*x))^2)
@test integrate((c*e+d*e*x)^-2*(a+b*arcsin(c+d*x)), x) == :(-1*b*d^-1*e^-2*arctanh((1+-1*(c+d*x)^2)^(1/2))+-1*d^-1*e^-2*(c+d*x)^-1*(a+b*arcsin(c+d*x)))
@test integrate((c*e+d*e*x)^-3*(a+b*arcsin(c+d*x)), x) == :(-1//2*d^-1*e^-3*(c+d*x)^-2*(a+b*arcsin(c+d*x))+-1//2*b*d^-1*e^-3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-1)
@test integrate((c*e+d*e*x)^-4*(a+b*arcsin(c+d*x)), x) == :(-1//3*d^-1*e^-4*(c+d*x)^-3*(a+b*arcsin(c+d*x))+-1//6*b*d^-1*e^-4*arctanh((1+-1*(c+d*x)^2)^(1/2))+-1//6*b*d^-1*e^-4*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-2)
@test integrate((c*e+d*e*x)^-5*(a+b*arcsin(c+d*x)), x) == :(-1//4*d^-1*e^-5*(c+d*x)^-4*(a+b*arcsin(c+d*x))+-1//6*b*d^-1*e^-5*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-1+-1//12*b*d^-1*e^-5*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-3)
@test integrate((c*e+d*e*x)^-6*(a+b*arcsin(c+d*x)), x) == :(-3//40*b*d^-1*e^-6*arctanh((1+-1*(c+d*x)^2)^(1/2))+-1//5*d^-1*e^-6*(c+d*x)^-5*(a+b*arcsin(c+d*x))+-3//40*b*d^-1*e^-6*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-2+-1//20*b*d^-1*e^-6*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-4)
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^4, x) == :(-16//75*x*b^2*e^4+-8//225*b^2*d^-1*e^4*(c+d*x)^3+-2//125*b^2*d^-1*e^4*(c+d*x)^5+1//5*d^-1*e^4*(a+b*arcsin(c+d*x))^2*(c+d*x)^5+16//75*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))+2//25*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^4*(a+b*arcsin(c+d*x))+8//75*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^2*(a+b*arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^3, x) == :(-3//32*d^-1*e^3*(a+b*arcsin(c+d*x))^2+-3//32*b^2*d^-1*e^3*(c+d*x)^2+-1//32*b^2*d^-1*e^3*(c+d*x)^4+1//4*d^-1*e^3*(a+b*arcsin(c+d*x))^2*(c+d*x)^4+1//8*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^3*(a+b*arcsin(c+d*x))+3//16*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^2, x) == :(-4//9*x*b^2*e^2+-2//27*b^2*d^-1*e^2*(c+d*x)^3+1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^2*(c+d*x)^3+4//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))+2//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^2*(a+b*arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^2+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^2*(c+d*x)^2+-1//4*e*b^2*d^-1*(c+d*x)^2+(1/2)*b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^2, x) == :(-2*x*b^2+d^-1*(a+b*arcsin(c+d*x))^2*(c+d*x)+2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^-1, x) == :(d^-1*e^-1*(a+b*arcsin(c+d*x))^2*log(1+-1*exp(2*im*arcsin(c+d*x)))+(1/2)*b^2*d^-1*e^-1*Polylogarithms.polylog(3,exp(2*im*arcsin(c+d*x)))+-1//3*im*b^-1*d^-1*e^-1*(a+b*arcsin(c+d*x))^3+-1*im*b*d^-1*e^-1*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^-2, x) == :(-1*d^-1*e^-2*(a+b*arcsin(c+d*x))^2*(c+d*x)^-1+-4*b*d^-1*e^-2*(a+b*arcsin(c+d*x))*arctanh(exp(im*arcsin(c+d*x)))+-2*im*b^2*d^-1*e^-2*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+2*im*b^2*d^-1*e^-2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^-3, x) == :(b^2*d^-1*e^-3*log(c+d*x)+-1//2*d^-1*e^-3*(a+b*arcsin(c+d*x))^2*(c+d*x)^-2+-1*b*d^-1*e^-3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-1*(a+b*arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^2*(c*e+d*e*x)^-4, x) == :(-1//3*b^2*d^-1*e^-4*(c+d*x)^-1+-1//3*d^-1*e^-4*(a+b*arcsin(c+d*x))^2*(c+d*x)^-3+-2//3*b*d^-1*e^-4*(a+b*arcsin(c+d*x))*arctanh(exp(im*arcsin(c+d*x)))+-1//3*im*b^2*d^-1*e^-4*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+1//3*im*b^2*d^-1*e^-4*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x)))+-1//3*b*d^-1*e^-4*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^-2*(a+b*arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^4, x) == :(-298//375*b^3*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)+-16//25*a*x*b^2*e^4+-6//625*b^3*d^-1*e^4*(1+-1*(c+d*x)^2)^5//2+1//5*d^-1*e^4*(a+b*arcsin(c+d*x))^3*(c+d*x)^5+76//1125*b^3*d^-1*e^4*(1+-1*(c+d*x)^2)^3//2+-16//25*b^3*d^-1*e^4*(c+d*x)*arcsin(c+d*x)+-8//75*b^2*d^-1*e^4*(c+d*x)^3*(a+b*arcsin(c+d*x))+-6//125*b^2*d^-1*e^4*(c+d*x)^5*(a+b*arcsin(c+d*x))+8//25*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2+3//25*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x)^4+4//25*b*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x)^2)
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^3, x) == :(-3//32*d^-1*e^3*(a+b*arcsin(c+d*x))^3+1//4*d^-1*e^3*(a+b*arcsin(c+d*x))^3*(c+d*x)^4+45//256*b^3*d^-1*e^3*arcsin(c+d*x)+-45//256*b^3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)+-9//32*b^2*d^-1*e^3*(c+d*x)^2*(a+b*arcsin(c+d*x))+-3//32*b^2*d^-1*e^3*(c+d*x)^4*(a+b*arcsin(c+d*x))+-3//128*b^3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^3+3//16*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x)^3+9//32*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^2, x) == :(-14//9*b^3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)+-4//3*a*x*b^2*e^2+1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^3*(c+d*x)^3+2//27*b^3*d^-1*e^2*(1+-1*(c+d*x)^2)^3//2+-4//3*b^3*d^-1*e^2*(c+d*x)*arcsin(c+d*x)+-2//9*b^2*d^-1*e^2*(c+d*x)^3*(a+b*arcsin(c+d*x))+2//3*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2+1//3*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x)^2)
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^3+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^3*(c+d*x)^2+3//8*e*b^3*d^-1*arcsin(c+d*x)+-3//4*e*b^2*d^-1*(c+d*x)^2*(a+b*arcsin(c+d*x))+-3//8*e*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)+3//4*b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^3, x) == :(d^-1*(a+b*arcsin(c+d*x))^3*(c+d*x)+-6*a*x*b^2+-6*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)+-6*b^3*d^-1*(c+d*x)*arcsin(c+d*x)+3*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2)
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^-1, x) == :(d^-1*e^-1*(a+b*arcsin(c+d*x))^3*log(1+-1*exp(2*im*arcsin(c+d*x)))+-1//4*im*b^-1*d^-1*e^-1*(a+b*arcsin(c+d*x))^4+3//2*b^2*d^-1*e^-1*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(3,exp(2*im*arcsin(c+d*x)))+3//4*im*b^3*d^-1*e^-1*Polylogarithms.polylog(4,exp(2*im*arcsin(c+d*x)))+-3//2*im*b*d^-1*e^-1*(a+b*arcsin(c+d*x))^2*Polylogarithms.polylog(2,exp(2*im*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^-2, x) == :(-1*d^-1*e^-2*(a+b*arcsin(c+d*x))^3*(c+d*x)^-1+-6*b^3*d^-1*e^-2*Polylogarithms.polylog(3,-1*exp(im*arcsin(c+d*x)))+6*b^3*d^-1*e^-2*Polylogarithms.polylog(3,exp(im*arcsin(c+d*x)))+-6*b*d^-1*e^-2*(a+b*arcsin(c+d*x))^2*arctanh(exp(im*arcsin(c+d*x)))+-6*im*b^2*d^-1*e^-2*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+6*im*b^2*d^-1*e^-2*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^-3, x) == :(-1//2*d^-1*e^-3*(a+b*arcsin(c+d*x))^3*(c+d*x)^-2+3*b^2*d^-1*e^-3*(a+b*arcsin(c+d*x))*log(1+-1*exp(2*im*arcsin(c+d*x)))+-3//2*im*b*d^-1*e^-3*(a+b*arcsin(c+d*x))^2+-3//2*im*b^3*d^-1*e^-3*Polylogarithms.polylog(2,exp(2*im*arcsin(c+d*x)))+-3//2*b*d^-1*e^-3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x)^-1)
@test integrate((a+b*arcsin(c+d*x))^3*(c*e+d*e*x)^-4, x) == :(b^3*d^-1*e^-4*Polylogarithms.polylog(3,exp(im*arcsin(c+d*x)))+-1*b^3*d^-1*e^-4*Polylogarithms.polylog(3,-1*exp(im*arcsin(c+d*x)))+-1*b^3*d^-1*e^-4*arctanh((1+-1*(c+d*x)^2)^(1/2))+-1//3*d^-1*e^-4*(a+b*arcsin(c+d*x))^3*(c+d*x)^-3+-1*b*d^-1*e^-4*(a+b*arcsin(c+d*x))^2*arctanh(exp(im*arcsin(c+d*x)))+-1*b^2*d^-1*e^-4*(c+d*x)^-1*(a+b*arcsin(c+d*x))+im*b^2*d^-1*e^-4*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x)))+-1*im*b^2*d^-1*e^-4*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+-1//2*b*d^-1*e^-4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2*(c+d*x)^-2)
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x)^3, x) == :(-3//32*d^-1*e^3*(a+b*arcsin(c+d*x))^4+1//4*d^-1*e^3*(a+b*arcsin(c+d*x))^4*(c+d*x)^4+3//128*b^4*d^-1*e^3*(c+d*x)^4+45//128*b^2*d^-1*e^3*(a+b*arcsin(c+d*x))^2+45//128*b^4*d^-1*e^3*(c+d*x)^2+-9//16*b^2*d^-1*e^3*(a+b*arcsin(c+d*x))^2*(c+d*x)^2+-3//16*b^2*d^-1*e^3*(a+b*arcsin(c+d*x))^2*(c+d*x)^4+-45//64*b^3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))*(c+d*x)+-3//32*b^3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^3*(a+b*arcsin(c+d*x))+1//4*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3*(c+d*x)^3+3//8*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x)^2, x) == :(160//27*x*b^4*e^2+1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^4*(c+d*x)^3+8//81*b^4*d^-1*e^2*(c+d*x)^3+-160//27*b^3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))+-8//3*b^2*d^-1*e^2*(a+b*arcsin(c+d*x))^2*(c+d*x)+-4//9*b^2*d^-1*e^2*(a+b*arcsin(c+d*x))^2*(c+d*x)^3+8//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3+-8//27*b^3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(c+d*x)^2*(a+b*arcsin(c+d*x))+4//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3*(c+d*x)^2)
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^4+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^4*(c+d*x)^2+3//4*e*b^2*d^-1*(a+b*arcsin(c+d*x))^2+3//4*e*b^4*d^-1*(c+d*x)^2+-3//2*e*b^2*d^-1*(a+b*arcsin(c+d*x))^2*(c+d*x)^2+b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3*(c+d*x)+-3//2*e*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^4, x) == :(24*x*b^4+d^-1*(a+b*arcsin(c+d*x))^4*(c+d*x)+-24*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))+-12*b^2*d^-1*(a+b*arcsin(c+d*x))^2*(c+d*x)+4*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3)
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x)^-1, x) == :(d^-1*e^-1*(a+b*arcsin(c+d*x))^4*log(1+-1*exp(2*im*arcsin(c+d*x)))+-3//2*b^4*d^-1*e^-1*Polylogarithms.polylog(5,exp(2*im*arcsin(c+d*x)))+3*b^2*d^-1*e^-1*(a+b*arcsin(c+d*x))^2*Polylogarithms.polylog(3,exp(2*im*arcsin(c+d*x)))+-1//5*im*b^-1*d^-1*e^-1*(a+b*arcsin(c+d*x))^5+-2*im*b*d^-1*e^-1*(a+b*arcsin(c+d*x))^3*Polylogarithms.polylog(2,exp(2*im*arcsin(c+d*x)))+3*im*b^3*d^-1*e^-1*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(4,exp(2*im*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x)^-2, x) == :(-1*d^-1*e^-2*(a+b*arcsin(c+d*x))^4*(c+d*x)^-1+-24*im*b^4*d^-1*e^-2*Polylogarithms.polylog(4,-1*exp(im*arcsin(c+d*x)))+-24*b^3*d^-1*e^-2*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(3,-1*exp(im*arcsin(c+d*x)))+-8*b*d^-1*e^-2*(a+b*arcsin(c+d*x))^3*arctanh(exp(im*arcsin(c+d*x)))+24*im*b^4*d^-1*e^-2*Polylogarithms.polylog(4,exp(im*arcsin(c+d*x)))+24*b^3*d^-1*e^-2*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(3,exp(im*arcsin(c+d*x)))+-12*im*b^2*d^-1*e^-2*(a+b*arcsin(c+d*x))^2*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+12*im*b^2*d^-1*e^-2*(a+b*arcsin(c+d*x))^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x)^-3, x) == :(3*b^4*d^-1*e^-3*Polylogarithms.polylog(3,exp(2*im*arcsin(c+d*x)))+-1//2*d^-1*e^-3*(a+b*arcsin(c+d*x))^4*(c+d*x)^-2+-2*im*b*d^-1*e^-3*(a+b*arcsin(c+d*x))^3+6*b^2*d^-1*e^-3*(a+b*arcsin(c+d*x))^2*log(1+-1*exp(2*im*arcsin(c+d*x)))+-6*im*b^3*d^-1*e^-3*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(2,exp(2*im*arcsin(c+d*x)))+-2*b*d^-1*e^-3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3*(c+d*x)^-1)
@test integrate((a+b*arcsin(c+d*x))^4*(c*e+d*e*x)^-4, x) == :(-1//3*d^-1*e^-4*(a+b*arcsin(c+d*x))^4*(c+d*x)^-3+-8*b^3*d^-1*e^-4*(a+b*arcsin(c+d*x))*arctanh(exp(im*arcsin(c+d*x)))+-4*im*b^4*d^-1*e^-4*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+-4*im*b^4*d^-1*e^-4*Polylogarithms.polylog(4,-1*exp(im*arcsin(c+d*x)))+-4*b^3*d^-1*e^-4*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(3,-1*exp(im*arcsin(c+d*x)))+-2*b^2*d^-1*e^-4*(a+b*arcsin(c+d*x))^2*(c+d*x)^-1+4*im*b^4*d^-1*e^-4*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x)))+4*im*b^4*d^-1*e^-4*Polylogarithms.polylog(4,exp(im*arcsin(c+d*x)))+4*b^3*d^-1*e^-4*(a+b*arcsin(c+d*x))*Polylogarithms.polylog(3,exp(im*arcsin(c+d*x)))+-4//3*b*d^-1*e^-4*(a+b*arcsin(c+d*x))^3*arctanh(exp(im*arcsin(c+d*x)))+-2*im*b^2*d^-1*e^-4*(a+b*arcsin(c+d*x))^2*Polylogarithms.polylog(2,exp(im*arcsin(c+d*x)))+2*im*b^2*d^-1*e^-4*(a+b*arcsin(c+d*x))^2*Polylogarithms.polylog(2,-1*exp(im*arcsin(c+d*x)))+-2//3*b*d^-1*e^-4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3*(c+d*x)^-2)
@test integrate((a+b*arcsin(c+d*x))^5, x) == :(d^-1*(a+b*arcsin(c+d*x))^5*(c+d*x)+120*a*x*b^4+120*b^5*d^-1*(1+-1*(c+d*x)^2)^(1/2)+-60*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^2+-20*b^2*d^-1*(a+b*arcsin(c+d*x))^3*(c+d*x)+5*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^4+120*b^5*d^-1*(c+d*x)*arcsin(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^-1*(c*e+d*e*x)^4, x) == :(-3//16*b^-1*d^-1*e^4*cos(3*a*b^-1)*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)+-3//16*b^-1*d^-1*e^4*sin(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+1//8*b^-1*d^-1*e^4*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c+d*x))+1//8*b^-1*d^-1*e^4*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+1//16*b^-1*d^-1*e^4*cos(5*a*b^-1)*cosintegral(5*arcsin(c+d*x)+5*a*b^-1)+1//16*b^-1*d^-1*e^4*sin(5*a*b^-1)*sinintegral(5*arcsin(c+d*x)+5*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1*(c*e+d*e*x)^3, x) == :(-1//4*b^-1*d^-1*e^3*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)*sin(2*a*b^-1)+-1//8*b^-1*d^-1*e^3*cos(4*a*b^-1)*sinintegral(4*arcsin(c+d*x)+4*a*b^-1)+1//4*b^-1*d^-1*e^3*cos(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+1//8*b^-1*d^-1*e^3*cosintegral(4*arcsin(c+d*x)+4*a*b^-1)*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1*(c*e+d*e*x)^2, x) == :(-1//4*b^-1*d^-1*e^2*cos(3*a*b^-1)*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)+-1//4*b^-1*d^-1*e^2*sin(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+1//4*b^-1*d^-1*e^2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c+d*x))+1//4*b^-1*d^-1*e^2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^-1*(c*e+d*e*x), x) == :((1/2)*e*b^-1*d^-1*cos(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+-1//2*e*b^-1*d^-1*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1, x) == :(b^-1*d^-1*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c+d*x)))+b^-1*d^-1*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^-2*(c*e+d*e*x)^4, x) == :(-9//16*b^-2*d^-1*e^4*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)*sin(3*a*b^-1)+-5//16*b^-2*d^-1*e^4*cos(5*a*b^-1)*sinintegral(5*arcsin(c+d*x)+5*a*b^-1)+-1//8*b^-2*d^-1*e^4*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+1//8*b^-2*d^-1*e^4*cosintegral(a*b^-1+arcsin(c+d*x))*sin(a*b^-1)+5//16*b^-2*d^-1*e^4*cosintegral(5*arcsin(c+d*x)+5*a*b^-1)*sin(5*a*b^-1)+9//16*b^-2*d^-1*e^4*cos(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+-1*b^-1*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^4)
@test integrate((a+b*arcsin(c+d*x))^-2*(c*e+d*e*x)^3, x) == :((1/2)*b^-2*d^-1*e^3*cos(2*a*b^-1)*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)+(1/2)*b^-2*d^-1*e^3*sin(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+-1//2*b^-2*d^-1*e^3*cos(4*a*b^-1)*cosintegral(4*arcsin(c+d*x)+4*a*b^-1)+-1//2*b^-2*d^-1*e^3*sin(4*a*b^-1)*sinintegral(4*arcsin(c+d*x)+4*a*b^-1)+-1*b^-1*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^3)
@test integrate((a+b*arcsin(c+d*x))^-2*(c*e+d*e*x)^2, x) == :(-3//4*b^-2*d^-1*e^2*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)*sin(3*a*b^-1)+-1//4*b^-2*d^-1*e^2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+1//4*b^-2*d^-1*e^2*cosintegral(a*b^-1+arcsin(c+d*x))*sin(a*b^-1)+3//4*b^-2*d^-1*e^2*cos(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+-1*b^-1*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^2)
@test integrate((a+b*arcsin(c+d*x))^-2*(c*e+d*e*x), x) == :(e*b^-2*d^-1*cos(2*a*b^-1)*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)+e*b^-2*d^-1*sin(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+-1*e*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^-2, x) == :(b^-2*d^-1*cosintegral(a*b^-1+arcsin(c+d*x))*sin(a*b^-1)+-1*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1+-1*b^-2*d^-1*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x)))
@test integrate((a+b*arcsin(c+d*x))^-3*(c*e+d*e*x)^4, x) == :(-2*b^-2*d^-1*e^4*(a+b*arcsin(c+d*x))^-1*(c+d*x)^3+-25//32*b^-3*d^-1*e^4*cos(5*a*b^-1)*cosintegral(5*arcsin(c+d*x)+5*a*b^-1)+-25//32*b^-3*d^-1*e^4*sin(5*a*b^-1)*sinintegral(5*arcsin(c+d*x)+5*a*b^-1)+-1//16*b^-3*d^-1*e^4*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c+d*x))+-1//16*b^-3*d^-1*e^4*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+5//2*b^-2*d^-1*e^4*(a+b*arcsin(c+d*x))^-1*(c+d*x)^5+27//32*b^-3*d^-1*e^4*cos(3*a*b^-1)*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)+27//32*b^-3*d^-1*e^4*sin(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+-1//2*b^-1*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-2*(c+d*x)^4)
@test integrate((a+b*arcsin(c+d*x))^-3*(c*e+d*e*x)^3, x) == :(b^-3*d^-1*e^3*cos(4*a*b^-1)*sinintegral(4*arcsin(c+d*x)+4*a*b^-1)+(1/2)*b^-3*d^-1*e^3*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)*sin(2*a*b^-1)+-1*b^-3*d^-1*e^3*cosintegral(4*arcsin(c+d*x)+4*a*b^-1)*sin(4*a*b^-1)+2*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-1*(c+d*x)^4+-3//2*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-1*(c+d*x)^2+-1//2*b^-3*d^-1*e^3*cos(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+-1//2*b^-1*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-2*(c+d*x)^3)
@test integrate((a+b*arcsin(c+d*x))^-3*(c*e+d*e*x)^2, x) == :(b^-3*d^-1*e^2*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c+d*x)))+b^-3*d^-1*e^2*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c+d*x)))+-1*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-1*(c+d*x)+-9//8*b^-3*d^-1*e^2*cos(a*b^-1)*cosintegral(a*b^-1+arcsin(c+d*x))+-9//8*b^-3*d^-1*e^2*sin(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+3//2*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-1*(c+d*x)^3+9//8*b^-3*d^-1*e^2*cos(3*a*b^-1)*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)+9//8*b^-3*d^-1*e^2*sin(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+-1//2*b^-1*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-2*(c+d*x)^2)
@test integrate((a+b*arcsin(c+d*x))^-3*(c*e+d*e*x), x) == :(-1//2*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1+e*b^-3*d^-1*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)*sin(2*a*b^-1)+e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1*(c+d*x)^2+-1*e*b^-3*d^-1*cos(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+-1//2*e*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-2*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^-3, x) == :((1/2)*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1*(c+d*x)+-1//2*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-2+-1//2*b^-3*d^-1*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c+d*x)))+-1//2*b^-3*d^-1*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c+d*x))))
@test integrate((a+b*arcsin(c+d*x))^-4*(c*e+d*e*x)^4, x) == :(-125//96*b^-4*d^-1*e^4*cosintegral(5*arcsin(c+d*x)+5*a*b^-1)*sin(5*a*b^-1)+-27//32*b^-4*d^-1*e^4*cos(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+-2//3*b^-2*d^-1*e^4*(a+b*arcsin(c+d*x))^-2*(c+d*x)^3+-1//48*b^-4*d^-1*e^4*cosintegral(a*b^-1+arcsin(c+d*x))*sin(a*b^-1)+1//48*b^-4*d^-1*e^4*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+5//6*b^-2*d^-1*e^4*(a+b*arcsin(c+d*x))^-2*(c+d*x)^5+27//32*b^-4*d^-1*e^4*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)*sin(3*a*b^-1)+125//96*b^-4*d^-1*e^4*cos(5*a*b^-1)*sinintegral(5*arcsin(c+d*x)+5*a*b^-1)+-2*b^-3*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^2+-1//3*b^-1*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3*(c+d*x)^4+25//6*b^-3*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^4)
@test integrate((a+b*arcsin(c+d*x))^-4*(c*e+d*e*x)^3, x) == :(-1//2*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-2*(c+d*x)^2+-1//3*b^-4*d^-1*e^3*cos(2*a*b^-1)*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)+-1//3*b^-4*d^-1*e^3*sin(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+2//3*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-2*(c+d*x)^4+4//3*b^-4*d^-1*e^3*cos(4*a*b^-1)*cosintegral(4*arcsin(c+d*x)+4*a*b^-1)+4//3*b^-4*d^-1*e^3*sin(4*a*b^-1)*sinintegral(4*arcsin(c+d*x)+4*a*b^-1)+-1*b^-3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)+-1//3*b^-1*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3*(c+d*x)^3+8//3*b^-3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^3)
@test integrate((a+b*arcsin(c+d*x))^-4*(c*e+d*e*x)^2, x) == :((1/2)*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-2*(c+d*x)^3+-9//8*b^-4*d^-1*e^2*cos(3*a*b^-1)*sinintegral(3*arcsin(c+d*x)+3*a*b^-1)+-1//3*b^-3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1+-1//3*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-2*(c+d*x)+-1//24*b^-4*d^-1*e^2*cosintegral(a*b^-1+arcsin(c+d*x))*sin(a*b^-1)+1//24*b^-4*d^-1*e^2*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+9//8*b^-4*d^-1*e^2*cosintegral(3*arcsin(c+d*x)+3*a*b^-1)*sin(3*a*b^-1)+-1//3*b^-1*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3*(c+d*x)^2+3//2*b^-3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x)^2)
@test integrate((a+b*arcsin(c+d*x))^-4*(c*e+d*e*x), x) == :(-1//6*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-2+-2//3*e*b^-4*d^-1*cos(2*a*b^-1)*cosintegral(2*arcsin(c+d*x)+2*a*b^-1)+-2//3*e*b^-4*d^-1*sin(2*a*b^-1)*sinintegral(2*arcsin(c+d*x)+2*a*b^-1)+1//3*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-2*(c+d*x)^2+-1//3*e*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3*(c+d*x)+2//3*e*b^-3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^-4, x) == :(-1//3*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3+-1//6*b^-4*d^-1*cosintegral(a*b^-1+arcsin(c+d*x))*sin(a*b^-1)+1//6*b^-4*d^-1*cos(a*b^-1)*sinintegral(a*b^-1+arcsin(c+d*x))+1//6*b^-3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1+1//6*b^-2*d^-1*(a+b*arcsin(c+d*x))^-2*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^-5, x) == :(-1//4*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-4+-1//24*b^-4*d^-1*(a+b*arcsin(c+d*x))^-1*(c+d*x)+1//12*b^-2*d^-1*(a+b*arcsin(c+d*x))^-3*(c+d*x)+1//24*b^-5*d^-1*cos(a*b^-1)*cosintegral(b^-1*(a+b*arcsin(c+d*x)))+1//24*b^-5*d^-1*sin(a*b^-1)*sinintegral(b^-1*(a+b*arcsin(c+d*x)))+1//24*b^-3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-2)
@test integrate((a+b*arcsin(c+d*x))^(1/2)*(c*e+d*e*x)^3, x) == :(-3//32*d^-1*e^3*(a+b*arcsin(c+d*x))^(1/2)+1//4*d^-1*e^3*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^4+1//16*pi^(1/2)*b^(1/2)*d^-1*e^3*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//16*pi^(1/2)*b^(1/2)*d^-1*e^3*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-1//128*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*e^3*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//128*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*e^3*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^(1/2)*(c*e+d*e*x)^2, x) == :(1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^3+-1//8*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*e^2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//72*6^(1/2)*pi^(1/2)*b^(1/2)*d^-1*e^2*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+1//8*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*e^2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+1//72*6^(1/2)*pi^(1/2)*b^(1/2)*d^-1*e^2*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^(1/2)*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^(1/2)+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^2+1//8*e*pi^(1/2)*b^(1/2)*d^-1*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//8*e*pi^(1/2)*b^(1/2)*d^-1*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^(1/2), x) == :(d^-1*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+(1/2)*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+-1//2*2^(1/2)*pi^(1/2)*b^(1/2)*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^3//2*(c*e+d*e*x)^3, x) == :(-3//32*d^-1*e^3*(a+b*arcsin(c+d*x))^3//2+1//4*d^-1*e^3*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^4+-3//64*pi^(1/2)*b^3//2*d^-1*e^3*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+3//32*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^3+3//64*pi^(1/2)*b^3//2*d^-1*e^3*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+9//64*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+-3//1024*2^(1/2)*pi^(1/2)*b^3//2*d^-1*e^3*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1)+3//1024*2^(1/2)*pi^(1/2)*b^3//2*d^-1*e^3*cos(4*a*b^-1)*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^3//2*(c*e+d*e*x)^2, x) == :(1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^3+1//3*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+1//6*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^2+-3//16*2^(1/2)*pi^(1/2)*b^3//2*d^-1*e^2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-3//16*2^(1/2)*pi^(1/2)*b^3//2*d^-1*e^2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+1//144*6^(1/2)*pi^(1/2)*b^3//2*d^-1*e^2*cos(3*a*b^-1)*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//144*6^(1/2)*pi^(1/2)*b^3//2*d^-1*e^2*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^3//2*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^3//2+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^2+-3//32*e*pi^(1/2)*b^3//2*d^-1*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+3//8*b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+3//32*e*pi^(1/2)*b^3//2*d^-1*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^3//2, x) == :(d^-1*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+3//2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+-3//4*2^(1/2)*pi^(1/2)*b^3//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-3//4*2^(1/2)*pi^(1/2)*b^3//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^5//2*(c*e+d*e*x)^3, x) == :(-3//32*d^-1*e^3*(a+b*arcsin(c+d*x))^5//2+1//4*d^-1*e^3*(a+b*arcsin(c+d*x))^5//2*(c+d*x)^4+225//2048*b^2*d^-1*e^3*(a+b*arcsin(c+d*x))^(1/2)+-45//256*b^2*d^-1*e^3*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^2+-15//256*b^2*d^-1*e^3*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^4+-15//256*pi^(1/2)*b^5//2*d^-1*e^3*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-15//256*pi^(1/2)*b^5//2*d^-1*e^3*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+5//32*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^3+15//64*b*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+15//8192*2^(1/2)*pi^(1/2)*b^5//2*d^-1*e^3*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+15//8192*2^(1/2)*pi^(1/2)*b^5//2*d^-1*e^3*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^5//2*(c*e+d*e*x)^2, x) == :(1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^5//2*(c+d*x)^3+-5//6*b^2*d^-1*e^2*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+-5//36*b^2*d^-1*e^2*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^3+5//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2+5//18*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^2+-15//32*2^(1/2)*pi^(1/2)*b^5//2*d^-1*e^2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+-5//864*6^(1/2)*pi^(1/2)*b^5//2*d^-1*e^2*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+5//864*6^(1/2)*pi^(1/2)*b^5//2*d^-1*e^2*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+15//32*2^(1/2)*pi^(1/2)*b^5//2*d^-1*e^2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^5//2*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^5//2+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^5//2*(c+d*x)^2+15//64*e*b^2*d^-1*(a+b*arcsin(c+d*x))^(1/2)+-15//32*e*b^2*d^-1*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^2+-15//128*e*pi^(1/2)*b^5//2*d^-1*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-15//128*e*pi^(1/2)*b^5//2*d^-1*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+5//8*b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^5//2, x) == :(d^-1*(a+b*arcsin(c+d*x))^5//2*(c+d*x)+-15//4*b^2*d^-1*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+5//2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^3//2+-15//8*2^(1/2)*pi^(1/2)*b^5//2*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+15//8*2^(1/2)*pi^(1/2)*b^5//2*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^7//2*(c*e+d*e*x)^2, x) == :(1//3*d^-1*e^2*(a+b*arcsin(c+d*x))^7//2*(c+d*x)^3+-175//54*b^3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+-35//18*b^2*d^-1*e^2*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+-35//108*b^2*d^-1*e^2*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^3+7//9*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^5//2+-35//216*b^3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)^2+7//18*b*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^5//2*(c+d*x)^2+-35//5184*6^(1/2)*pi^(1/2)*b^7//2*d^-1*e^2*cos(3*a*b^-1)*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-35//5184*6^(1/2)*pi^(1/2)*b^7//2*d^-1*e^2*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+105//64*2^(1/2)*pi^(1/2)*b^7//2*d^-1*e^2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+105//64*2^(1/2)*pi^(1/2)*b^7//2*d^-1*e^2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^7//2*(c*e+d*e*x), x) == :(-1//4*e*d^-1*(a+b*arcsin(c+d*x))^7//2+(1/2)*e*d^-1*(a+b*arcsin(c+d*x))^7//2*(c+d*x)^2+35//64*e*b^2*d^-1*(a+b*arcsin(c+d*x))^3//2+-35//32*e*b^2*d^-1*(a+b*arcsin(c+d*x))^3//2*(c+d*x)^2+-105//128*e*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)*(c+d*x)+-105//512*e*pi^(1/2)*b^7//2*d^-1*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+7//8*b*e*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^5//2*(c+d*x)+105//512*e*pi^(1/2)*b^7//2*d^-1*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^7//2, x) == :(d^-1*(a+b*arcsin(c+d*x))^7//2*(c+d*x)+-105//8*b^3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^(1/2)+-35//4*b^2*d^-1*(a+b*arcsin(c+d*x))^3//2*(c+d*x)+7//2*b*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^5//2+105//16*2^(1/2)*pi^(1/2)*b^7//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+105//16*2^(1/2)*pi^(1/2)*b^7//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1//2*(c*e+d*e*x)^4, x) == :(-1//16*6^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^4*cos(3*a*b^-1)*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//16*6^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^4*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+1//8*2^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^4*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//8*2^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^4*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+1//80*10^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^4*cos(5*a*b^-1)*fresnelc(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//80*10^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^4*fresnels(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(5*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1//2*(c*e+d*e*x)^3, x) == :(-1//4*pi^(1/2)*b^-1//2*d^-1*e^3*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+1//4*pi^(1/2)*b^-1//2*d^-1*e^3*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//16*2^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^3*cos(4*a*b^-1)*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//16*2^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^3*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1//2*(c*e+d*e*x)^2, x) == :(-1//12*6^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^2*cos(3*a*b^-1)*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//12*6^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^2*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+1//4*2^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//4*2^(1/2)*pi^(1/2)*b^-1//2*d^-1*e^2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1//2*(c*e+d*e*x), x) == :((1/2)*e*pi^(1/2)*b^-1//2*d^-1*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//2*e*pi^(1/2)*b^-1//2*d^-1*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-1//2, x) == :(2^(1/2)*pi^(1/2)*b^-1//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2^(1/2)*pi^(1/2)*b^-1//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-3//2*(c*e+d*e*x)^4, x) == :(-2*b^-1*d^-1*e^4*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^4+-3//8*6^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^4*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+-1//4*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^4*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//8*10^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^4*cos(5*a*b^-1)*fresnels(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+1//4*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^4*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+1//8*10^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^4*fresnelc(10^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(5*a*b^-1)+3//8*6^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^4*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^-3//2*(c*e+d*e*x)^3, x) == :(pi^(1/2)*b^-3//2*d^-1*e^3*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+pi^(1/2)*b^-3//2*d^-1*e^3*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-2*b^-1*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^3+-1//2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^3*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^3*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-3//2*(c*e+d*e*x)^2, x) == :(-2*b^-1*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^2+(1/2)*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+(1/2)*6^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^2*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//2*6^(1/2)*pi^(1/2)*b^-3//2*d^-1*e^2*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-3//2*(c*e+d*e*x), x) == :(-2*e*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)+2*e*pi^(1/2)*b^-3//2*d^-1*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2*e*pi^(1/2)*b^-3//2*d^-1*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-3//2, x) == :(-2*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+-2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+2*2^(1/2)*pi^(1/2)*b^-3//2*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-5//2*(c*e+d*e*x)^3, x) == :(-4*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^2+16//3*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^4+-4//3*pi^(1/2)*b^-5//2*d^-1*e^3*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-2//3*b^-1*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^3+4//3*pi^(1/2)*b^-5//2*d^-1*e^3*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-4//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*e^3*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1)+4//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*e^3*cos(4*a*b^-1)*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((a+b*arcsin(c+d*x))^-5//2*(c*e+d*e*x)^2, x) == :(4*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^3+-8//3*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)+-2//3*b^-1*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^2+6^(1/2)*pi^(1/2)*b^-5//2*d^-1*e^2*cos(3*a*b^-1)*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+6^(1/2)*pi^(1/2)*b^-5//2*d^-1*e^2*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1)+-1//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*e^2*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-1//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*e^2*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-5//2*(c*e+d*e*x), x) == :(-4//3*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1//2+8//3*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^2+-8//3*e*pi^(1/2)*b^-5//2*d^-1*cos(2*a*b^-1)*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-2//3*e*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)+8//3*e*pi^(1/2)*b^-5//2*d^-1*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-5//2, x) == :(-2//3*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-3//2+1//3*b^-2*d^-1*(a+b*arcsin(c+d*x))^-1//2*(4c+4*d*x)+-4//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*cos(a*b^-1)*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-4//3*2^(1/2)*pi^(1/2)*b^-5//2*d^-1*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-7//2*(c*e+d*e*x)^3, x) == :(-4//5*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^2+16//15*b^-2*d^-1*e^3*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^4+-16//5*b^-3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)+-16//15*pi^(1/2)*b^-7//2*d^-1*e^3*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-16//15*pi^(1/2)*b^-7//2*d^-1*e^3*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-2//5*b^-1*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2*(c+d*x)^3+128//15*b^-3*d^-1*e^3*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^3+32//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*e^3*cos(4*a*b^-1)*fresnelc(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+32//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*e^3*fresnels(2*2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(4*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-7//2*(c*e+d*e*x)^2, x) == :(-16//15*b^-3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+-8//15*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)+4//5*b^-2*d^-1*e^2*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^3+-2//5*b^-1*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2*(c+d*x)^2+24//5*b^-3*d^-1*e^2*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x)^2+-6//5*6^(1/2)*pi^(1/2)*b^-7//2*d^-1*e^2*cos(3*a*b^-1)*fresnels(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-2//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*e^2*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+2//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*e^2*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+6//5*6^(1/2)*pi^(1/2)*b^-7//2*d^-1*e^2*fresnelc(6^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(3*a*b^-1))
@test integrate((a+b*arcsin(c+d*x))^-7//2*(c*e+d*e*x), x) == :(-4//15*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-3//2+8//15*e*b^-2*d^-1*(a+b*arcsin(c+d*x))^-3//2*(c+d*x)^2+-32//15*e*pi^(1/2)*b^-7//2*d^-1*cos(2*a*b^-1)*fresnelc(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))+-32//15*e*pi^(1/2)*b^-7//2*d^-1*fresnels(2*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(2*a*b^-1)+-2//5*e*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2*(c+d*x)+32//15*e*b^-3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2*(c+d*x))
@test integrate((a+b*arcsin(c+d*x))^-7//2, x) == :(-2//5*b^-1*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-5//2+1//15*b^-2*d^-1*(a+b*arcsin(c+d*x))^-3//2*(4c+4*d*x)+8//15*b^-3*d^-1*(1+-1*(c+d*x)^2)^(1/2)*(a+b*arcsin(c+d*x))^-1//2+-8//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*fresnelc(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2))*sin(a*b^-1)+8//15*2^(1/2)*pi^(1/2)*b^-7//2*d^-1*cos(a*b^-1)*fresnels(2^(1/2)*pi^-1//2*b^-1//2*(a+b*arcsin(c+d*x))^(1/2)))
@test integrate((c*e+d*e*x)^7//2*(a+b*arcsin(c+d*x)), x) == :(2//9*d^-1*e^-1*(e*(c+d*x))^9//2*(a+b*arcsin(c+d*x))+4//81*b*d^-1*(e*(c+d*x))^7//2*(1+-1*(c+d*x)^2)^(1/2)+28//405*b*d^-1*e^2*(e*(c+d*x))^3//2*(1+-1*(c+d*x)^2)^(1/2)+28//135*b*d^-1*e^3*(e*(c+d*x))^(1/2)*(c+d*x)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1c+-1*d*x)^(1/2)),2))
@test integrate((c*e+d*e*x)^5//2*(a+b*arcsin(c+d*x)), x) == :(-20//147*b*d^-1*e^5//2*Elliptic.F(arcsin(e^-1//2*(e*(c+d*x))^(1/2)),-1)+2//7*d^-1*e^-1*(e*(c+d*x))^7//2*(a+b*arcsin(c+d*x))+4//49*b*d^-1*(e*(c+d*x))^5//2*(1+-1*(c+d*x)^2)^(1/2)+20//147*b*d^-1*e^2*(e*(c+d*x))^(1/2)*(1+-1*(c+d*x)^2)^(1/2))
@test integrate((c*e+d*e*x)^3//2*(a+b*arcsin(c+d*x)), x) == :(2//5*d^-1*e^-1*(e*(c+d*x))^5//2*(a+b*arcsin(c+d*x))+4//25*b*d^-1*(e*(c+d*x))^3//2*(1+-1*(c+d*x)^2)^(1/2)+12//25*b*e*d^-1*(e*(c+d*x))^(1/2)*(c+d*x)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1c+-1*d*x)^(1/2)),2))
@test integrate((c*e+d*e*x)^(1/2)*(a+b*arcsin(c+d*x)), x) == :(-4//9*b*d^-1*e^(1/2)*Elliptic.F(arcsin(e^-1//2*(e*(c+d*x))^(1/2)),-1)+2//3*d^-1*e^-1*(e*(c+d*x))^3//2*(a+b*arcsin(c+d*x))+4//9*b*d^-1*(e*(c+d*x))^(1/2)*(1+-1*(c+d*x)^2)^(1/2))
@test integrate((c*e+d*e*x)^-1//2*(a+b*arcsin(c+d*x)), x) == :(2*d^-1*e^-1*(e*(c+d*x))^(1/2)*(a+b*arcsin(c+d*x))+4*b*d^-1*e^-1*(e*(c+d*x))^(1/2)*(c+d*x)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1c+-1*d*x)^(1/2)),2))
@test integrate((c*e+d*e*x)^-3//2*(a+b*arcsin(c+d*x)), x) == :(-1*d^-1*e^-1*(e*(c+d*x))^-1//2*(2a+2*b*arcsin(c+d*x))+4*b*d^-1*e^-3//2*Elliptic.F(arcsin(e^-1//2*(e*(c+d*x))^(1/2)),-1))
@test integrate((c*e+d*e*x)^-5//2*(a+b*arcsin(c+d*x)), x) == :(-1//3*d^-1*e^-1*(e*(c+d*x))^-3//2*(2a+2*b*arcsin(c+d*x))+-4//3*b*d^-1*e^-2*(e*(c+d*x))^-1//2*(1+-1*(c+d*x)^2)^(1/2)+4//3*b*d^-1*e^-3*(e*(c+d*x))^(1/2)*(c+d*x)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1c+-1*d*x)^(1/2)),2))
@test integrate((c*e+d*e*x)^-7//2*(a+b*arcsin(c+d*x)), x) == :(-1//5*d^-1*e^-1*(e*(c+d*x))^-5//2*(2a+2*b*arcsin(c+d*x))+4//15*b*d^-1*e^-7//2*Elliptic.F(arcsin(e^-1//2*(e*(c+d*x))^(1/2)),-1)+-4//15*b*d^-1*e^-2*(e*(c+d*x))^-3//2*(1+-1*(c+d*x)^2)^(1/2))
@test integrate((c*e+d*e*x)^-9//2*(a+b*arcsin(c+d*x)), x) == :(-1//7*d^-1*e^-1*(e*(c+d*x))^-7//2*(2a+2*b*arcsin(c+d*x))+-12//35*b*d^-1*e^-4*(e*(c+d*x))^-1//2*(1+-1*(c+d*x)^2)^(1/2)+-4//35*b*d^-1*e^-2*(e*(c+d*x))^-5//2*(1+-1*(c+d*x)^2)^(1/2)+12//35*b*d^-1*e^-5*(e*(c+d*x))^(1/2)*(c+d*x)^-1//2*Elliptic.E(arcsin((1/2)*2^(1/2)*(1+-1c+-1*d*x)^(1/2)),2))
@test integrate((c*e+d*e*x)^-11//2*(a+b*arcsin(c+d*x)), x) == :(-1//9*d^-1*e^-1*(e*(c+d*x))^-9//2*(2a+2*b*arcsin(c+d*x))+20//189*b*d^-1*e^-11//2*Elliptic.F(arcsin(e^-1//2*(e*(c+d*x))^(1/2)),-1)+-20//189*b*d^-1*e^-4*(e*(c+d*x))^-3//2*(1+-1*(c+d*x)^2)^(1/2)+-4//63*b*d^-1*e^-2*(e*(c+d*x))^-7//2*(1+-1*(c+d*x)^2)^(1/2))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x)^3, x) == :(1//8*b^-1*arcsin(a+b*x)^4+3//8*b^-1*(a+b*x)^2+3//8*b^-1*arcsin(a+b*x)^2+-3//4*b^-1*(a+b*x)^2*arcsin(a+b*x)^2+(1/2)*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^3*(a+b*x)+-1//4*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(3a+3*b*x)*arcsin(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x)^2, x) == :(1//4*b^-1*arcsin(a+b*x)+1//6*b^-1*arcsin(a+b*x)^3+-1//2*b^-1*(a+b*x)^2*arcsin(a+b*x)+-1//4*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)+(1/2)*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2*(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x), x) == :(-1//4*b^-1*(a+b*x)^2+1//4*b^-1*arcsin(a+b*x)^2+(1/2)*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(a+b*x)*arcsin(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x)^-1, x) == :((1/2)*b^-1*cosintegral(2*arcsin(a+b*x))+(1/2)*b^-1*log(arcsin(a+b*x)))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x)^-2, x) == :(-1*b^-1*sinintegral(2*arcsin(a+b*x))+-1*b^-1*arcsin(a+b*x)^-1*(1+-1*(a+b*x)^2))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x)^-3, x) == :(-1*b^-1*cosintegral(2*arcsin(a+b*x))+(1/2)*b^-1*arcsin(a+b*x)^-2*(-1+(a+b*x)^2)+b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^-1*(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^(1/2)*arcsin(a+b*x)^-4, x) == :(1//3*b^-1*arcsin(a+b*x)^-1+2//3*b^-1*sinintegral(2*arcsin(a+b*x))+-2//3*b^-1*(a+b*x)^2*arcsin(a+b*x)^-1+-1//3*b^-1*arcsin(a+b*x)^-3*(1+-1*(a+b*x)^2)+1//3*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^-2*(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x)^3, x) == :(-3//128*b^-1*(a+b*x)^4+3//32*b^-1*arcsin(a+b*x)^4+27//128*b^-1*arcsin(a+b*x)^2+51//128*b^-1*(a+b*x)^2+-9//16*b^-1*(a+b*x)^2*arcsin(a+b*x)^2+3//16*b^-1*(1+-1*(a+b*x)^2)^2*arcsin(a+b*x)^2+-1//32*b^-1*(1+-1*(a+b*x)^2)^3//2*(3a+3*b*x)*arcsin(a+b*x)+-1//64*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(45a+45*b*x)*arcsin(a+b*x)+1//4*b^-1*(1+-1*(a+b*x)^2)^3//2*arcsin(a+b*x)^3*(a+b*x)+1//8*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^3*(3a+3*b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x)^2, x) == :(1//8*b^-1*arcsin(a+b*x)^3+9//64*b^-1*arcsin(a+b*x)+-3//8*b^-1*(a+b*x)^2*arcsin(a+b*x)+-1//32*b^-1*(1+-1*(a+b*x)^2)^3//2*(a+b*x)+-1//64*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(15a+15*b*x)+1//8*b^-1*(1+-1*(a+b*x)^2)^2*arcsin(a+b*x)+1//4*b^-1*(1+-1*(a+b*x)^2)^3//2*arcsin(a+b*x)^2*(a+b*x)+1//8*b^-1*(1+-1*(a+b*x)^2)^(1/2)*arcsin(a+b*x)^2*(3a+3*b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x), x) == :(-5//16*b^-1*(a+b*x)^2+1//16*b^-1*(a+b*x)^4+3//16*b^-1*arcsin(a+b*x)^2+1//4*b^-1*(1+-1*(a+b*x)^2)^3//2*(a+b*x)*arcsin(a+b*x)+1//8*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(3a+3*b*x)*arcsin(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x)^-1, x) == :((1/2)*b^-1*cosintegral(2*arcsin(a+b*x))+1//8*b^-1*cosintegral(4*arcsin(a+b*x))+3//8*b^-1*log(arcsin(a+b*x)))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x)^-2, x) == :(-1*b^-1*sinintegral(2*arcsin(a+b*x))+-1//2*b^-1*sinintegral(4*arcsin(a+b*x))+-1*b^-1*(1+-1*(a+b*x)^2)^2*arcsin(a+b*x)^-1)
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x)^-3, x) == :(-1*b^-1*cosintegral(2*arcsin(a+b*x))+-1*b^-1*cosintegral(4*arcsin(a+b*x))+-1//2*b^-1*(1+-1*(a+b*x)^2)^2*arcsin(a+b*x)^-2+b^-1*(1+-1*(a+b*x)^2)^3//2*arcsin(a+b*x)^-1*(2a+2*b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^3//2*arcsin(a+b*x)^-4, x) == :(2//3*b^-1*sinintegral(2*arcsin(a+b*x))+4//3*b^-1*sinintegral(4*arcsin(a+b*x))+-1//3*b^-1*(1+-1*(a+b*x)^2)^2*arcsin(a+b*x)^-3+1//3*b^-1*arcsin(a+b*x)^-1*(2+-2*(a+b*x)^2)+-8//3*b^-1*(a+b*x)^2*arcsin(a+b*x)^-1*(1+-1*(a+b*x)^2)+1//3*b^-1*(1+-1*(a+b*x)^2)^3//2*arcsin(a+b*x)^-2*(2a+2*b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1//2*arcsin(a+b*x)^n, x) == :(b^-1*(1+n)^-1*arcsin(a+b*x)^(1+n))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1//2*arcsin(a+b*x)^2, x) == :(1//3*b^-1*arcsin(a+b*x)^3)
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1//2*arcsin(a+b*x), x) == :((1/2)*b^-1*arcsin(a+b*x)^2)
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1//2*arcsin(a+b*x)^-1, x) == :(b^-1*log(arcsin(a+b*x)))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1//2*arcsin(a+b*x)^-2, x) == :(-1*b^-1*arcsin(a+b*x)^-1)
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-1//2*arcsin(a+b*x)^-3, x) == :(-1//2*b^-1*arcsin(a+b*x)^-2)
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-3//2*arcsin(a+b*x)^3, x) == :(3//2*b^-1*Polylogarithms.polylog(3,-1*exp(2*im*arcsin(a+b*x)))+-1*im*b^-1*arcsin(a+b*x)^3+3*b^-1*arcsin(a+b*x)^2*log(1+exp(2*im*arcsin(a+b*x)))+b^-1*(1+-1*(a+b*x)^2)^-1//2*arcsin(a+b*x)^3*(a+b*x)+-3*im*b^-1*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a+b*x)))*arcsin(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-3//2*arcsin(a+b*x)^2, x) == :(-1*im*b^-1*arcsin(a+b*x)^2+-1*im*b^-1*Polylogarithms.polylog(2,-1*exp(2*im*arcsin(a+b*x)))+2*b^-1*arcsin(a+b*x)*log(1+exp(2*im*arcsin(a+b*x)))+b^-1*(1+-1*(a+b*x)^2)^-1//2*arcsin(a+b*x)^2*(a+b*x))
@test integrate((1+-1*a^2+-1*b^2*x^2+-2*a*b*x)^-3//2*arcsin(a+b*x), x) == :((1/2)*b^-1*log(1+-1*(a+b*x)^2)+b^-1*(1+-1*(a+b*x)^2)^-1//2*(a+b*x)*arcsin(a+b*x))
@test integrate((c+-1*c*(a+b*x)^2)^-1//2*arcsin(a+b*x), x) == :((1/2)*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(c+-1*c*(a+b*x)^2)^-1//2*arcsin(a+b*x)^2)
@test integrate((c*(1+-1*a^2)+-1*c*b^2*x^2+-2*a*b*c*x)^-1//2*arcsin(a+b*x), x) == :((1/2)*b^-1*(1+-1*(a+b*x)^2)^(1/2)*(c+-1*c*(a+b*x)^2)^-1//2*arcsin(a+b*x)^2)
@test integrate(x^9*(a+b*arcsin(c*x^2)), x) == :(1//10*x^10*(a+b*arcsin(c*x^2))+-1//15*b*c^-5*(1+-1*c^2*x^4)^3//2+1//10*b*c^-5*(1+-1*c^2*x^4)^(1/2)+1//50*b*c^-5*(1+-1*c^2*x^4)^5//2)
@test integrate(x^7*(a+b*arcsin(c*x^2)), x) == :(1//8*x^8*(a+b*arcsin(c*x^2))+-3//64*b*c^-4*arcsin(c*x^2)+1//32*b*c^-1*x^6*(1+-1*c^2*x^4)^(1/2)+3//64*b*c^-3*x^2*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^5*(a+b*arcsin(c*x^2)), x) == :(1//6*x^6*(a+b*arcsin(c*x^2))+-1//18*b*c^-3*(1+-1*c^2*x^4)^3//2+1//6*b*c^-3*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^3*(a+b*arcsin(c*x^2)), x) == :(1//4*x^4*(a+b*arcsin(c*x^2))+-1//8*b*c^-2*arcsin(c*x^2)+1//8*b*c^-1*x^2*(1+-1*c^2*x^4)^(1/2))
@test integrate(x*(a+b*arcsin(c*x^2)), x) == :((1/2)*a*x^2+(1/2)*b*c^-1*(1+-1*c^2*x^4)^(1/2)+(1/2)*b*x^2*arcsin(c*x^2))
@test integrate(x^-1*(a+b*arcsin(c*x^2)), x) == :(a*log(x)+(1/2)*b*arcsin(c*x^2)*log(1+-1*exp(2*im*arcsin(c*x^2)))+-1//4*im*b*arcsin(c*x^2)^2+-1//4*im*b*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x^2))))
@test integrate(x^-3*(a+b*arcsin(c*x^2)), x) == :(-1//2*x^-2*(a+b*arcsin(c*x^2))+-1//2*b*c*arctanh((1+-1*c^2*x^4)^(1/2)))
@test integrate(x^-5*(a+b*arcsin(c*x^2)), x) == :(-1//4*x^-4*(a+b*arcsin(c*x^2))+-1//4*b*c*x^-2*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-7*(a+b*arcsin(c*x^2)), x) == :(-1//6*x^-6*(a+b*arcsin(c*x^2))+-1//12*b*c^3*arctanh((1+-1*c^2*x^4)^(1/2))+-1//12*b*c*x^-4*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-9*(a+b*arcsin(c*x^2)), x) == :(-1//8*x^-8*(a+b*arcsin(c*x^2))+-1//12*b*c^3*x^-2*(1+-1*c^2*x^4)^(1/2)+-1//24*b*c*x^-6*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-11*(a+b*arcsin(c*x^2)), x) == :(-1//10*x^-10*(a+b*arcsin(c*x^2))+-3//80*b*c^5*arctanh((1+-1*c^2*x^4)^(1/2))+-3//80*b*c^3*x^-4*(1+-1*c^2*x^4)^(1/2)+-1//40*b*c*x^-8*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-13*(a+b*arcsin(c*x^2)), x) == :(-1//12*x^-12*(a+b*arcsin(c*x^2))+-2//45*b*c^5*x^-2*(1+-1*c^2*x^4)^(1/2)+-1//45*b*c^3*x^-6*(1+-1*c^2*x^4)^(1/2)+-1//60*b*c*x^-10*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^6*(a+b*arcsin(c*x^2)), x) == :(1//7*x^7*(a+b*arcsin(c*x^2))+-10//147*b*c^-7//2*Elliptic.F(arcsin(x*c^(1/2)),-1)+2//49*b*c^-1*x^5*(1+-1*c^2*x^4)^(1/2)+10//147*b*x*c^-3*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^4*(a+b*arcsin(c*x^2)), x) == :(1//5*x^5*(a+b*arcsin(c*x^2))+-6//25*b*c^-5//2*Elliptic.E(arcsin(x*c^(1/2)),-1)+6//25*b*c^-5//2*Elliptic.F(arcsin(x*c^(1/2)),-1)+2//25*b*c^-1*x^3*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^2*(a+b*arcsin(c*x^2)), x) == :(1//3*x^3*(a+b*arcsin(c*x^2))+-2//9*b*c^-3//2*Elliptic.F(arcsin(x*c^(1/2)),-1)+2//9*b*x*c^-1*(1+-1*c^2*x^4)^(1/2))
@test integrate(a+b*arcsin(c*x^2), x) == :(a*x+b*x*arcsin(c*x^2)+-2*b*c^-1//2*Elliptic.E(arcsin(x*c^(1/2)),-1)+2*b*c^-1//2*Elliptic.F(arcsin(x*c^(1/2)),-1))
@test integrate(x^-2*(a+b*arcsin(c*x^2)), x) == :(-1*x^-1*(a+b*arcsin(c*x^2))+2*b*c^(1/2)*Elliptic.F(arcsin(x*c^(1/2)),-1))
@test integrate(x^-4*(a+b*arcsin(c*x^2)), x) == :(-1//3*x^-3*(a+b*arcsin(c*x^2))+-2//3*b*c^3//2*Elliptic.E(arcsin(x*c^(1/2)),-1)+2//3*b*c^3//2*Elliptic.F(arcsin(x*c^(1/2)),-1)+-2//3*b*c*x^-1*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-6*(a+b*arcsin(c*x^2)), x) == :(-1//5*x^-5*(a+b*arcsin(c*x^2))+2//15*b*c^5//2*Elliptic.F(arcsin(x*c^(1/2)),-1)+-2//15*b*c*x^-3*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-8*(a+b*arcsin(c*x^2)), x) == :(-1//7*x^-7*(a+b*arcsin(c*x^2))+-6//35*b*c^7//2*Elliptic.E(arcsin(x*c^(1/2)),-1)+6//35*b*c^7//2*Elliptic.F(arcsin(x*c^(1/2)),-1)+-6//35*b*c^3*x^-1*(1+-1*c^2*x^4)^(1/2)+-2//35*b*c*x^-5*(1+-1*c^2*x^4)^(1/2))
@test integrate(x^-1*arcsin(a*x^5), x) == :(-1//10*im*arcsin(a*x^5)^2+-1//10*im*Polylogarithms.polylog(2,exp(2*im*arcsin(a*x^5)))+1//5*arcsin(a*x^5)*log(1+-1*exp(2*im*arcsin(a*x^5))))
@test integrate(x^2*arcsin(x^(1/2)), x) == :(5//96*arcsin(1+-2x)+1//3*x^3*arcsin(x^(1/2))+1//18*x^5//2*(1+-1x)^(1/2)+5//48*x^(1/2)*(1+-1x)^(1/2)+5//72*x^3//2*(1+-1x)^(1/2))
@test integrate(x*arcsin(x^(1/2)), x) == :(3//32*arcsin(1+-2x)+(1/2)*x^2*arcsin(x^(1/2))+1//8*x^3//2*(1+-1x)^(1/2)+3//16*x^(1/2)*(1+-1x)^(1/2))
@test integrate(arcsin(x^(1/2)), x) == :(1//4*arcsin(1+-2x)+x*arcsin(x^(1/2))+(1/2)*x^(1/2)*(1+-1x)^(1/2))
@test integrate(x^-1*arcsin(x^(1/2)), x) == :(-1*im*arcsin(x^(1/2))^2+-1*im*Polylogarithms.polylog(2,exp(2*im*arcsin(x^(1/2))))+2*arcsin(x^(1/2))*log(1+-1*exp(2*im*arcsin(x^(1/2)))))
@test integrate(x^-2*arcsin(x^(1/2)), x) == :(-1*x^-1*arcsin(x^(1/2))+-1*x^-1//2*(1+-1x)^(1/2))
@test integrate(x^-3*arcsin(x^(1/2)), x) == :(-1//2*x^-2*arcsin(x^(1/2))+-1//3*x^-1//2*(1+-1x)^(1/2)+-1//6*x^-3//2*(1+-1x)^(1/2))
@test integrate(x^-4*arcsin(x^(1/2)), x) == :(-8//45*x^-1//2*(1+-1x)^(1/2)+-4//45*x^-3//2*(1+-1x)^(1/2)+-1//3*x^-3*arcsin(x^(1/2))+-1//15*x^-5//2*(1+-1x)^(1/2))
@test integrate(x^-5*arcsin(x^(1/2)), x) == :(-4//35*x^-1//2*(1+-1x)^(1/2)+-3//70*x^-5//2*(1+-1x)^(1/2)+-2//35*x^-3//2*(1+-1x)^(1/2)+-1//4*x^-4*arcsin(x^(1/2))+-1//28*x^-7//2*(1+-1x)^(1/2))
@test integrate(x^4*(a+b*arcsin(c*x^-1)), x) == :(1//5*x^5*(a+b*arcsin(c*x^-1))+3//40*b*c^5*arctanh((1+-1*c^2*x^-2)^(1/2))+1//20*b*c*x^4*(1+-1*c^2*x^-2)^(1/2)+3//40*b*c^3*x^2*(1+-1*c^2*x^-2)^(1/2))
@test integrate(x^3*(a+b*arcsin(c*x^-1)), x) == :(1//4*x^4*(a+b*arcsin(c*x^-1))+1//6*b*x*c^3*(1+-1*c^2*x^-2)^(1/2)+1//12*b*c*x^3*(1+-1*c^2*x^-2)^(1/2))
@test integrate(x^2*(a+b*arcsin(c*x^-1)), x) == :(1//3*x^3*(a+b*arcsin(c*x^-1))+1//6*b*c^3*arctanh((1+-1*c^2*x^-2)^(1/2))+1//6*b*c*x^2*(1+-1*c^2*x^-2)^(1/2))
@test integrate(x*(a+b*arcsin(c*x^-1)), x) == :((1/2)*x^2*(a+b*arcsin(c*x^-1))+(1/2)*b*c*x*(1+-1*c^2*x^-2)^(1/2))
@test integrate(a+b*arcsin(c*x^-1), x) == :(a*x+b*c*arctanh((1+-1*c^2*x^-2)^(1/2))+b*x*arccsc(x*c^-1))
@test integrate(x^-1*(a+b*arcsin(c*x^-1)), x) == :(a*log(x)+(1/2)*im*b*arcsin(c*x^-1)^2+(1/2)*im*b*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x^-1)))+-1*b*arcsin(c*x^-1)*log(1+-1*exp(2*im*arcsin(c*x^-1))))
@test integrate(x^-2*(a+b*arcsin(c*x^-1)), x) == :(-1*a*x^-1+-1*b*c^-1*(1+-1*c^2*x^-2)^(1/2)+-1*b*x^-1*arccsc(x*c^-1))
@test integrate(x^-3*(a+b*arcsin(c*x^-1)), x) == :(-1//2*x^-2*(a+b*arcsin(c*x^-1))+1//4*b*c^-2*arccsc(x*c^-1)+-1//4*b*c^-1*x^-1*(1+-1*c^2*x^-2)^(1/2))
@test integrate(x^-4*(a+b*arcsin(c*x^-1)), x) == :(-1//3*x^-3*(a+b*arcsin(c*x^-1))+-1//3*b*c^-3*(1+-1*c^2*x^-2)^(1/2)+1//9*b*c^-3*(1+-1*c^2*x^-2)^3//2)
@test integrate(x^-5*(a+b*arcsin(c*x^-1)), x) == :(-1//4*x^-4*(a+b*arcsin(c*x^-1))+3//32*b*c^-4*arccsc(x*c^-1)+-3//32*b*c^-3*x^-1*(1+-1*c^2*x^-2)^(1/2)+-1//16*b*c^-1*x^-3*(1+-1*c^2*x^-2)^(1/2))
@test integrate(x^-1*(a+b*arcsin(c*x^n)), x) == :(a*log(x)+b*n^-1*arcsin(c*x^n)*log(1+-1*exp(2*im*arcsin(c*x^n)))+-1//2*im*b*n^-1*arcsin(c*x^n)^2+-1//2*im*b*n^-1*Polylogarithms.polylog(2,exp(2*im*arcsin(c*x^n))))
@test integrate(x^5*(a+b*arcsin(c+d*x^2)), x) == :(1//6*x^6*(a+b*arcsin(c+d*x^2))+1//18*b*d^-1*x^4*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+1//36*b*d^-3*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)*(4+11*c^2+-5*c*d*x^2)+1//12*b*c*d^-3*(3+2*c^2)*arcsin(c+d*x^2))
@test integrate(x^3*(a+b*arcsin(c+d*x^2)), x) == :(1//4*x^4*(a+b*arcsin(c+d*x^2))+-3//8*b*c*d^-2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-1//8*b*d^-2*(1+2*c^2)*arcsin(c+d*x^2)+1//8*b*d^-1*x^2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2))
@test integrate(x*(a+b*arcsin(c+d*x^2)), x) == :((1/2)*a*x^2+(1/2)*b*d^-1*(1+-1*(c+d*x^2)^2)^(1/2)+(1/2)*b*d^-1*(c+d*x^2)*arcsin(c+d*x^2))
@test integrate(x^-1*(a+b*arcsin(c+d*x^2)), x) == :(a*log(x)+(1/2)*b*arcsin(c+d*x^2)*log(1+-1*((1+-1*c^2)^(1/2)+im*c)^-1*exp(im*arcsin(c+d*x^2)))+(1/2)*b*arcsin(c+d*x^2)*log(1+-1*(-1*(1+-1*c^2)^(1/2)+im*c)^-1*exp(im*arcsin(c+d*x^2)))+-1//2*im*b*Polylogarithms.polylog(2,((1+-1*c^2)^(1/2)+im*c)^-1*exp(im*arcsin(c+d*x^2)))+-1//2*im*b*Polylogarithms.polylog(2,(-1*(1+-1*c^2)^(1/2)+im*c)^-1*exp(im*arcsin(c+d*x^2)))+-1//4*im*b*arcsin(c+d*x^2)^2)
@test integrate(x^-3*(a+b*arcsin(c+d*x^2)), x) == :(-1//2*x^-2*(a+b*arcsin(c+d*x^2))+-1//2*b*d*(1+-1*c^2)^-1//2*arctanh((1+-1*c^2)^-1//2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+-1*c^2+-1*c*d*x^2)))
@test integrate(x^-5*(a+b*arcsin(c+d*x^2)), x) == :(-1//4*x^-4*(a+b*arcsin(c+d*x^2))+-1*b*d*x^-2*(4+-4*c^2)^-1*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-1//4*b*c*d^2*(1+-1*c^2)^-3//2*arctanh((1+-1*c^2)^-1//2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+-1*c^2+-1*c*d*x^2)))
@test integrate(x^-7*(a+b*arcsin(c+d*x^2)), x) == :(-1//6*x^-6*(a+b*arcsin(c+d*x^2))+-1*b*d*x^-4*(12+-12*c^2)^-1*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-1//12*b*d^3*(1+-1*c^2)^-5//2*(1+2*c^2)*arctanh((1+-1*c^2)^-1//2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+-1*c^2+-1*c*d*x^2))+-1//4*b*c*d^2*x^-2*(1+-1*c^2)^-2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2))
@test integrate(x^4*(a+b*arcsin(c+d*x^2)), x) == :(1//5*x^5*(a+b*arcsin(c+d*x^2))+2//25*b*d^-1*x^3*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-16//75*b*c*x*d^-2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-2//75*b*d^-5//2*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+c)*(9+23*c^2)*Elliptic.E(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c))+2//75*b*d^-5//2*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+c)*(9+8c+15*c^2)*Elliptic.F(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c)))
@test integrate(x^2*(a+b*arcsin(c+d*x^2)), x) == :(1//3*x^3*(a+b*arcsin(c+d*x^2))+2//9*b*x*d^-1*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-2//9*b*d^-3//2*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+c)*(1+3c)*Elliptic.F(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c))+8//9*b*c*d^-3//2*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+c)*Elliptic.E(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c)))
@test integrate(a+b*arcsin(c+d*x^2), x) == :(a*x+b*x*arcsin(c+d*x^2)+-2*b*d^-1//2*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+c)*Elliptic.E(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c))+2*b*d^-1//2*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+c)*Elliptic.F(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c)))
@test integrate(x^-2*(a+b*arcsin(c+d*x^2)), x) == :(-1*x^-1*(a+b*arcsin(c+d*x^2))+2*b*d^(1/2)*(1+-1c)^(1/2)*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*Elliptic.F(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c)))
@test integrate(x^-4*(a+b*arcsin(c+d*x^2)), x) == :(-1//3*x^-3*(a+b*arcsin(c+d*x^2))+-2*b*d*x^-1*(3+-3*c^2)^-1*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-2//3*b*d^3//2*(1+-1c)^-1//2*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*Elliptic.E(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c))+2//3*b*d^3//2*(1+-1c)^-1//2*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*Elliptic.F(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c)))
@test integrate(x^-6*(a+b*arcsin(c+d*x^2)), x) == :(-1//5*x^-5*(a+b*arcsin(c+d*x^2))+-2*b*d*x^-3*(15+-15*c^2)^-1*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-8//15*b*c*d^2*x^-1*(1+-1*c^2)^-2*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^(1/2)+-8//15*b*c*d^5//2*(1+-1c)^-1//2*(1+-1*c^2)^-1*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*Elliptic.E(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c))+2//15*b*d^5//2*(1+-1c)^-1//2*(1+-1*c^2)^-1*(1+d*x^2*(1+c)^-1)^(1/2)*(1+-1*d*x^2*(1+-1c)^-1)^(1/2)*(1+-1*c^2+-1*d^2*x^4+-2*c*d*x^2)^-1//2*(1+3c)*Elliptic.F(arcsin(x*d^(1/2)*(1+-1c)^-1//2),-1*(1+c)^-1*(1+-1c)))
@test integrate(x^3*arcsin(a+b*x^4), x) == :(1//4*b^-1*(1+-1*(a+b*x^4)^2)^(1/2)+1//4*b^-1*(a+b*x^4)*arcsin(a+b*x^4))
@test integrate(x^(-1+n)*arcsin(a+b*x^n), x) == :(b^-1*n^-1*(1+-1*(a+b*x^n)^2)^(1/2)+b^-1*n^-1*(a+b*x^n)*arcsin(a+b*x^n))
@test integrate((a+b*arcsin(1+d*x^2))^4, x) == :(x*(a+b*arcsin(1+d*x^2))^4+384*x*b^4+-48*x*b^2*(a+b*arcsin(1+d*x^2))^2+-192*b^3*d^-1*x^-1*(-1*d^2*x^4+-2*d*x^2)^(1/2)*(a+b*arcsin(1+d*x^2))+8*b*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^3*(-1*d^2*x^4+-2*d*x^2)^(1/2))
@test integrate((a+b*arcsin(1+d*x^2))^3, x) == :(x*(a+b*arcsin(1+d*x^2))^3+-24*a*x*b^2+-24*x*b^3*arcsin(1+d*x^2)+-48*b^3*d^-1*x^-1*(-1*d^2*x^4+-2*d*x^2)^(1/2)+6*b*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^2*(-1*d^2*x^4+-2*d*x^2)^(1/2))
@test integrate((a+b*arcsin(1+d*x^2))^2, x) == :(x*(a+b*arcsin(1+d*x^2))^2+-8*x*b^2+4*b*d^-1*x^-1*(-1*d^2*x^4+-2*d*x^2)^(1/2)*(a+b*arcsin(1+d*x^2)))
@test integrate(a+b*arcsin(1+d*x^2), x) == :(a*x+b*x*arcsin(1+d*x^2)+2*b*d^-1*x^-1*(-1*d^2*x^4+-2*d*x^2)^(1/2))
@test integrate((a+b*arcsin(1+d*x^2))^-1, x) == :(-1//2*x*b^-1*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*cosintegral((1/2)*b^-1*(a+b*arcsin(1+d*x^2)))+-1//2*x*b^-1*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*sinintegral((1/2)*b^-1*(a+b*arcsin(1+d*x^2))))
@test integrate((a+b*arcsin(1+d*x^2))^-2, x) == :(-1//2*b^-1*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^-1*(-1*d^2*x^4+-2*d*x^2)^(1/2)+-1//4*x*b^-2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*cosintegral((1/2)*b^-1*(a+b*arcsin(1+d*x^2)))+1//4*x*b^-2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*sinintegral((1/2)*b^-1*(a+b*arcsin(1+d*x^2))))
@test integrate((a+b*arcsin(1+d*x^2))^-3, x) == :(1//8*x*b^-2*(a+b*arcsin(1+d*x^2))^-1+-1//4*b^-1*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^-2*(-1*d^2*x^4+-2*d*x^2)^(1/2)+1//16*x*b^-3*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*cosintegral((1/2)*b^-1*(a+b*arcsin(1+d*x^2)))+1//16*x*b^-3*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*sinintegral((1/2)*b^-1*(a+b*arcsin(1+d*x^2))))
@test integrate((a+b*arcsin(-1+d*x^2))^4, x) == :(x*(a+-1*b*arcsin(1+-1*d*x^2))^4+384*x*b^4+-48*x*b^2*(a+-1*b*arcsin(1+-1*d*x^2))^2+-192*b^3*d^-1*x^-1*(-1*d^2*x^4+2*d*x^2)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))+8*b*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^3*(-1*d^2*x^4+2*d*x^2)^(1/2))
@test integrate((a+b*arcsin(-1+d*x^2))^3, x) == :(x*(a+-1*b*arcsin(1+-1*d*x^2))^3+-24*a*x*b^2+24*x*b^3*arcsin(1+-1*d*x^2)+-48*b^3*d^-1*x^-1*(-1*d^2*x^4+2*d*x^2)^(1/2)+6*b*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^2*(-1*d^2*x^4+2*d*x^2)^(1/2))
@test integrate((a+b*arcsin(-1+d*x^2))^2, x) == :(x*(a+-1*b*arcsin(1+-1*d*x^2))^2+-8*x*b^2+4*b*d^-1*x^-1*(-1*d^2*x^4+2*d*x^2)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2)))
@test integrate(a+b*arcsin(-1+d*x^2), x) == :(a*x+-1*b*x*arcsin(1+-1*d*x^2)+2*b*d^-1*x^-1*(-1*d^2*x^4+2*d*x^2)^(1/2))
@test integrate((a+b*arcsin(-1+d*x^2))^-1, x) == :((1/2)*x*b^-1*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*cosintegral(-1//2*b^-1*(a+-1*b*arcsin(1+-1*d*x^2)))+-1//2*x*b^-1*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*sinintegral(-1//2*arcsin(1+-1*d*x^2)+(1/2)*a*b^-1))
@test integrate((a+b*arcsin(-1+d*x^2))^-2, x) == :(-1//2*b^-1*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^-1*(-1*d^2*x^4+2*d*x^2)^(1/2)+-1//4*x*b^-2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*cosintegral(-1//2*b^-1*(a+-1*b*arcsin(1+-1*d*x^2)))+-1//4*x*b^-2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*sinintegral(-1//2*arcsin(1+-1*d*x^2)+(1/2)*a*b^-1))
@test integrate((a+b*arcsin(-1+d*x^2))^-3, x) == :(1//8*x*b^-2*(a+-1*b*arcsin(1+-1*d*x^2))^-1+-1//4*b^-1*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^-2*(-1*d^2*x^4+2*d*x^2)^(1/2)+-1//16*x*b^-3*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*cosintegral(-1//2*b^-1*(a+-1*b*arcsin(1+-1*d*x^2)))+1//16*x*b^-3*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*sinintegral(-1//2*arcsin(1+-1*d*x^2)+(1/2)*a*b^-1))
@test integrate(arcsin(1+x^2)^2, x) == :(-8x+x*arcsin(1+x^2)^2+4*x^-1*(-1*x^4+-2*x^2)^(1/2)*arcsin(1+x^2))
@test integrate(arcsin(1+-1*x^2)^2, x) == :(-8x+x*arcsin(1+-1*x^2)^2+-4*x^-1*(-1*x^4+2*x^2)^(1/2)*arcsin(1+-1*x^2))
@test integrate((a+b*arcsin(1+d*x^2))^5//2, x) == :(x*(a+b*arcsin(1+d*x^2))^5//2+-15*x*b^2*(a+b*arcsin(1+d*x^2))^(1/2)+5*b*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^3//2*(-1*d^2*x^4+-2*d*x^2)^(1/2)+-15*x*pi^(1/2)*(b^-1)^-5//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2))+15*x*pi^(1/2)*(b^-1)^-5//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(1+d*x^2))^3//2, x) == :(x*(a+b*arcsin(1+d*x^2))^3//2+3*b*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^(1/2)*(-1*d^2*x^4+-2*d*x^2)^(1/2)+3*x*pi^(1/2)*b^3//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*b^-1//2*(a+b*arcsin(1+d*x^2))^(1/2))+3*x*pi^(1/2)*b^3//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*b^-1//2*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(1+d*x^2))^(1/2), x) == :(x*(a+b*arcsin(1+d*x^2))^(1/2)+x*pi^(1/2)*(b^-1)^-1//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2))+-1*x*pi^(1/2)*(b^-1)^-1//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(1+d*x^2))^-1//2, x) == :(-1*x*pi^(1/2)*b^-1//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*b^-1//2*(a+b*arcsin(1+d*x^2))^(1/2))+-1*x*pi^(1/2)*b^-1//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*b^-1//2*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(1+d*x^2))^-3//2, x) == :(-1*b^-1*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^-1//2*(-1*d^2*x^4+-2*d*x^2)^(1/2)+x*pi^(1/2)*(b^-1)^3//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2))+-1*x*pi^(1/2)*(b^-1)^3//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(1+d*x^2))^-5//2, x) == :(1//3*x*b^-2*(a+b*arcsin(1+d*x^2))^-1//2+-1//3*b^-1*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^-3//2*(-1*d^2*x^4+-2*d*x^2)^(1/2)+1//3*x*pi^(1/2)*b^-5//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*b^-1//2*(a+b*arcsin(1+d*x^2))^(1/2))+1//3*x*pi^(1/2)*b^-5//2*(-1*sin((1/2)*arcsin(1+d*x^2))+cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*b^-1//2*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(1+d*x^2))^-7//2, x) == :(1//15*x*b^-2*(a+b*arcsin(1+d*x^2))^-3//2+-1//5*b^-1*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^-5//2*(-1*d^2*x^4+-2*d*x^2)^(1/2)+1//15*b^-3*d^-1*x^-1*(a+b*arcsin(1+d*x^2))^-1//2*(-1*d^2*x^4+-2*d*x^2)^(1/2)+x*pi^(1/2)*(b^-1)^7//2*(-15*sin((1/2)*arcsin(1+d*x^2))+15*cos((1/2)*arcsin(1+d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2))+-1*x*pi^(1/2)*(b^-1)^7//2*(-15*sin((1/2)*arcsin(1+d*x^2))+15*cos((1/2)*arcsin(1+d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(b^-1)^(1/2)*(a+b*arcsin(1+d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^5//2, x) == :(x*(a+-1*b*arcsin(1+-1*d*x^2))^5//2+-15*x*b^2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)+5*b*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^3//2*(-1*d^2*x^4+2*d*x^2)^(1/2)+-15*x*pi^(1/2)*(-1*b^-1)^-5//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+15*x*pi^(1/2)*(-1*b^-1)^-5//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^3//2, x) == :(x*(a+-1*b*arcsin(1+-1*d*x^2))^3//2+3*b*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)*(-1*d^2*x^4+2*d*x^2)^(1/2)+3*x*pi^(1/2)*(-1b)^3//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1b)^-1//2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+3*x*pi^(1/2)*(-1b)^3//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1b)^-1//2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^(1/2), x) == :(x*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)+x*pi^(1/2)*(-1*b^-1)^-1//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+-1*x*pi^(1/2)*(-1*b^-1)^-1//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^-1//2, x) == :(-1*x*pi^(1/2)*(-1b)^-1//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1b)^-1//2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+-1*x*pi^(1/2)*(-1b)^-1//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1b)^-1//2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^-3//2, x) == :(-1*b^-1*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^-1//2*(-1*d^2*x^4+2*d*x^2)^(1/2)+x*pi^(1/2)*(-1*b^-1)^3//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+-1*x*pi^(1/2)*(-1*b^-1)^3//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^-5//2, x) == :(1//3*x*b^-2*(a+-1*b*arcsin(1+-1*d*x^2))^-1//2+-1//3*b^-1*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^-3//2*(-1*d^2*x^4+2*d*x^2)^(1/2)+1//3*x*pi^(1/2)*(-1b)^-5//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1b)^-1//2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+1//3*x*pi^(1/2)*(-1b)^-5//2*(-1*sin((1/2)*arcsin(1+-1*d*x^2))+cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1b)^-1//2*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((a+b*arcsin(-1+d*x^2))^-7//2, x) == :(1//15*x*b^-2*(a+-1*b*arcsin(1+-1*d*x^2))^-3//2+-1//5*b^-1*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^-5//2*(-1*d^2*x^4+2*d*x^2)^(1/2)+1//15*b^-3*d^-1*x^-1*(a+-1*b*arcsin(1+-1*d*x^2))^-1//2*(-1*d^2*x^4+2*d*x^2)^(1/2)+x*pi^(1/2)*(-1*b^-1)^7//2*(-15*sin((1/2)*arcsin(1+-1*d*x^2))+15*cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(-1*sin((1/2)*a*b^-1)+cos((1/2)*a*b^-1))*fresnelc(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2))+-1*x*pi^(1/2)*(-1*b^-1)^7//2*(-15*sin((1/2)*arcsin(1+-1*d*x^2))+15*cos((1/2)*arcsin(1+-1*d*x^2)))^-1*(cos((1/2)*a*b^-1)+sin((1/2)*a*b^-1))*fresnels(pi^-1//2*(-1*b^-1)^(1/2)*(a+-1*b*arcsin(1+-1*d*x^2))^(1/2)))
@test integrate((1+-1*c^2*x^2)^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^3, x) == :(-1*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^3*log(1+-1*exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+-3//2*b^2*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))*Polylogarithms.polylog(3,exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+-3//4*im*b^3*c^-1*Polylogarithms.polylog(4,exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+1//4*im*b^-1*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^4+3//2*im*b*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^2*Polylogarithms.polylog(2,exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))))
@test integrate((1+-1*c^2*x^2)^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^2, x) == :(-1*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^2*log(1+-1*exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+-1//2*b^2*c^-1*Polylogarithms.polylog(3,exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+1//3*im*b^-1*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^3+im*b*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))*Polylogarithms.polylog(2,exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))))
@test integrate((1+-1*c^2*x^2)^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))), x) == :(-1*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))*log(1+-1*exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+(1/2)*im*b*c^-1*Polylogarithms.polylog(2,exp(2*im*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2))))+(1/2)*im*b^-1*c^-1*(a+b*arcsin((1+c*x)^-1//2*(1+-1*c*x)^(1/2)))^2)
@test integrate(arcsin(exp(x))*exp(x), x) == :((1+-1*exp(2x))^(1/2)+arcsin(exp(x))*exp(x))
@test integrate(arcsin(c*exp(a+b*x)), x) == :(b^-1*arcsin(c*exp(a+b*x))*log(1+-1*exp(2*im*arcsin(c*exp(a+b*x))))+-1//2*im*b^-1*arcsin(c*exp(a+b*x))^2+-1//2*im*b^-1*Polylogarithms.polylog(2,exp(2*im*arcsin(c*exp(a+b*x)))))
@test integrate(x^3*exp(arcsin(a*x)), x) == :(-1//10*a^-4*cos(2*arcsin(a*x))*exp(arcsin(a*x))+-1//136*a^-4*exp(arcsin(a*x))*sin(4*arcsin(a*x))+1//20*a^-4*exp(arcsin(a*x))*sin(2*arcsin(a*x))+1//34*a^-4*cos(4*arcsin(a*x))*exp(arcsin(a*x)))
@test integrate(x^2*exp(arcsin(a*x)), x) == :(-3//40*a^-3*exp(arcsin(a*x))*sin(3*arcsin(a*x))+-1//40*a^-3*cos(3*arcsin(a*x))*exp(arcsin(a*x))+1//8*x*a^-2*exp(arcsin(a*x))+1//8*a^-3*(1+-1*a^2*x^2)^(1/2)*exp(arcsin(a*x)))
@test integrate(x*exp(arcsin(a*x)), x) == :(-1//5*a^-2*cos(2*arcsin(a*x))*exp(arcsin(a*x))+1//10*a^-2*exp(arcsin(a*x))*sin(2*arcsin(a*x)))
@test integrate(exp(arcsin(a*x)), x) == :((1/2)*x*exp(arcsin(a*x))+(1/2)*a^-1*(1+-1*a^2*x^2)^(1/2)*exp(arcsin(a*x)))
@test integrate(x^3*exp(arcsin(a*x)^2), x) == :(-1//16*ℯ*im*pi^(1/2)*a^-4*erfi(im+arcsin(a*x))+-1//32*im*pi^(1/2)*a^-4*erfi(-2im+arcsin(a*x))*exp(4)+1//16*ℯ*im*pi^(1/2)*a^-4*erfi(-1im+arcsin(a*x))+1//32*im*pi^(1/2)*a^-4*erfi(2im+arcsin(a*x))*exp(4))
@test integrate(x^2*exp(arcsin(a*x)^2), x) == :(-1//16*pi^(1/2)*a^-3*erfi(-3//2*im+arcsin(a*x))*exp(9//4)+-1//16*pi^(1/2)*a^-3*erfi(3//2*im+arcsin(a*x))*exp(9//4)+1//16*pi^(1/2)*a^-3*erfi((1/2)*im+arcsin(a*x))*exp(1//4)+1//16*pi^(1/2)*a^-3*erfi(-1//2*im+arcsin(a*x))*exp(1//4))
@test integrate(x*exp(arcsin(a*x)^2), x) == :(-1//8*ℯ*im*pi^(1/2)*a^-2*erfi(im+arcsin(a*x))+1//8*ℯ*im*pi^(1/2)*a^-2*erfi(-1im+arcsin(a*x)))
@test integrate(exp(arcsin(a*x)^2), x) == :(1//4*pi^(1/2)*a^-1*erfi((1/2)*im+arcsin(a*x))*exp(1//4)+1//4*pi^(1/2)*a^-1*erfi(-1//2*im+arcsin(a*x))*exp(1//4))
@test integrate(x^3*exp(arcsin(a+b*x)), x) == :(-1//10*b^-4*cos(2*arcsin(a+b*x))*exp(arcsin(a+b*x))+-1//136*b^-4*exp(arcsin(a+b*x))*sin(4*arcsin(a+b*x))+1//20*b^-4*exp(arcsin(a+b*x))*sin(2*arcsin(a+b*x))+1//34*b^-4*cos(4*arcsin(a+b*x))*exp(arcsin(a+b*x))+-3//5*a^2*b^-4*cos(2*arcsin(a+b*x))*exp(arcsin(a+b*x))+-3//8*a*b^-4*(1+-1*(a+b*x)^2)^(1/2)*exp(arcsin(a+b*x))+-3//8*a*b^-4*(a+b*x)*exp(arcsin(a+b*x))+-1//2*a^3*b^-4*(1+-1*(a+b*x)^2)^(1/2)*exp(arcsin(a+b*x))+-1//2*a^3*b^-4*(a+b*x)*exp(arcsin(a+b*x))+3//10*a^2*b^-4*exp(arcsin(a+b*x))*sin(2*arcsin(a+b*x))+3//40*a*b^-4*cos(3*arcsin(a+b*x))*exp(arcsin(a+b*x))+9//40*a*b^-4*exp(arcsin(a+b*x))*sin(3*arcsin(a+b*x)))
@test integrate(x^2*exp(arcsin(a+b*x)), x) == :(-3//40*b^-3*exp(arcsin(a+b*x))*sin(3*arcsin(a+b*x))+-1//40*b^-3*cos(3*arcsin(a+b*x))*exp(arcsin(a+b*x))+1//8*b^-3*(1+-1*(a+b*x)^2)^(1/2)*exp(arcsin(a+b*x))+1//8*b^-3*(a+b*x)*exp(arcsin(a+b*x))+(1/2)*a^2*b^-3*(1+-1*(a+b*x)^2)^(1/2)*exp(arcsin(a+b*x))+(1/2)*a^2*b^-3*(a+b*x)*exp(arcsin(a+b*x))+-1//5*a*b^-3*exp(arcsin(a+b*x))*sin(2*arcsin(a+b*x))+2//5*a*b^-3*cos(2*arcsin(a+b*x))*exp(arcsin(a+b*x)))
@test integrate(x*exp(arcsin(a+b*x)), x) == :(-1//5*b^-2*cos(2*arcsin(a+b*x))*exp(arcsin(a+b*x))+1//10*b^-2*exp(arcsin(a+b*x))*sin(2*arcsin(a+b*x))+-1//2*a*b^-2*(1+-1*(a+b*x)^2)^(1/2)*exp(arcsin(a+b*x))+-1//2*a*b^-2*(a+b*x)*exp(arcsin(a+b*x)))
@test integrate(exp(arcsin(a+b*x)), x) == :((1/2)*b^-1*(1+-1*(a+b*x)^2)^(1/2)*exp(arcsin(a+b*x))+(1/2)*b^-1*(a+b*x)*exp(arcsin(a+b*x)))
@test integrate(x^3*exp(arcsin(a+b*x)^2), x) == :(-3//16*a*pi^(1/2)*b^-4*erfi((1/2)*im+arcsin(a+b*x))*exp(1//4)+-3//16*a*pi^(1/2)*b^-4*erfi(-1//2*im+arcsin(a+b*x))*exp(1//4)+-1//4*pi^(1/2)*a^3*b^-4*erfi((1/2)*im+arcsin(a+b*x))*exp(1//4)+-1//4*pi^(1/2)*a^3*b^-4*erfi(-1//2*im+arcsin(a+b*x))*exp(1//4)+-1//16*ℯ*im*pi^(1/2)*b^-4*erfi(im+arcsin(a+b*x))+-1//32*im*pi^(1/2)*b^-4*erfi(-2im+arcsin(a+b*x))*exp(4)+1//16*ℯ*im*pi^(1/2)*b^-4*erfi(-1im+arcsin(a+b*x))+1//32*im*pi^(1/2)*b^-4*erfi(2im+arcsin(a+b*x))*exp(4)+3//16*a*pi^(1/2)*b^-4*erfi(-3//2*im+arcsin(a+b*x))*exp(9//4)+3//16*a*pi^(1/2)*b^-4*erfi(3//2*im+arcsin(a+b*x))*exp(9//4)+-3//8*ℯ*im*pi^(1/2)*a^2*b^-4*erfi(im+arcsin(a+b*x))+3//8*ℯ*im*pi^(1/2)*a^2*b^-4*erfi(-1im+arcsin(a+b*x)))
@test integrate(x^2*exp(arcsin(a+b*x)^2), x) == :(-1//16*pi^(1/2)*b^-3*erfi(-3//2*im+arcsin(a+b*x))*exp(9//4)+-1//16*pi^(1/2)*b^-3*erfi(3//2*im+arcsin(a+b*x))*exp(9//4)+1//16*pi^(1/2)*b^-3*erfi((1/2)*im+arcsin(a+b*x))*exp(1//4)+1//16*pi^(1/2)*b^-3*erfi(-1//2*im+arcsin(a+b*x))*exp(1//4)+1//4*pi^(1/2)*a^2*b^-3*erfi((1/2)*im+arcsin(a+b*x))*exp(1//4)+1//4*pi^(1/2)*a^2*b^-3*erfi(-1//2*im+arcsin(a+b*x))*exp(1//4)+-1//4*ℯ*im*a*pi^(1/2)*b^-3*erfi(-1im+arcsin(a+b*x))+1//4*ℯ*im*a*pi^(1/2)*b^-3*erfi(im+arcsin(a+b*x)))
@test integrate(x*exp(arcsin(a+b*x)^2), x) == :(-1//4*a*pi^(1/2)*b^-2*erfi((1/2)*im+arcsin(a+b*x))*exp(1//4)+-1//4*a*pi^(1/2)*b^-2*erfi(-1//2*im+arcsin(a+b*x))*exp(1//4)+-1//8*ℯ*im*pi^(1/2)*b^-2*erfi(im+arcsin(a+b*x))+1//8*ℯ*im*pi^(1/2)*b^-2*erfi(-1im+arcsin(a+b*x)))
@test integrate(exp(arcsin(a+b*x)^2), x) == :(1//4*pi^(1/2)*b^-1*erfi((1/2)*im+arcsin(a+b*x))*exp(1//4)+1//4*pi^(1/2)*b^-1*erfi(-1//2*im+arcsin(a+b*x))*exp(1//4))
@test integrate((1+-1*a^2*x^2)^5//2*exp(arcsin(a*x)), x) == :(144//629*a^-1*exp(arcsin(a*x))+1//37*a^-1*(1+-1*a^2*x^2)^3*exp(arcsin(a*x))+6//37*x*(1+-1*a^2*x^2)^5//2*exp(arcsin(a*x))+30//629*a^-1*(1+-1*a^2*x^2)^2*exp(arcsin(a*x))+72//629*a^-1*(1+-1*a^2*x^2)*exp(arcsin(a*x))+120//629*x*(1+-1*a^2*x^2)^3//2*exp(arcsin(a*x))+144//629*x*(1+-1*a^2*x^2)^(1/2)*exp(arcsin(a*x)))
@test integrate((1+-1*a^2*x^2)^3//2*exp(arcsin(a*x)), x) == :(24//85*a^-1*exp(arcsin(a*x))+1//17*a^-1*(1+-1*a^2*x^2)^2*exp(arcsin(a*x))+4//17*x*(1+-1*a^2*x^2)^3//2*exp(arcsin(a*x))+12//85*a^-1*(1+-1*a^2*x^2)*exp(arcsin(a*x))+24//85*x*(1+-1*a^2*x^2)^(1/2)*exp(arcsin(a*x)))
@test integrate((1+-1*a^2*x^2)^(1/2)*exp(arcsin(a*x)), x) == :(2//5*a^-1*exp(arcsin(a*x))+1//5*a^-1*(1+-1*a^2*x^2)*exp(arcsin(a*x))+2//5*x*(1+-1*a^2*x^2)^(1/2)*exp(arcsin(a*x)))
@test integrate((1+-1*a^2*x^2)^-1//2*exp(arcsin(a*x)), x) == :(a^-1*exp(arcsin(a*x)))
@test integrate(arcsin(c*(a+b*x)^-1), x) == :(c*b^-1*arctanh((1+-1*c^2*(a+b*x)^-2)^(1/2))+b^-1*(a+b*x)*arccsc(a*c^-1+b*x*c^-1))
@test integrate(x*arcsin(sin(x))^-1, x) == :((-1*arcsin(sin(x))+x*(cos(x)^2)^(1/2)*sec(x))*log(arcsin(sin(x)))+arcsin(sin(x)))
@test integrate((1+b*x^2)^-1//2*arcsin((1+b*x^2)^(1/2))^n, x) == :(b^-1*x^-1*(-1*b*x^2)^(1/2)*(1+n)^-1*arcsin((1+b*x^2)^(1/2))^(1+n))
@test integrate((1+b*x^2)^-1//2*arcsin((1+b*x^2)^(1/2))^-1, x) == :(b^-1*x^-1*(-1*b*x^2)^(1/2)*log(arcsin((1+b*x^2)^(1/2))))
@test integrate(x*(1+-1*x^2)^-1+(1+-1*x^2)^-1//2*arcsin(x)^-1, x) == :(-1//2*log(1+-1*x^2)+log(arcsin(x)))
@test integrate((-1*x^2*arcsin(x)+arcsin(x))^-1*((1+-1*x^2)^(1/2)+x*arcsin(x)), x) == :(-1//2*log(1+-1*x^2)+log(arcsin(x)))

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