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

@test integrate(x^3*(a+b*log(c*x^n))*(d+e*x), x) == :((a+b*log(c*x^n))*(1//4*d*x^4+1//5*e*x^5)+-1//16*b*d*n*x^4+-1//25*b*e*n*x^5)
@test integrate(x^2*(a+b*log(c*x^n))*(d+e*x), x) == :((a+b*log(c*x^n))*(1//3*d*x^3+1//4*e*x^4)+-1//9*b*d*n*x^3+-1//16*b*e*n*x^4)
@test integrate(x*(a+b*log(c*x^n))*(d+e*x), x) == :((a+b*log(c*x^n))*((1/2)*d*x^2+1//3*e*x^3)+-1//4*b*d*n*x^2+-1//9*b*e*n*x^3)
@test integrate((a+b*log(c*x^n))*(d+e*x), x) == :(d*x*(a+b*log(c*x^n))+(1/2)*e*x^2*(a+b*log(c*x^n))+-1*b*d*n*x+-1//4*b*e*n*x^2)
@test integrate(x^-1*(a+b*log(c*x^n))*(d+e*x), x) == :(a*e*x+b*e*x*log(c*x^n)+(1/2)*d*b^-1*n^-1*(a+b*log(c*x^n))^2+-1*b*e*n*x)
@test integrate(x^-3*(a+b*log(c*x^n))*(d+e*x), x) == :(-1*b*e*n*x^-1+-1//2*d^-1*x^-2*(d+e*x)^2*(a+b*log(c*x^n))+-1//4*b*d*n*x^-2+(1/2)*b*n*d^-1*e^2*log(x))
@test integrate(x^-4*(a+b*log(c*x^n))*(d+e*x), x) == :(-1//2*e*x^-2*(a+b*log(c*x^n))+-1//3*d*x^-3*(a+b*log(c*x^n))+-1//4*b*e*n*x^-2+-1//9*b*d*n*x^-3)
@test integrate(x^3*(d+e*x)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//4*d^2*x^4+1//6*e^2*x^6+2//5*d*e*x^5)+-1//16*b*n*d^2*x^4+-1//36*b*n*e^2*x^6+-2//25*b*d*e*n*x^5)
@test integrate(x^2*(d+e*x)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//3*d^2*x^3+1//5*e^2*x^5+(1/2)*d*e*x^4)+-1//9*b*n*d^2*x^3+-1//25*b*n*e^2*x^5+-1//8*b*d*e*n*x^4)
@test integrate(x*(d+e*x)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*((1/2)*d^2*x^2+1//4*e^2*x^4+2//3*d*e*x^3)+-1//4*b*n*d^2*x^2+-1//16*b*n*e^2*x^4+-2//9*b*d*e*n*x^3)
@test integrate((d+e*x)^2*(a+b*log(c*x^n)), x) == :(1//3*e^-1*(d+e*x)^3*(a+b*log(c*x^n))+-1*b*n*x*d^2+-1//9*b*n*e^2*x^3+-1//2*b*d*e*n*x^2+-1//3*b*n*d^3*e^-1*log(x))
@test integrate(x^-1*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(d^2*(a+b*log(c*x^n))*log(x)+(1/2)*e^2*x^2*(a+b*log(c*x^n))+-1//4*b*n*(4d+e*x)^2+2*d*e*x*(a+b*log(c*x^n))+-1//2*b*n*d^2*log(x)^2)
@test integrate(x^-2*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(x*e^2*(a+b*log(c*x^n))+-1*d^2*x^-1*(a+b*log(c*x^n))+-1*b*n*x*e^2+-1*b*n*d^2*x^-1+2*d*e*(a+b*log(c*x^n))*log(x)+-1*b*d*e*n*log(x)^2)
@test integrate(x^-3*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(e^2*(a+b*log(c*x^n))*log(x)+-1//2*d^2*x^-2*(a+b*log(c*x^n))+-2*d*e*x^-1*(a+b*log(c*x^n))+-1//2*b*n*e^2*log(x)^2+-1//4*b*n*x^-2*(d+4*e*x)^2)
@test integrate(x^-4*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(-1*b*n*e^2*x^-1+-1//3*d^-1*x^-3*(d+e*x)^3*(a+b*log(c*x^n))+-1//9*b*n*d^2*x^-3+-1//2*b*d*e*n*x^-2+1//3*b*n*d^-1*e^3*log(x))
@test integrate(x^-5*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(-1//2*e^2*x^-2*(a+b*log(c*x^n))+-1//4*d^2*x^-4*(a+b*log(c*x^n))+-2//3*d*e*x^-3*(a+b*log(c*x^n))+-1//4*b*n*e^2*x^-2+-1//16*b*n*d^2*x^-4+-2//9*b*d*e*n*x^-3)
@test integrate(x^-6*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(-1//3*e^2*x^-3*(a+b*log(c*x^n))+-1//5*d^2*x^-5*(a+b*log(c*x^n))+-1//2*d*e*x^-4*(a+b*log(c*x^n))+-1//9*b*n*e^2*x^-3+-1//25*b*n*d^2*x^-5+-1//8*b*d*e*n*x^-4)
@test integrate(x^3*(d+e*x)^3*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//4*d^3*x^4+1//7*e^3*x^7+(1/2)*d*e^2*x^6+3//5*e*d^2*x^5)+-1//16*b*n*d^3*x^4+-1//49*b*n*e^3*x^7+-3//25*b*e*n*d^2*x^5+-1//12*b*d*n*e^2*x^6)
@test integrate(x^2*(d+e*x)^3*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//3*d^3*x^3+1//6*e^3*x^6+3//4*e*d^2*x^4+3//5*d*e^2*x^5)+-1//9*b*n*d^3*x^3+-1//36*b*n*e^3*x^6+-3//16*b*e*n*d^2*x^4+-3//25*b*d*n*e^2*x^5)
@test integrate(x*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(-1*(a+b*log(c*x^n))*(-1//5*e^-2*(d+e*x)^5+1//4*d*e^-2*(d+e*x)^4)+-1//25*b*n*e^-2*(d+e*x)^5+3//20*b*n*d^3*x^2+1//5*b*n*x*d^4*e^-1+1//15*b*e*n*d^2*x^3+1//20*b*n*d^5*e^-2*log(x)+1//80*b*d*n*e^2*x^4)
@test integrate((d+e*x)^3*(a+b*log(c*x^n)), x) == :(1//4*e^-1*(d+e*x)^4*(a+b*log(c*x^n))+-1*b*n*x*d^3+-1//16*b*n*e^3*x^4+-3//4*b*e*n*d^2*x^2+-1//3*b*d*n*e^2*x^3+-1//4*b*n*d^4*e^-1*log(x))
@test integrate(x^-1*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(d^3*(a+b*log(c*x^n))*log(x)+1//3*e^3*x^3*(a+b*log(c*x^n))+3*e*x*d^2*(a+b*log(c*x^n))+-1//2*b*n*d^3*log(x)^2+-1//9*b*n*e^3*x^3+3//2*d*e^2*x^2*(a+b*log(c*x^n))+-3*b*e*n*x*d^2+-3//4*b*d*n*e^2*x^2)
@test integrate(x^-2*(d+e*x)^3*(a+b*log(c*x^n)), x) == :((1/2)*e^3*x^2*(a+b*log(c*x^n))+-1*d^3*x^-1*(a+b*log(c*x^n))+-1*b*n*d^3*x^-1+3*d*x*e^2*(a+b*log(c*x^n))+3*e*d^2*(a+b*log(c*x^n))*log(x)+-1//4*b*n*e^3*x^2+-3*b*d*n*x*e^2+-3//2*b*e*n*d^2*log(x)^2)
@test integrate(x^-3*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(x*e^3*(a+b*log(c*x^n))+-1//2*d^3*x^-2*(a+b*log(c*x^n))+-1*b*n*x*e^3+-3*e*d^2*x^-1*(a+b*log(c*x^n))+3*d*e^2*(a+b*log(c*x^n))*log(x)+-1//4*b*n*d^3*x^-2+-3*b*e*n*d^2*x^-1+-3//2*b*d*n*e^2*log(x)^2)
@test integrate(x^-4*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(e^3*(a+b*log(c*x^n))*log(x)+-1//3*d^3*x^-3*(a+b*log(c*x^n))+-3*d*e^2*x^-1*(a+b*log(c*x^n))+-3//2*e*d^2*x^-2*(a+b*log(c*x^n))+-1//2*b*n*e^3*log(x)^2+-1//9*b*n*d^3*x^-3+-3*b*d*n*e^2*x^-1+-3//4*b*e*n*d^2*x^-2)
@test integrate(x^-5*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(-1*b*n*e^3*x^-1+-1//4*d^-1*x^-4*(d+e*x)^4*(a+b*log(c*x^n))+-1//16*b*n*d^3*x^-4+-3//4*b*d*n*e^2*x^-2+-1//3*b*e*n*d^2*x^-3+1//4*b*n*d^-1*e^4*log(x))
@test integrate(x^-6*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(-1//5*d^-1*x^-5*(d+e*x)^4*(a+b*log(c*x^n))+3//20*b*n*e^3*x^-2+-1//20*b*n*d^-2*e^5*log(x)+-1//25*b*n*d^-2*x^-5*(d+e*x)^5+1//5*b*n*d^-1*e^4*x^-1+1//15*b*d*n*e^2*x^-3+1//20*e*d^-2*x^-4*(d+e*x)^4*(a+b*log(c*x^n))+1//80*b*e*n*d^2*x^-4)
@test integrate(x^-7*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(-1//3*e^3*x^-3*(a+b*log(c*x^n))+-1//6*d^3*x^-6*(a+b*log(c*x^n))+-3//4*d*e^2*x^-4*(a+b*log(c*x^n))+-3//5*e*d^2*x^-5*(a+b*log(c*x^n))+-1//9*b*n*e^3*x^-3+-1//36*b*n*d^3*x^-6+-3//16*b*d*n*e^2*x^-4+-3//25*b*e*n*d^2*x^-5)
@test integrate(x^-8*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(-1//4*e^3*x^-4*(a+b*log(c*x^n))+-1//7*d^3*x^-7*(a+b*log(c*x^n))+-3//5*d*e^2*x^-5*(a+b*log(c*x^n))+-1//2*e*d^2*x^-6*(a+b*log(c*x^n))+-1//16*b*n*e^3*x^-4+-1//49*b*n*d^3*x^-7+-3//25*b*d*n*e^2*x^-5+-1//12*b*e*n*d^2*x^-6)
@test integrate(x^3*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :(1//3*e^-1*x^3*(a+b*log(c*x^n))+a*x*d^2*e^-3+-1*d^3*e^-4*(a+b*log(c*x^n))*log(1+e*x*d^-1)+-1//2*d*e^-2*x^2*(a+b*log(c*x^n))+-1//9*b*n*e^-1*x^3+b*x*d^2*e^-3*log(c*x^n)+-1*b*n*x*d^2*e^-3+-1*b*n*d^3*e^-4*Polylogarithms.polylog(2,-1*e*x*d^-1)+1//4*b*d*n*e^-2*x^2)
@test integrate(x^2*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :((1/2)*e^-1*x^2*(a+b*log(c*x^n))+d^2*e^-3*(a+b*log(c*x^n))*log(1+e*x*d^-1)+-1*a*d*x*e^-2+-1//4*b*n*e^-1*x^2+b*d*n*x*e^-2+b*n*d^2*e^-3*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1*b*d*x*e^-2*log(c*x^n))
@test integrate(x*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :(a*x*e^-1+b*x*e^-1*log(c*x^n)+-1*b*n*x*e^-1+-1*d*e^-2*(a+b*log(c*x^n))*log(1+e*x*d^-1)+-1*b*d*n*e^-2*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate((d+e*x)^-1*(a+b*log(c*x^n)), x) == :(e^-1*(a+b*log(c*x^n))*log(1+e*x*d^-1)+b*n*e^-1*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^-1*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :(-1*d^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+b*n*d^-1*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-2*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :(-1*d^-1*x^-1*(a+b*log(c*x^n))+e*d^-2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+-1*b*n*d^-1*x^-1+-1*b*e*n*d^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-3*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :(-1//2*d^-1*x^-2*(a+b*log(c*x^n))+e*d^-2*x^-1*(a+b*log(c*x^n))+-1*d^-3*e^2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+-1//4*b*n*d^-1*x^-2+b*e*n*d^-2*x^-1+b*n*d^-3*e^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-4*(d+e*x)^-1*(a+b*log(c*x^n)), x) == :(-1//3*d^-1*x^-3*(a+b*log(c*x^n))+d^-4*e^3*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+(1/2)*e*d^-2*x^-2*(a+b*log(c*x^n))+-1*d^-3*e^2*x^-1*(a+b*log(c*x^n))+-1//9*b*n*d^-1*x^-3+-1*b*n*d^-4*e^3*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-1*b*n*d^-3*e^2*x^-1+1//4*b*e*n*d^-2*x^-2)
@test integrate(x^3*(d+e*x)^-2*(a+b*log(c*x^n)), x) == :((1/2)*e^-2*x^2*(3a+b*n+3*b*log(c*x^n))+d^2*e^-4*(3a+b*n+3*b*log(c*x^n))*log(1+e*x*d^-1)+-1*d*x*e^-3*(3a+b*n)+-1*e^-1*x^3*(d+e*x)^-1*(a+b*log(c*x^n))+-3//4*b*n*e^-2*x^2+-3*b*d*x*e^-3*log(c*x^n)+3*b*d*n*x*e^-3+3*b*n*d^2*e^-4*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x*(d+e*x)^-2*(a+b*log(c*x^n)), x) == :(e^-2*(a+b*n+b*log(c*x^n))*log(1+e*x*d^-1)+b*n*e^-2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1*x*e^-1*(d+e*x)^-1*(a+b*log(c*x^n)))
@test integrate((d+e*x)^-2*(a+b*log(c*x^n)), x) == :(x*d^-1*(d+e*x)^-1*(a+b*log(c*x^n))+-1*b*n*d^-1*e^-1*log(d+e*x))
@test integrate(x^-1*(d+e*x)^-2*(a+b*log(c*x^n)), x) == :(-1*d^-2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+b*n*d^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+b*n*d^-2*log(d+e*x)+-1*e*x*d^-2*(d+e*x)^-1*(a+b*log(c*x^n)))
@test integrate(x^-2*(d+e*x)^-2*(a+b*log(c*x^n)), x) == :(-1*d^-2*x^-1*(a+b*log(c*x^n))+-1*b*n*d^-2*x^-1+2*e*d^-3*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+x*d^-3*e^2*(d+e*x)^-1*(a+b*log(c*x^n))+-1*b*e*n*d^-3*log(d+e*x)+-2*b*e*n*d^-3*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-3*(d+e*x)^-2*(a+b*log(c*x^n)), x) == :(-1//2*d^-2*x^-2*(a+b*log(c*x^n))+-3*d^-4*e^2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+2*e*d^-3*x^-1*(a+b*log(c*x^n))+-1//4*b*n*d^-2*x^-2+b*n*d^-4*e^2*log(d+e*x)+-1*x*d^-4*e^3*(d+e*x)^-1*(a+b*log(c*x^n))+2*b*e*n*d^-3*x^-1+3*b*n*d^-4*e^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^3*(d+e*x)^-3*(a+b*log(c*x^n)), x) == :((1/2)*x*e^-3*(6a+5*b*n)+-3*b*n*x*e^-3+3*b*x*e^-3*log(c*x^n)+-1//2*d*e^-4*(6a+5*b*n+6*b*log(c*x^n))*log(1+e*x*d^-1)+-1//2*e^-1*x^3*(d+e*x)^-2*(a+b*log(c*x^n))+-1//2*e^-2*x^2*(d+e*x)^-1*(3a+b*n+3*b*log(c*x^n))+-3*b*d*n*e^-4*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^2*(d+e*x)^-3*(a+b*log(c*x^n)), x) == :((1/2)*e^-3*(2a+2*b*log(c*x^n)+3*b*n)*log(1+e*x*d^-1)+b*n*e^-3*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1//2*x*e^-2*(d+e*x)^-1*(2a+b*n+2*b*log(c*x^n))+-1//2*e^-1*x^2*(d+e*x)^-2*(a+b*log(c*x^n)))
@test integrate(x*(d+e*x)^-3*(a+b*log(c*x^n)), x) == :((1/2)*d^-1*x^2*(d+e*x)^-2*(a+b*log(c*x^n))+-1//2*b*n*e^-2*(d+e*x)^-1+-1//2*b*n*d^-1*e^-2*log(d+e*x))
@test integrate((d+e*x)^-3*(a+b*log(c*x^n)), x) == :(-1//2*e^-1*(d+e*x)^-2*(a+b*log(c*x^n))+(1/2)*b*n*d^-1*e^-1*(d+e*x)^-1+(1/2)*b*n*d^-2*e^-1*log(x)+-1//2*b*n*d^-2*e^-1*log(d+e*x))
@test integrate(x^-1*(d+e*x)^-3*(a+b*log(c*x^n)), x) == :((1/2)*d^-1*(d+e*x)^-2*(a+b*log(c*x^n))+-1*d^-3*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+b*n*d^-3*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-1//2*b*n*d^-3*log(x)+-1//2*b*n*d^-2*(d+e*x)^-1+3//2*b*n*d^-3*log(d+e*x)+-1*e*x*d^-3*(d+e*x)^-1*(a+b*log(c*x^n)))
@test integrate(x^-2*(d+e*x)^-3*(a+b*log(c*x^n)), x) == :(-1*d^-3*x^-1*(a+b*log(c*x^n))+-1*b*n*d^-3*x^-1+3*e*d^-4*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+-1//2*e*d^-2*(d+e*x)^-2*(a+b*log(c*x^n))+(1/2)*b*e*n*d^-4*log(x)+(1/2)*b*e*n*d^-3*(d+e*x)^-1+-3*b*e*n*d^-4*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+2*x*d^-4*e^2*(d+e*x)^-1*(a+b*log(c*x^n))+-5//2*b*e*n*d^-4*log(d+e*x))
@test integrate(x^-3*(d+e*x)^-3*(a+b*log(c*x^n)), x) == :(-1//2*d^-3*x^-2*(a+b*log(c*x^n))+(1/2)*d^-3*e^2*(d+e*x)^-2*(a+b*log(c*x^n))+-6*d^-5*e^2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+3*e*d^-4*x^-1*(a+b*log(c*x^n))+-1//4*b*n*d^-3*x^-2+-3*x*d^-5*e^3*(d+e*x)^-1*(a+b*log(c*x^n))+3*b*e*n*d^-4*x^-1+6*b*n*d^-5*e^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-1//2*b*n*d^-5*e^2*log(x)+-1//2*b*n*d^-4*e^2*(d+e*x)^-1+7//2*b*n*d^-5*e^2*log(d+e*x))
@test integrate(x^5*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(1//12*e^-4*x^2*(60a+47*b*n+60*b*log(c*x^n))+-5//2*b*n*e^-4*x^2+-1//3*e^-1*x^5*(d+e*x)^-3*(a+b*log(c*x^n))+-1//6*d*x*e^-5*(60a+47*b*n)+-1//6*e^-3*x^3*(d+e*x)^-1*(20a+9*b*n+20*b*log(c*x^n))+-1//6*e^-2*x^4*(d+e*x)^-2*(5a+b*n+5*b*log(c*x^n))+1//6*d^2*e^-6*(60a+47*b*n+60*b*log(c*x^n))*log(1+e*x*d^-1)+-10*b*d*x*e^-5*log(c*x^n)+10*b*d*n*x*e^-5+10*b*n*d^2*e^-6*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^4*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(1//3*x*e^-4*(12a+13*b*n)+-4*b*n*x*e^-4+4*b*x*e^-4*log(c*x^n)+-1//3*d*e^-5*(12a+12*b*log(c*x^n)+13*b*n)*log(1+e*x*d^-1)+-1//3*e^-1*x^4*(d+e*x)^-3*(a+b*log(c*x^n))+-1//6*e^-3*x^2*(d+e*x)^-1*(12a+7*b*n+12*b*log(c*x^n))+-1//6*e^-2*x^3*(d+e*x)^-2*(4a+b*n+4*b*log(c*x^n))+-4*b*d*n*e^-5*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^3*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(1//6*e^-4*(6a+6*b*log(c*x^n)+11*b*n)*log(1+e*x*d^-1)+b*n*e^-4*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1//3*e^-1*x^3*(d+e*x)^-3*(a+b*log(c*x^n))+-1//6*x*e^-3*(d+e*x)^-1*(6a+5*b*n+6*b*log(c*x^n))+-1//6*e^-2*x^2*(d+e*x)^-2*(3a+b*n+3*b*log(c*x^n)))
@test integrate(x^2*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(-2//3*b*n*e^-3*(d+e*x)^-1+1//3*d^-1*x^3*(d+e*x)^-3*(a+b*log(c*x^n))+-1//3*b*n*d^-1*e^-3*log(d+e*x)+1//6*b*d*n*e^-3*(d+e*x)^-2)
@test integrate(x*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(-1//2*e^-2*(d+e*x)^-2*(a+b*log(c*x^n))+-1//6*b*n*e^-2*(d+e*x)^-2+1//3*d*e^-2*(d+e*x)^-3*(a+b*log(c*x^n))+-1//6*b*n*d^-2*e^-2*log(d+e*x)+1//6*b*n*d^-1*e^-2*(d+e*x)^-1+1//6*b*n*d^-2*e^-2*log(x))
@test integrate((d+e*x)^-4*(a+b*log(c*x^n)), x) == :(-1//3*e^-1*(d+e*x)^-3*(a+b*log(c*x^n))+-1//3*b*n*d^-3*e^-1*log(d+e*x)+1//3*b*n*d^-3*e^-1*log(x)+1//3*b*n*d^-2*e^-1*(d+e*x)^-1+1//6*b*n*d^-1*e^-1*(d+e*x)^-2)
@test integrate(x^-1*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :((1/2)*d^-2*(d+e*x)^-2*(a+b*log(c*x^n))+-1*d^-4*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+1//3*d^-1*(d+e*x)^-3*(a+b*log(c*x^n))+b*n*d^-4*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-5//6*b*n*d^-4*log(x)+-5//6*b*n*d^-3*(d+e*x)^-1+-1//6*b*n*d^-2*(d+e*x)^-2+11//6*b*n*d^-4*log(d+e*x)+-1*e*x*d^-4*(d+e*x)^-1*(a+b*log(c*x^n)))
@test integrate(x^-2*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(-1*d^-4*x^-1*(a+b*log(c*x^n))+-1*b*n*d^-4*x^-1+-1*e*d^-3*(d+e*x)^-2*(a+b*log(c*x^n))+4*e*d^-5*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+-1//3*e*d^-2*(d+e*x)^-3*(a+b*log(c*x^n))+-4*b*e*n*d^-5*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+3*x*d^-5*e^2*(d+e*x)^-1*(a+b*log(c*x^n))+-13//3*b*e*n*d^-5*log(d+e*x)+1//6*b*e*n*d^-3*(d+e*x)^-2+4//3*b*e*n*d^-5*log(x)+4//3*b*e*n*d^-4*(d+e*x)^-1)
@test integrate(x^-3*(d+e*x)^-4*(a+b*log(c*x^n)), x) == :(-1//2*d^-4*x^-2*(a+b*log(c*x^n))+-10*d^-6*e^2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+4*e*d^-5*x^-1*(a+b*log(c*x^n))+-1//4*b*n*d^-4*x^-2+1//3*d^-3*e^2*(d+e*x)^-3*(a+b*log(c*x^n))+3//2*d^-4*e^2*(d+e*x)^-2*(a+b*log(c*x^n))+-6*x*d^-6*e^3*(d+e*x)^-1*(a+b*log(c*x^n))+4*b*e*n*d^-5*x^-1+10*b*n*d^-6*e^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-11//6*b*n*d^-6*e^2*log(x)+-11//6*b*n*d^-5*e^2*(d+e*x)^-1+-1//6*b*n*d^-4*e^2*(d+e*x)^-2+47//6*b*n*d^-6*e^2*log(d+e*x))
@test integrate(x^8*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(1//20*e^-7*x^2*(280a+280*b*log(c*x^n)+341*b*n)+-7*b*n*e^-7*x^2+-1//6*e^-1*x^8*(d+e*x)^-6*(a+b*log(c*x^n))+-1//10*d*x*e^-8*(280a+341*b*n)+-1//30*e^-2*x^7*(d+e*x)^-5*(8a+b*n+8*b*log(c*x^n))+-1//90*e^-6*x^3*(d+e*x)^-1*(840a+743*b*n+840*b*log(c*x^n))+-1//120*e^-3*x^6*(d+e*x)^-4*(56a+15*b*n+56*b*log(c*x^n))+-1//180*e^-4*x^5*(d+e*x)^-3*(168a+73*b*n+168*b*log(c*x^n))+-1//360*e^-5*x^4*(d+e*x)^-2*(840a+533*b*n+840*b*log(c*x^n))+1//10*d^2*e^-9*(280a+280*b*log(c*x^n)+341*b*n)*log(1+e*x*d^-1)+-28*b*d*x*e^-8*log(c*x^n)+28*b*d*n*x*e^-8+28*b*n*d^2*e^-9*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^7*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(1//20*x*e^-7*(140a+223*b*n)+-7*b*n*x*e^-7+7*b*x*e^-7*log(c*x^n)+-1//6*e^-1*x^7*(d+e*x)^-6*(a+b*log(c*x^n))+-1//20*d*e^-8*(140a+140*b*log(c*x^n)+223*b*n)*log(1+e*x*d^-1)+-1//30*e^-2*x^6*(d+e*x)^-5*(7a+b*n+7*b*log(c*x^n))+-1//40*e^-6*x^2*(d+e*x)^-1*(140a+140*b*log(c*x^n)+153*b*n)+-1//120*e^-3*x^5*(d+e*x)^-4*(42a+13*b*n+42*b*log(c*x^n))+-1//360*e^-5*x^3*(d+e*x)^-2*(420a+319*b*n+420*b*log(c*x^n))+-1//360*e^-4*x^4*(d+e*x)^-3*(210a+107*b*n+210*b*log(c*x^n))+-7*b*d*n*e^-8*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^6*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(1//20*e^-7*(20a+20*b*log(c*x^n)+49*b*n)*log(1+e*x*d^-1)+b*n*e^-7*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1//6*e^-1*x^6*(d+e*x)^-6*(a+b*log(c*x^n))+-1//20*x*e^-6*(d+e*x)^-1*(20a+20*b*log(c*x^n)+29*b*n)+-1//30*e^-2*x^5*(d+e*x)^-5*(6a+b*n+6*b*log(c*x^n))+-1//40*e^-5*x^2*(d+e*x)^-2*(20a+19*b*n+20*b*log(c*x^n))+-1//120*e^-3*x^4*(d+e*x)^-4*(30a+11*b*n+30*b*log(c*x^n))+-1//180*e^-4*x^3*(d+e*x)^-3*(60a+37*b*n+60*b*log(c*x^n)))
@test integrate(x^5*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-5//6*b*n*e^-6*(d+e*x)^-1+1//6*d^-1*x^6*(d+e*x)^-6*(a+b*log(c*x^n))+-5//9*b*n*d^2*e^-6*(d+e*x)^-3+-1//6*b*n*d^-1*e^-6*log(d+e*x)+-1//30*b*n*d^4*e^-6*(d+e*x)^-5+5//6*b*d*n*e^-6*(d+e*x)^-2+5//24*b*n*d^3*e^-6*(d+e*x)^-4)
@test integrate(x^4*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(1//6*d^-1*x^5*(d+e*x)^-6*(a+b*log(c*x^n))+1//10*b*n*e^-5*(d+e*x)^-2+1//30*d^-2*x^5*(d+e*x)^-5*(a+b*log(c*x^n))+-2//15*b*n*d^-1*e^-5*(d+e*x)^-1+-2//45*b*d*n*e^-5*(d+e*x)^-3+-1//30*b*n*d^-2*e^-5*log(d+e*x)+-1//30*b*n*d^-2*x^5*(d+e*x)^-5+1//120*b*n*d^2*e^-5*(d+e*x)^-4)
@test integrate(x^3*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-1//3*e^-4*(d+e*x)^-3*(a+b*log(c*x^n))+-19//180*b*n*e^-4*(d+e*x)^-3+-3//5*d^2*e^-4*(d+e*x)^-5*(a+b*log(c*x^n))+1//6*d^3*e^-4*(d+e*x)^-6*(a+b*log(c*x^n))+3//4*d*e^-4*(d+e*x)^-4*(a+b*log(c*x^n))+-1//30*b*n*d^2*e^-4*(d+e*x)^-5+-1//60*b*n*d^-3*e^-4*log(d+e*x)+1//60*b*n*d^-3*e^-4*log(x)+1//60*b*n*d^-2*e^-4*(d+e*x)^-1+1//120*b*n*d^-1*e^-4*(d+e*x)^-2+13//120*b*d*n*e^-4*(d+e*x)^-4)
@test integrate(x^2*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-1//4*e^-3*(d+e*x)^-4*(a+b*log(c*x^n))+-7//120*b*n*e^-3*(d+e*x)^-4+-1//6*d^2*e^-3*(d+e*x)^-6*(a+b*log(c*x^n))+2//5*d*e^-3*(d+e*x)^-5*(a+b*log(c*x^n))+-1//60*b*n*d^-4*e^-3*log(d+e*x)+1//30*b*d*n*e^-3*(d+e*x)^-5+1//60*b*n*d^-4*e^-3*log(x)+1//60*b*n*d^-3*e^-3*(d+e*x)^-1+1//120*b*n*d^-2*e^-3*(d+e*x)^-2+1//180*b*n*d^-1*e^-3*(d+e*x)^-3)
@test integrate(x*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-1//5*e^-2*(d+e*x)^-5*(a+b*log(c*x^n))+-1//30*b*n*e^-2*(d+e*x)^-5+1//6*d*e^-2*(d+e*x)^-6*(a+b*log(c*x^n))+-1//30*b*n*d^-5*e^-2*log(d+e*x)+1//30*b*n*d^-5*e^-2*log(x)+1//30*b*n*d^-4*e^-2*(d+e*x)^-1+1//60*b*n*d^-3*e^-2*(d+e*x)^-2+1//90*b*n*d^-2*e^-2*(d+e*x)^-3+1//120*b*n*d^-1*e^-2*(d+e*x)^-4)
@test integrate((d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-1//6*e^-1*(d+e*x)^-6*(a+b*log(c*x^n))+-1//6*b*n*d^-6*e^-1*log(d+e*x)+1//6*b*n*d^-6*e^-1*log(x)+1//6*b*n*d^-5*e^-1*(d+e*x)^-1+1//12*b*n*d^-4*e^-1*(d+e*x)^-2+1//18*b*n*d^-3*e^-1*(d+e*x)^-3+1//24*b*n*d^-2*e^-1*(d+e*x)^-4+1//30*b*n*d^-1*e^-1*(d+e*x)^-5)
@test integrate(x^-1*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :((1/2)*d^-5*(d+e*x)^-2*(a+b*log(c*x^n))+-1*d^-7*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+1//3*d^-4*(d+e*x)^-3*(a+b*log(c*x^n))+1//4*d^-3*(d+e*x)^-4*(a+b*log(c*x^n))+1//5*d^-2*(d+e*x)^-5*(a+b*log(c*x^n))+1//6*d^-1*(d+e*x)^-6*(a+b*log(c*x^n))+b*n*d^-7*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-37//180*b*n*d^-4*(d+e*x)^-3+-29//20*b*n*d^-7*log(x)+-29//20*b*n*d^-6*(d+e*x)^-1+-19//40*b*n*d^-5*(d+e*x)^-2+-11//120*b*n*d^-3*(d+e*x)^-4+-1//30*b*n*d^-2*(d+e*x)^-5+49//20*b*n*d^-7*log(d+e*x)+-1*e*x*d^-7*(d+e*x)^-1*(a+b*log(c*x^n)))
@test integrate(x^-2*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-1*d^-7*x^-1*(a+b*log(c*x^n))+-1*b*n*d^-7*x^-1+7*e*d^-8*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+-5//2*e*d^-6*(d+e*x)^-2*(a+b*log(c*x^n))+-4//3*e*d^-5*(d+e*x)^-3*(a+b*log(c*x^n))+-3//4*e*d^-4*(d+e*x)^-4*(a+b*log(c*x^n))+-2//5*e*d^-3*(d+e*x)^-5*(a+b*log(c*x^n))+-1//6*e*d^-2*(d+e*x)^-6*(a+b*log(c*x^n))+-7*b*e*n*d^-8*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+6*x*d^-8*e^2*(d+e*x)^-1*(a+b*log(c*x^n))+-223//20*b*e*n*d^-8*log(d+e*x)+1//30*b*e*n*d^-3*(d+e*x)^-5+17//120*b*e*n*d^-4*(d+e*x)^-4+53//40*b*e*n*d^-6*(d+e*x)^-2+79//180*b*e*n*d^-5*(d+e*x)^-3+103//20*b*e*n*d^-8*log(x)+103//20*b*e*n*d^-7*(d+e*x)^-1)
@test integrate(x^-3*(d+e*x)^-7*(a+b*log(c*x^n)), x) == :(-1//2*d^-7*x^-2*(a+b*log(c*x^n))+-28*d^-9*e^2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+7*e*d^-8*x^-1*(a+b*log(c*x^n))+-1//4*b*n*d^-7*x^-2+1//6*d^-3*e^2*(d+e*x)^-6*(a+b*log(c*x^n))+3//2*d^-5*e^2*(d+e*x)^-4*(a+b*log(c*x^n))+3//5*d^-4*e^2*(d+e*x)^-5*(a+b*log(c*x^n))+10//3*d^-6*e^2*(d+e*x)^-3*(a+b*log(c*x^n))+15//2*d^-7*e^2*(d+e*x)^-2*(a+b*log(c*x^n))+-21*x*d^-9*e^3*(d+e*x)^-1*(a+b*log(c*x^n))+7*b*e*n*d^-8*x^-1+28*b*n*d^-9*e^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-131//10*b*n*d^-9*e^2*log(x)+-131//10*b*n*d^-8*e^2*(d+e*x)^-1+-34//45*b*n*d^-6*e^2*(d+e*x)^-3+-23//120*b*n*d^-5*e^2*(d+e*x)^-4+-14//5*b*n*d^-7*e^2*(d+e*x)^-2+-1//30*b*n*d^-4*e^2*(d+e*x)^-5+341//10*b*n*d^-9*e^2*log(d+e*x))
@test integrate((1+-1*c*x)^-1*log(c*x), x) == :(c^-1*Polylogarithms.polylog(2,1+-1*c*x))
@test integrate((c+-1x)^-1*log(x*c^-1), x) == :(Polylogarithms.polylog(2,1+-1*x*c^-1))
@test integrate(x^2*(a+b*log(c*x^n))^2*(d+e*x), x) == :(1//3*d*x^3*(a+b*log(c*x^n))^2+1//4*e*x^4*(a+b*log(c*x^n))^2+1//32*e*b^2*n^2*x^4+2//27*d*b^2*n^2*x^3+-2//9*b*d*n*x^3*(a+b*log(c*x^n))+-1//8*b*e*n*x^4*(a+b*log(c*x^n)))
@test integrate(x*(a+b*log(c*x^n))^2*(d+e*x), x) == :((1/2)*d*x^2*(a+b*log(c*x^n))^2+1//3*e*x^3*(a+b*log(c*x^n))^2+1//4*d*b^2*n^2*x^2+2//27*e*b^2*n^2*x^3+-2//9*b*e*n*x^3*(a+b*log(c*x^n))+-1//2*b*d*n*x^2*(a+b*log(c*x^n)))
@test integrate((a+b*log(c*x^n))^2*(d+e*x), x) == :(d*x*(a+b*log(c*x^n))^2+(1/2)*e*x^2*(a+b*log(c*x^n))^2+2*d*x*b^2*n^2+1//4*e*b^2*n^2*x^2+-2*a*b*d*n*x+-2*d*n*x*b^2*log(c*x^n)+-1//2*b*e*n*x^2*(a+b*log(c*x^n)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x), x) == :(e*x*(a+b*log(c*x^n))^2+2*e*x*b^2*n^2+1//3*d*b^-1*n^-1*(a+b*log(c*x^n))^3+-2*a*b*e*n*x+-2*e*n*x*b^2*log(c*x^n))
@test integrate(x^-2*(a+b*log(c*x^n))^2*(d+e*x), x) == :(-1*d*x^-1*(a+b*log(c*x^n))^2+-2*d*b^2*n^2*x^-1+1//3*e*b^-1*n^-1*(a+b*log(c*x^n))^3+-2*b*d*n*x^-1*(a+b*log(c*x^n)))
@test integrate(x^-3*(a+b*log(c*x^n))^2*(d+e*x), x) == :(-1*e*x^-1*(a+b*log(c*x^n))^2+-1//2*d*x^-2*(a+b*log(c*x^n))^2+-2*e*b^2*n^2*x^-1+-1//4*d*b^2*n^2*x^-2+-2*b*e*n*x^-1*(a+b*log(c*x^n))+-1//2*b*d*n*x^-2*(a+b*log(c*x^n)))
@test integrate(x^-4*(a+b*log(c*x^n))^2*(d+e*x), x) == :(-1//2*e*x^-2*(a+b*log(c*x^n))^2+-1//3*d*x^-3*(a+b*log(c*x^n))^2+-2//27*d*b^2*n^2*x^-3+-1//4*e*b^2*n^2*x^-2+-2//9*b*d*n*x^-3*(a+b*log(c*x^n))+-1//2*b*e*n*x^-2*(a+b*log(c*x^n)))
@test integrate(x^-5*(a+b*log(c*x^n))^2*(d+e*x), x) == :(-1//3*e*x^-3*(a+b*log(c*x^n))^2+-1//4*d*x^-4*(a+b*log(c*x^n))^2+-2//27*e*b^2*n^2*x^-3+-1//32*d*b^2*n^2*x^-4+-2//9*b*e*n*x^-3*(a+b*log(c*x^n))+-1//8*b*d*n*x^-4*(a+b*log(c*x^n)))
@test integrate(x^2*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :(1//3*d^2*x^3*(a+b*log(c*x^n))^2+1//5*e^2*x^5*(a+b*log(c*x^n))^2+(1/2)*d*e*x^4*(a+b*log(c*x^n))^2+2//27*b^2*d^2*n^2*x^3+2//125*b^2*e^2*n^2*x^5+-2//9*b*n*d^2*x^3*(a+b*log(c*x^n))+-2//25*b*n*e^2*x^5*(a+b*log(c*x^n))+1//16*d*e*b^2*n^2*x^4+-1//4*b*d*e*n*x^4*(a+b*log(c*x^n)))
@test integrate(x*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :((1/2)*d^2*x^2*(a+b*log(c*x^n))^2+1//4*e^2*x^4*(a+b*log(c*x^n))^2+1//4*b^2*d^2*n^2*x^2+1//32*b^2*e^2*n^2*x^4+2//3*d*e*x^3*(a+b*log(c*x^n))^2+-1//2*b*n*d^2*x^2*(a+b*log(c*x^n))+-1//8*b*n*e^2*x^4*(a+b*log(c*x^n))+4//27*d*e*b^2*n^2*x^3+-4//9*b*d*e*n*x^3*(a+b*log(c*x^n)))
@test integrate((a+b*log(c*x^n))^2*(d+e*x)^2, x) == :(1//3*e^-1*(a+b*log(c*x^n))^2*(d+e*x)^3+2*x*b^2*d^2*n^2+2//27*b^2*e^2*n^2*x^3+(1/2)*d*e*b^2*n^2*x^2+-2*b*n*x*d^2*(a+b*log(c*x^n))+-2//9*b*n*e^2*x^3*(a+b*log(c*x^n))+1//3*b^2*d^3*e^-1*n^2*log(x)^2+-1*b*d*e*n*x^2*(a+b*log(c*x^n))+-2//3*b*n*d^3*e^-1*(a+b*log(c*x^n))*log(x))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :((1/2)*e^2*x^2*(a+b*log(c*x^n))^2+2*d*e*x*(a+b*log(c*x^n))^2+1//3*b^-1*d^2*n^-1*(a+b*log(c*x^n))^3+1//4*b^2*e^2*n^2*x^2+4*d*e*x*b^2*n^2+-1//2*b*n*e^2*x^2*(a+b*log(c*x^n))+-4*a*b*d*e*n*x+-4*d*e*n*x*b^2*log(c*x^n))
@test integrate(x^-2*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :(x*e^2*(a+b*log(c*x^n))^2+-1*d^2*x^-1*(a+b*log(c*x^n))^2+-2*b^2*d^2*n^2*x^-1+2*x*b^2*e^2*n^2+-2*a*b*n*x*e^2+-2*b*n*d^2*x^-1*(a+b*log(c*x^n))+-2*n*x*b^2*e^2*log(c*x^n)+2//3*d*e*b^-1*n^-1*(a+b*log(c*x^n))^3)
@test integrate(x^-3*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :(-1//2*d^2*x^-2*(a+b*log(c*x^n))^2+-2*d*e*x^-1*(a+b*log(c*x^n))^2+-1//4*b^2*d^2*n^2*x^-2+1//3*b^-1*e^2*n^-1*(a+b*log(c*x^n))^3+-4*d*e*b^2*n^2*x^-1+-1//2*b*n*d^2*x^-2*(a+b*log(c*x^n))+-4*b*d*e*n*x^-1*(a+b*log(c*x^n)))
@test integrate(x^-4*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :(-1*e^2*x^-1*(a+b*log(c*x^n))^2+-1//3*d^2*x^-3*(a+b*log(c*x^n))^2+-1*d*e*x^-2*(a+b*log(c*x^n))^2+-2*b^2*e^2*n^2*x^-1+-2//27*b^2*d^2*n^2*x^-3+-2*b*n*e^2*x^-1*(a+b*log(c*x^n))+-2//9*b*n*d^2*x^-3*(a+b*log(c*x^n))+-1//2*d*e*b^2*n^2*x^-2+-1*b*d*e*n*x^-2*(a+b*log(c*x^n)))
@test integrate(x^-5*(a+b*log(c*x^n))^2*(d+e*x)^2, x) == :(-1//2*e^2*x^-2*(a+b*log(c*x^n))^2+-1//4*d^2*x^-4*(a+b*log(c*x^n))^2+-2//3*d*e*x^-3*(a+b*log(c*x^n))^2+-1//4*b^2*e^2*n^2*x^-2+-1//32*b^2*d^2*n^2*x^-4+-4//27*d*e*b^2*n^2*x^-3+-1//2*b*n*e^2*x^-2*(a+b*log(c*x^n))+-1//8*b*n*d^2*x^-4*(a+b*log(c*x^n))+-4//9*b*d*e*n*x^-3*(a+b*log(c*x^n)))
@test integrate(x^3*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(1//3*e^-1*x^3*(a+b*log(c*x^n))^2+x*d^2*e^-3*(a+b*log(c*x^n))^2+-1*d^3*e^-4*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+-1//2*d*e^-2*x^2*(a+b*log(c*x^n))^2+2//27*b^2*e^-1*n^2*x^3+2*x*b^2*d^2*e^-3*n^2+2*b^2*d^3*e^-4*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+-2//9*b*n*e^-1*x^3*(a+b*log(c*x^n))+-1//4*d*b^2*e^-2*n^2*x^2+(1/2)*b*d*n*e^-2*x^2*(a+b*log(c*x^n))+-2*a*b*n*x*d^2*e^-3+-2*b*n*d^3*e^-4*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1)+-2*n*x*b^2*d^2*e^-3*log(c*x^n))
@test integrate(x^2*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :((1/2)*e^-1*x^2*(a+b*log(c*x^n))^2+d^2*e^-3*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+-1*d*x*e^-2*(a+b*log(c*x^n))^2+1//4*b^2*e^-1*n^2*x^2+-2*d*x*b^2*e^-2*n^2+-2*b^2*d^2*e^-3*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+-1//2*b*n*e^-1*x^2*(a+b*log(c*x^n))+2*a*b*d*n*x*e^-2+2*b*n*d^2*e^-3*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1)+2*d*n*x*b^2*e^-2*log(c*x^n))
@test integrate(x*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(x*e^-1*(a+b*log(c*x^n))^2+-1*d*e^-2*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+2*x*b^2*e^-1*n^2+-2*a*b*n*x*e^-1+-2*n*x*b^2*e^-1*log(c*x^n)+2*d*b^2*e^-2*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+-2*b*d*n*e^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate((a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(e^-1*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+-2*b^2*e^-1*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+2*b*n*e^-1*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(-1*d^-1*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+2*b^2*d^-1*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+2*b*n*d^-1*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-2*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(-1*d^-1*x^-1*(a+b*log(c*x^n))^2+e*d^-2*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+-2*b^2*d^-1*n^2*x^-1+-2*b*n*d^-1*x^-1*(a+b*log(c*x^n))+-2*e*b^2*d^-2*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+-2*b*e*n*d^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-3*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(-1//2*d^-1*x^-2*(a+b*log(c*x^n))^2+e*d^-2*x^-1*(a+b*log(c*x^n))^2+-1*d^-3*e^2*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+-1//4*b^2*d^-1*n^2*x^-2+2*e*b^2*d^-2*n^2*x^-1+2*b^2*d^-3*e^2*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+-1//2*b*n*d^-1*x^-2*(a+b*log(c*x^n))+2*b*e*n*d^-2*x^-1*(a+b*log(c*x^n))+2*b*n*d^-3*e^2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x^-4*(a+b*log(c*x^n))^2*(d+e*x)^-1, x) == :(-1//3*d^-1*x^-3*(a+b*log(c*x^n))^2+d^-4*e^3*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+(1/2)*e*d^-2*x^-2*(a+b*log(c*x^n))^2+-1*d^-3*e^2*x^-1*(a+b*log(c*x^n))^2+-2//27*b^2*d^-1*n^2*x^-3+-2*b^2*d^-4*e^3*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+-2*b^2*d^-3*e^2*n^2*x^-1+-2//9*b*n*d^-1*x^-3*(a+b*log(c*x^n))+1//4*e*b^2*d^-2*n^2*x^-2+(1/2)*b*e*n*d^-2*x^-2*(a+b*log(c*x^n))+-2*b*n*d^-4*e^3*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-2*b*n*d^-3*e^2*x^-1*(a+b*log(c*x^n)))
@test integrate(x^3*(a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :((1/2)*e^-2*x^2*(a+b*log(c*x^n))^2+-2*d*x*e^-3*(a+b*log(c*x^n))^2+3*d^2*e^-4*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+1//4*b^2*e^-2*n^2*x^2+-1*x*d^2*e^-3*(a+b*log(c*x^n))^2*(d+e*x)^-1+-6*b^2*d^2*e^-4*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+-4*d*x*b^2*e^-3*n^2+2*b^2*d^2*e^-4*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1//2*b*n*e^-2*x^2*(a+b*log(c*x^n))+2*b*n*d^2*e^-4*(a+b*log(c*x^n))*log(1+e*x*d^-1)+4*a*b*d*n*x*e^-3+4*d*n*x*b^2*e^-3*log(c*x^n)+6*b*n*d^2*e^-4*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1))
@test integrate(x^2*(a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :(x*e^-2*(a+b*log(c*x^n))^2+-2*d*e^-3*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+2*x*b^2*e^-2*n^2+d*x*e^-2*(a+b*log(c*x^n))^2*(d+e*x)^-1+-2*a*b*n*x*e^-2+-2*d*b^2*e^-3*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-2*n*x*b^2*e^-2*log(c*x^n)+4*d*b^2*e^-3*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+-4*b*d*n*e^-3*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1)+-2*b*d*n*e^-3*(a+b*log(c*x^n))*log(1+e*x*d^-1))
@test integrate(x*(a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :(e^-2*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+-1*x*e^-1*(a+b*log(c*x^n))^2*(d+e*x)^-1+-2*b^2*e^-2*n^2*Polylogarithms.polylog(3,-1*e*x*d^-1)+2*b^2*e^-2*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+2*b*n*e^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1)+2*b*n*e^-2*(a+b*log(c*x^n))*log(1+e*x*d^-1))
@test integrate((a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :(x*d^-1*(a+b*log(c*x^n))^2*(d+e*x)^-1+-2*b^2*d^-1*e^-1*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-2*b*n*d^-1*e^-1*(a+b*log(c*x^n))*log(1+e*x*d^-1))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :(-1*d^-2*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+2*b^2*d^-2*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+2*b^2*d^-2*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+-1*e*x*d^-2*(a+b*log(c*x^n))^2*(d+e*x)^-1+2*b*n*d^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+2*b*n*d^-2*(a+b*log(c*x^n))*log(1+e*x*d^-1))
@test integrate(x^-2*(a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :(-1*d^-2*x^-1*(a+b*log(c*x^n))^2+-2*b^2*d^-2*n^2*x^-1+2*e*d^-3*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+x*d^-3*e^2*(a+b*log(c*x^n))^2*(d+e*x)^-1+-4*e*b^2*d^-3*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+-2*b*n*d^-2*x^-1*(a+b*log(c*x^n))+-2*e*b^2*d^-3*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-4*b*e*n*d^-3*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-2*b*e*n*d^-3*(a+b*log(c*x^n))*log(1+e*x*d^-1))
@test integrate(x^-3*(a+b*log(c*x^n))^2*(d+e*x)^-2, x) == :(-1//2*d^-2*x^-2*(a+b*log(c*x^n))^2+-3*d^-4*e^2*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^-1)+2*e*d^-3*x^-1*(a+b*log(c*x^n))^2+-1//4*b^2*d^-2*n^2*x^-2+-1*x*d^-4*e^3*(a+b*log(c*x^n))^2*(d+e*x)^-1+2*b^2*d^-4*e^2*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+4*e*b^2*d^-3*n^2*x^-1+6*b^2*d^-4*e^2*n^2*Polylogarithms.polylog(3,-1*d*e^-1*x^-1)+-1//2*b*n*d^-2*x^-2*(a+b*log(c*x^n))+2*b*n*d^-4*e^2*(a+b*log(c*x^n))*log(1+e*x*d^-1)+4*b*e*n*d^-3*x^-1*(a+b*log(c*x^n))+6*b*n*d^-4*e^2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^-1))
@test integrate(x*(a+b*log(c*x^n))^2*(d+e*x)^-3, x) == :((1/2)*d^-1*x^2*(a+b*log(c*x^n))^2*(d+e*x)^-2+-1*b^2*d^-1*e^-2*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1*b*n*d^-1*e^-2*(a+b*n+b*log(c*x^n))*log(1+e*x*d^-1)+b*n*x*d^-1*e^-1*(d+e*x)^-1*(a+b*log(c*x^n)))
@test integrate((a+b*log(c*x^n))^2*(d+e*x)^-3, x) == :(-1//2*e^-1*(a+b*log(c*x^n))^2*(d+e*x)^-2+b^2*d^-2*e^-1*n^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+b^2*d^-2*e^-1*n^2*log(d+e*x)+-1*b*n*x*d^-2*(d+e*x)^-1*(a+b*log(c*x^n))+-1*b*n*d^-2*e^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1))
@test integrate(x^2*(a+b*log(c*x^n))^2*(d+e*x)^-4, x) == :(1//3*d^-1*x^3*(a+b*log(c*x^n))^2*(d+e*x)^-3+-2//3*b^2*d^-1*e^-3*n^2*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1//3*b*n*d^-1*e^-3*(2a+2*b*log(c*x^n)+3*b*n)*log(1+e*x*d^-1)+1//3*b*n*x*d^-1*e^-2*(d+e*x)^-1*(2a+b*n+2*b*log(c*x^n))+1//3*b*n*d^-1*e^-1*x^2*(d+e*x)^-2*(a+b*log(c*x^n)))
@test integrate((a+b*log(c*x^n))^2*(d+e*x)^-4, x) == :(-1//3*e^-1*(a+b*log(c*x^n))^2*(d+e*x)^-3+b^2*d^-3*e^-1*n^2*log(d+e*x)+-1//3*b^2*d^-3*e^-1*n^2*log(x)+-1//3*b^2*d^-2*e^-1*n^2*(d+e*x)^-1+2//3*b^2*d^-3*e^-1*n^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+-2//3*b*n*x*d^-3*(d+e*x)^-1*(a+b*log(c*x^n))+-2//3*b*n*d^-3*e^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^-1)+1//3*b*n*d^-1*e^-1*(d+e*x)^-2*(a+b*log(c*x^n)))
@test integrate(x^-1*(a+b*log(c*x^n))^3*(d+e*x)^-1, x) == :(-1*d^-1*(a+b*log(c*x^n))^3*log(1+d*e^-1*x^-1)+6*b^3*d^-1*n^3*Polylogarithms.polylog(4,-1*d*e^-1*x^-1)+3*b*n*d^-1*(a+b*log(c*x^n))^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+6*b^2*d^-1*n^2*(a+b*log(c*x^n))*Polylogarithms.polylog(3,-1*d*e^-1*x^-1))
@test integrate(x^-1*(a+b*log(c*x^n))^3*(d+e*x)^-2, x) == :(-1*d^-2*(a+b*log(c*x^n))^3*log(1+d*e^-1*x^-1)+-6*b^3*d^-2*n^3*Polylogarithms.polylog(3,-1*e*x*d^-1)+6*b^3*d^-2*n^3*Polylogarithms.polylog(4,-1*d*e^-1*x^-1)+-1*e*x*d^-2*(a+b*log(c*x^n))^3*(d+e*x)^-1+3*b*n*d^-2*(a+b*log(c*x^n))^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-1)+3*b*n*d^-2*(a+b*log(c*x^n))^2*log(1+e*x*d^-1)+6*b^2*d^-2*n^2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*x*d^-1)+6*b^2*d^-2*n^2*(a+b*log(c*x^n))*Polylogarithms.polylog(3,-1*d*e^-1*x^-1))
@test integrate((a+b*log(c*x^n))^(1/2)*(d+e*x), x) == :(d*x*(a+b*log(c*x^n))^(1/2)+(1/2)*e*x^2*(a+b*log(c*x^n))^(1/2)+-1//2*d*x*pi^(1/2)*b^(1/2)*n^(1/2)*(c*x^n)^(-1*n^-1)*erfi(b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-1*a*b^-1*n^-1)+-1//8*e*2^(1/2)*pi^(1/2)*b^(1/2)*n^(1/2)*x^2*(c*x^n)^(-2*n^-1)*erfi(2^(1/2)*b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-2*a*b^-1*n^-1))
@test integrate((a+b*log(c*x^n))^(1/2)*(d+e*x)^2, x) == :(x*d^2*(a+b*log(c*x^n))^(1/2)+1//3*e^2*x^3*(a+b*log(c*x^n))^(1/2)+d*e*x^2*(a+b*log(c*x^n))^(1/2)+-1//2*x*pi^(1/2)*b^(1/2)*d^2*n^(1/2)*(c*x^n)^(-1*n^-1)*erfi(b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-1*a*b^-1*n^-1)+-1//18*3^(1/2)*pi^(1/2)*b^(1/2)*e^2*n^(1/2)*x^3*(c*x^n)^(-3*n^-1)*erfi(3^(1/2)*b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-3*a*b^-1*n^-1)+-1//4*d*e*2^(1/2)*pi^(1/2)*b^(1/2)*n^(1/2)*x^2*(c*x^n)^(-2*n^-1)*erfi(2^(1/2)*b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-2*a*b^-1*n^-1))
@test integrate((a+b*log(c*x^n))^(1/2)*(d+e*x)^3, x) == :(x*d^3*(a+b*log(c*x^n))^(1/2)+1//4*e^3*x^4*(a+b*log(c*x^n))^(1/2)+d*e^2*x^3*(a+b*log(c*x^n))^(1/2)+3//2*e*d^2*x^2*(a+b*log(c*x^n))^(1/2)+-1//2*x*pi^(1/2)*b^(1/2)*d^3*n^(1/2)*(c*x^n)^(-1*n^-1)*erfi(b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-1*a*b^-1*n^-1)+-1//16*pi^(1/2)*b^(1/2)*e^3*n^(1/2)*x^4*(c*x^n)^(-4*n^-1)*erfi(2*b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-4*a*b^-1*n^-1)+-3//8*e*2^(1/2)*pi^(1/2)*b^(1/2)*d^2*n^(1/2)*x^2*(c*x^n)^(-2*n^-1)*erfi(2^(1/2)*b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-2*a*b^-1*n^-1)+-1//6*d*3^(1/2)*pi^(1/2)*b^(1/2)*e^2*n^(1/2)*x^3*(c*x^n)^(-3*n^-1)*erfi(3^(1/2)*b^-1//2*n^-1//2*(a+b*log(c*x^n))^(1/2))*exp(-3*a*b^-1*n^-1))
@test integrate(x^3*(d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(2//9*e^-4*(d+e*x)^9//2*(a+b*log(c*x^n))+-6//7*d*e^-4*(d+e*x)^7//2*(a+b*log(c*x^n))+-4//81*b*n*e^-4*(d+e*x)^9//2+-2//3*d^3*e^-4*(d+e*x)^3//2*(a+b*log(c*x^n))+6//5*d^2*e^-4*(d+e*x)^5//2*(a+b*log(c*x^n))+-356//1575*b*n*d^2*e^-4*(d+e*x)^5//2+-64//315*b*n*d^9//2*e^-4*arctanh(d^-1//2*(d+e*x)^(1/2))+64//315*b*n*d^4*e^-4*(d+e*x)^(1/2)+64//945*b*n*d^3*e^-4*(d+e*x)^3//2+80//441*b*d*n*e^-4*(d+e*x)^7//2)
@test integrate(x^2*(d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(2//7*e^-3*(d+e*x)^7//2*(a+b*log(c*x^n))+-4//5*d*e^-3*(d+e*x)^5//2*(a+b*log(c*x^n))+-4//49*b*n*e^-3*(d+e*x)^7//2+2//3*d^2*e^-3*(d+e*x)^3//2*(a+b*log(c*x^n))+-32//105*b*n*d^3*e^-3*(d+e*x)^(1/2)+-32//315*b*n*d^2*e^-3*(d+e*x)^3//2+32//105*b*n*d^7//2*e^-3*arctanh(d^-1//2*(d+e*x)^(1/2))+36//175*b*d*n*e^-3*(d+e*x)^5//2)
@test integrate(x*(d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(2//5*e^-2*(d+e*x)^5//2*(a+b*log(c*x^n))+-4//25*b*n*e^-2*(d+e*x)^5//2+-2//3*d*e^-2*(d+e*x)^3//2*(a+b*log(c*x^n))+-8//15*b*n*d^5//2*e^-2*arctanh(d^-1//2*(d+e*x)^(1/2))+8//15*b*n*d^2*e^-2*(d+e*x)^(1/2)+8//45*b*d*n*e^-2*(d+e*x)^3//2)
@test integrate((d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(2//3*e^-1*(d+e*x)^3//2*(a+b*log(c*x^n))+-4//9*b*n*e^-1*(d+e*x)^3//2+-4//3*b*d*n*e^-1*(d+e*x)^(1/2)+4//3*b*n*d^3//2*e^-1*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate(x^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(2*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4*b*n*(d+e*x)^(1/2)+-2*d^(1/2)*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-2*b*n*d^(1/2)*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+2*b*n*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))^2+4*b*n*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))+-4*b*n*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-2*(d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(-1*x^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-1*b*n*x^-1*(d+e*x)^(1/2)+-1*e*d^-1//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+b*e*n*d^-1//2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+-1*b*e*n*d^-1//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+-1*b*e*n*d^-1//2*arctanh(d^-1//2*(d+e*x)^(1/2))+-2*b*e*n*d^-1//2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-3*(d+e*x)^(1/2)*(a+b*log(c*x^n)), x) == :(-1//2*x^-2*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-1//4*b*n*x^-2*(d+e*x)^(1/2)+1//4*d^-3//2*e^2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-1//4*b*n*d^-3//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+-1//4*e*d^-1*x^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-1//8*b*n*d^-3//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))+1//4*b*n*d^-3//2*e^2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+(1/2)*b*n*d^-3//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+-3//8*b*e*n*d^-1*x^-1*(d+e*x)^(1/2))
@test integrate(x^3*(d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(2//11*e^-4*(d+e*x)^11//2*(a+b*log(c*x^n))+-4//121*b*n*e^-4*(d+e*x)^11//2+-2//3*d*e^-4*(d+e*x)^9//2*(a+b*log(c*x^n))+-2//5*d^3*e^-4*(d+e*x)^5//2*(a+b*log(c*x^n))+6//7*d^2*e^-4*(d+e*x)^7//2*(a+b*log(c*x^n))+-172//1617*b*n*d^2*e^-4*(d+e*x)^7//2+-64//1155*b*n*d^11//2*e^-4*arctanh(d^-1//2*(d+e*x)^(1/2))+32//297*b*d*n*e^-4*(d+e*x)^9//2+64//1155*b*n*d^5*e^-4*(d+e*x)^(1/2)+64//3465*b*n*d^4*e^-4*(d+e*x)^3//2+64//5775*b*n*d^3*e^-4*(d+e*x)^5//2)
@test integrate(x^2*(d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(2//9*e^-3*(d+e*x)^9//2*(a+b*log(c*x^n))+-4//7*d*e^-3*(d+e*x)^7//2*(a+b*log(c*x^n))+-4//81*b*n*e^-3*(d+e*x)^9//2+2//5*d^2*e^-3*(d+e*x)^5//2*(a+b*log(c*x^n))+-32//315*b*n*d^4*e^-3*(d+e*x)^(1/2)+-32//945*b*n*d^3*e^-3*(d+e*x)^3//2+-32//1575*b*n*d^2*e^-3*(d+e*x)^5//2+32//315*b*n*d^9//2*e^-3*arctanh(d^-1//2*(d+e*x)^(1/2))+44//441*b*d*n*e^-3*(d+e*x)^7//2)
@test integrate(x*(d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(2//7*e^-2*(d+e*x)^7//2*(a+b*log(c*x^n))+-4//49*b*n*e^-2*(d+e*x)^7//2+-2//5*d*e^-2*(d+e*x)^5//2*(a+b*log(c*x^n))+-8//35*b*n*d^7//2*e^-2*arctanh(d^-1//2*(d+e*x)^(1/2))+8//35*b*n*d^3*e^-2*(d+e*x)^(1/2)+8//105*b*n*d^2*e^-2*(d+e*x)^3//2+8//175*b*d*n*e^-2*(d+e*x)^5//2)
@test integrate((d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(2//5*e^-1*(d+e*x)^5//2*(a+b*log(c*x^n))+-4//25*b*n*e^-1*(d+e*x)^5//2+-4//5*b*n*d^2*e^-1*(d+e*x)^(1/2)+-4//15*b*d*n*e^-1*(d+e*x)^3//2+4//5*b*n*d^5//2*e^-1*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate(x^-1*(d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(2//3*(d+e*x)^3//2*(a+b*log(c*x^n))+-2*d^3//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+2*d*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4//9*b*n*(d+e*x)^3//2+-2*b*n*d^3//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+2*b*n*d^3//2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+-16//3*b*d*n*(d+e*x)^(1/2)+16//3*b*n*d^3//2*arctanh(d^-1//2*(d+e*x)^(1/2))+-4*b*n*d^3//2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-2*(d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(-1*x^-1*(d+e*x)^3//2*(a+b*log(c*x^n))+3*e*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4*b*e*n*(d+e*x)^(1/2)+-3*e*d^(1/2)*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-1*b*d*n*x^-1*(d+e*x)^(1/2)+-3*b*e*n*d^(1/2)*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+3*b*e*n*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))^2+3*b*e*n*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))+-6*b*e*n*d^(1/2)*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-3*(d+e*x)^3//2*(a+b*log(c*x^n)), x) == :(-1//2*x^-2*(d+e*x)^3//2*(a+b*log(c*x^n))+-3//4*e*x^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-3//4*d^-1//2*e^2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-11//8*b*e*n*x^-1*(d+e*x)^(1/2)+-9//8*b*n*d^-1//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))+-3//4*b*n*d^-1//2*e^2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+-1//4*b*d*n*x^-2*(d+e*x)^(1/2)+3//4*b*n*d^-1//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+-3//2*b*n*d^-1//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^3*(d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(2//7*e^-4*(d+e*x)^7//2*(a+b*log(c*x^n))+-2*d^3*e^-4*(d+e*x)^(1/2)*(a+b*log(c*x^n))+2*d^2*e^-4*(d+e*x)^3//2*(a+b*log(c*x^n))+-6//5*d*e^-4*(d+e*x)^5//2*(a+b*log(c*x^n))+-4//49*b*n*e^-4*(d+e*x)^7//2+-76//105*b*n*d^2*e^-4*(d+e*x)^3//2+-64//35*b*n*d^7//2*e^-4*arctanh(d^-1//2*(d+e*x)^(1/2))+64//35*b*n*d^3*e^-4*(d+e*x)^(1/2)+64//175*b*d*n*e^-4*(d+e*x)^5//2)
@test integrate(x^2*(d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(2//5*e^-3*(d+e*x)^5//2*(a+b*log(c*x^n))+2*d^2*e^-3*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4//3*d*e^-3*(d+e*x)^3//2*(a+b*log(c*x^n))+-4//25*b*n*e^-3*(d+e*x)^5//2+-32//15*b*n*d^2*e^-3*(d+e*x)^(1/2)+28//45*b*d*n*e^-3*(d+e*x)^3//2+32//15*b*n*d^5//2*e^-3*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate(x*(d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(2//3*e^-2*(d+e*x)^3//2*(a+b*log(c*x^n))+-2*d*e^-2*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4//9*b*n*e^-2*(d+e*x)^3//2+-8//3*b*n*d^3//2*e^-2*arctanh(d^-1//2*(d+e*x)^(1/2))+8//3*b*d*n*e^-2*(d+e*x)^(1/2))
@test integrate((d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(2*e^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4*b*n*e^-1*(d+e*x)^(1/2)+4*b*n*d^(1/2)*e^-1*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate(x^-1*(d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-2*d^-1//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-2*b*n*d^-1//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+2*b*n*d^-1//2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+-4*b*n*d^-1//2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-2*(d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(e*d^-3//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-1*d^-1*x^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n))+b*e*n*d^-3//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+-1*b*e*n*d^-3//2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+-1*b*e*n*d^-3//2*arctanh(d^-1//2*(d+e*x)^(1/2))+-1*b*n*d^-1*x^-1*(d+e*x)^(1/2)+2*b*e*n*d^-3//2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-3*(d+e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-3//4*d^-5//2*e^2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-1//2*d^-1*x^-2*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-3//4*b*n*d^-5//2*e^2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+-1//4*b*n*d^-1*x^-2*(d+e*x)^(1/2)+3//4*b*n*d^-5//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+3//4*e*d^-2*x^-1*(d+e*x)^(1/2)*(a+b*log(c*x^n))+7//8*b*n*d^-5//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))+-3//2*b*n*d^-5//2*e^2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+5//8*b*e*n*d^-2*x^-1*(d+e*x)^(1/2))
@test integrate(x^3*(d+e*x)^-3//2*(a+b*log(c*x^n)), x) == :(2//5*e^-4*(d+e*x)^5//2*(a+b*log(c*x^n))+-2*d*e^-4*(d+e*x)^3//2*(a+b*log(c*x^n))+2*d^3*e^-4*(d+e*x)^-1//2*(a+b*log(c*x^n))+6*d^2*e^-4*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4//25*b*n*e^-4*(d+e*x)^5//2+-44//5*b*n*d^2*e^-4*(d+e*x)^(1/2)+16//15*b*d*n*e^-4*(d+e*x)^3//2+64//5*b*n*d^5//2*e^-4*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate(x^2*(d+e*x)^-3//2*(a+b*log(c*x^n)), x) == :(2//3*e^-3*(d+e*x)^3//2*(a+b*log(c*x^n))+-4*d*e^-3*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-2*d^2*e^-3*(d+e*x)^-1//2*(a+b*log(c*x^n))+-4//9*b*n*e^-3*(d+e*x)^3//2+-32//3*b*n*d^3//2*e^-3*arctanh(d^-1//2*(d+e*x)^(1/2))+20//3*b*d*n*e^-3*(d+e*x)^(1/2))
@test integrate(x*(d+e*x)^-3//2*(a+b*log(c*x^n)), x) == :(2*e^-2*(d+e*x)^(1/2)*(a+b*log(c*x^n))+-4*b*n*e^-2*(d+e*x)^(1/2)+2*d*e^-2*(d+e*x)^-1//2*(a+b*log(c*x^n))+8*b*n*d^(1/2)*e^-2*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate((d+e*x)^-3//2*(a+b*log(c*x^n)), x) == :(-1*e^-1*(d+e*x)^-1//2*(2a+2*b*log(c*x^n))+-4*b*n*d^-1//2*e^-1*arctanh(d^-1//2*(d+e*x)^(1/2)))
@test integrate(x^-1*(d+e*x)^-3//2*(a+b*log(c*x^n)), x) == :(d^-1*(d+e*x)^-1//2*(2a+2*b*log(c*x^n))+-2*d^-3//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-2*b*n*d^-3//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+2*b*n*d^-3//2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+4*b*n*d^-3//2*arctanh(d^-1//2*(d+e*x)^(1/2))+-4*b*n*d^-3//2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate(x^-2*(d+e*x)^-3//2*(a+b*log(c*x^n)), x) == :(-1*d^-1*x^-1*(d+e*x)^-1//2*(a+b*log(c*x^n))+-3*e*d^-2*(d+e*x)^-1//2*(a+b*log(c*x^n))+3*e*d^-5//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x)^(1/2))+-1*b*n*d^-2*x^-1*(d+e*x)^(1/2)+-5*b*e*n*d^-5//2*arctanh(d^-1//2*(d+e*x)^(1/2))+-3*b*e*n*d^-5//2*arctanh(d^-1//2*(d+e*x)^(1/2))^2+3*b*e*n*d^-5//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1)+6*b*e*n*d^-5//2*arctanh(d^-1//2*(d+e*x)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x)^(1/2))^-1))
@test integrate((f*x)^m*(d+e*x)^3*(a+b*log(c*x^n)), x) == :(d^3*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e^3*f^-4*(f*x)^(4+m)*(4+m)^-1*(a+b*log(c*x^n))+-1*b*n*d^3*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*n*e^3*f^-4*(f*x)^(4+m)*(4+m)^-2+3*d*e^2*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*log(c*x^n))+3*e*d^2*f^-2*(f*x)^(2+m)*(2+m)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*f^-3*(f*x)^(3+m)*(3+m)^-2+-3*b*e*n*d^2*f^-2*(f*x)^(2+m)*(2+m)^-2)
@test integrate((f*x)^m*(d+e*x)^2*(a+b*log(c*x^n)), x) == :(d^2*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e^2*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*log(c*x^n))+-1*b*n*d^2*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*n*e^2*f^-3*(f*x)^(3+m)*(3+m)^-2+2*d*e*f^-2*(f*x)^(2+m)*(2+m)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*f^-2*(f*x)^(2+m)*(2+m)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n))*(d+e*x), x) == :(d*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e*f^-2*(f*x)^(2+m)*(2+m)^-1*(a+b*log(c*x^n))+-1*b*d*n*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*e*n*f^-2*(f*x)^(2+m)*(2+m)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n)), x) == :(f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+-1*b*n*f^-1*(f*x)^(1+m)*(1+m)^-2)
@test integrate(x^5*(a+b*log(c*x^n))*(d+e*x^2), x) == :((a+b*log(c*x^n))*(1//6*d*x^6+1//8*e*x^8)+-1//36*b*d*n*x^6+-1//64*b*e*n*x^8)
@test integrate(x^3*(a+b*log(c*x^n))*(d+e*x^2), x) == :((a+b*log(c*x^n))*(1//4*d*x^4+1//6*e*x^6)+-1//16*b*d*n*x^4+-1//36*b*e*n*x^6)
@test integrate(x*(a+b*log(c*x^n))*(d+e*x^2), x) == :((a+b*log(c*x^n))*((1/2)*d*x^2+1//4*e*x^4)+-1//4*b*d*n*x^2+-1//16*b*e*n*x^4)
@test integrate(x^-1*(a+b*log(c*x^n))*(d+e*x^2), x) == :((1/2)*e*x^2*(a+b*log(c*x^n))+(1/2)*d*b^-1*n^-1*(a+b*log(c*x^n))^2+-1//4*b*e*n*x^2)
@test integrate(x^-5*(a+b*log(c*x^n))*(d+e*x^2), x) == :(-1//2*e*x^-2*(a+b*log(c*x^n))+-1//4*d*x^-4*(a+b*log(c*x^n))+-1//4*b*e*n*x^-2+-1//16*b*d*n*x^-4)
@test integrate(x^4*(a+b*log(c*x^n))*(d+e*x^2), x) == :((a+b*log(c*x^n))*(1//5*d*x^5+1//7*e*x^7)+-1//25*b*d*n*x^5+-1//49*b*e*n*x^7)
@test integrate(x^2*(a+b*log(c*x^n))*(d+e*x^2), x) == :((a+b*log(c*x^n))*(1//3*d*x^3+1//5*e*x^5)+-1//9*b*d*n*x^3+-1//25*b*e*n*x^5)
@test integrate((a+b*log(c*x^n))*(d+e*x^2), x) == :(d*x*(a+b*log(c*x^n))+1//3*e*x^3*(a+b*log(c*x^n))+-1*b*d*n*x+-1//9*b*e*n*x^3)
@test integrate(x^-2*(a+b*log(c*x^n))*(d+e*x^2), x) == :(e*x*(a+b*log(c*x^n))+-1*d*x^-1*(a+b*log(c*x^n))+-1*b*d*n*x^-1+-1*b*e*n*x)
@test integrate(x^-4*(a+b*log(c*x^n))*(d+e*x^2), x) == :(-1*e*x^-1*(a+b*log(c*x^n))+-1//3*d*x^-3*(a+b*log(c*x^n))+-1*b*e*n*x^-1+-1//9*b*d*n*x^-3)
@test integrate(x^-6*(a+b*log(c*x^n))*(d+e*x^2), x) == :(-1//3*e*x^-3*(a+b*log(c*x^n))+-1//5*d*x^-5*(a+b*log(c*x^n))+-1//9*b*e*n*x^-3+-1//25*b*d*n*x^-5)
@test integrate(x^5*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//6*d^2*x^6+1//10*e^2*x^10+1//4*d*e*x^8)+-1//36*b*n*d^2*x^6+-1//100*b*n*e^2*x^10+-1//32*b*d*e*n*x^8)
@test integrate(x^3*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//4*d^2*x^4+1//8*e^2*x^8+1//3*d*e*x^6)+-1//16*b*n*d^2*x^4+-1//64*b*n*e^2*x^8+-1//18*b*d*e*n*x^6)
@test integrate(x*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(1//6*e^-1*(d+e*x^2)^3*(a+b*log(c*x^n))+-1//4*b*n*d^2*x^2+-1//36*b*n*e^2*x^6+-1//6*b*n*d^3*e^-1*log(x)+-1//8*b*d*e*n*x^4)
@test integrate(x^-1*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(d^2*(a+b*log(c*x^n))*log(x)+1//4*e^2*x^4*(a+b*log(c*x^n))+d*e*x^2*(a+b*log(c*x^n))+-1//2*b*n*d^2*log(x)^2+-1//16*b*n*e^2*x^4+-1//2*b*d*e*n*x^2)
@test integrate(x^-3*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :((1/2)*e^2*x^2*(a+b*log(c*x^n))+-1//2*d^2*x^-2*(a+b*log(c*x^n))+2*d*e*(a+b*log(c*x^n))*log(x)+-1//4*b*n*d^2*x^-2+-1//4*b*n*e^2*x^2+-1*b*d*e*n*log(x)^2)
@test integrate(x^-5*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(e^2*(a+b*log(c*x^n))*log(x)+-1//4*d^2*x^-4*(a+b*log(c*x^n))+-1*d*e*x^-2*(a+b*log(c*x^n))+-1//2*b*n*e^2*log(x)^2+-1//16*b*n*d^2*x^-4+-1//2*b*d*e*n*x^-2)
@test integrate(x^4*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//5*d^2*x^5+1//9*e^2*x^9+2//7*d*e*x^7)+-1//25*b*n*d^2*x^5+-1//81*b*n*e^2*x^9+-2//49*b*d*e*n*x^7)
@test integrate(x^2*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//3*d^2*x^3+1//7*e^2*x^7+2//5*d*e*x^5)+-1//9*b*n*d^2*x^3+-1//49*b*n*e^2*x^7+-2//25*b*d*e*n*x^5)
@test integrate((d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(x*d^2*(a+b*log(c*x^n))+1//5*e^2*x^5*(a+b*log(c*x^n))+-1*b*n*x*d^2+-1//25*b*n*e^2*x^5+2//3*d*e*x^3*(a+b*log(c*x^n))+-2//9*b*d*e*n*x^3)
@test integrate(x^-2*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(-1*d^2*x^-1*(a+b*log(c*x^n))+1//3*e^2*x^3*(a+b*log(c*x^n))+-1*b*n*d^2*x^-1+2*d*e*x*(a+b*log(c*x^n))+-1//9*b*n*e^2*x^3+-2*b*d*e*n*x)
@test integrate(x^-4*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(x*e^2*(a+b*log(c*x^n))+-1//3*d^2*x^-3*(a+b*log(c*x^n))+-1*b*n*x*e^2+-2*d*e*x^-1*(a+b*log(c*x^n))+-1//9*b*n*d^2*x^-3+-2*b*d*e*n*x^-1)
@test integrate(x^-6*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(-1*e^2*x^-1*(a+b*log(c*x^n))+-1//5*d^2*x^-5*(a+b*log(c*x^n))+-1*b*n*e^2*x^-1+-2//3*d*e*x^-3*(a+b*log(c*x^n))+-1//25*b*n*d^2*x^-5+-2//9*b*d*e*n*x^-3)
@test integrate(x^-8*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(-1//3*e^2*x^-3*(a+b*log(c*x^n))+-1//7*d^2*x^-7*(a+b*log(c*x^n))+-2//5*d*e*x^-5*(a+b*log(c*x^n))+-1//9*b*n*e^2*x^-3+-1//49*b*n*d^2*x^-7+-2//25*b*d*e*n*x^-5)
@test integrate(x^5*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//6*d^3*x^6+1//12*e^3*x^12+3//8*e*d^2*x^8+3//10*d*e^2*x^10)+-1//36*b*n*d^3*x^6+-1//144*b*n*e^3*x^12+-3//64*b*e*n*d^2*x^8+-3//100*b*d*n*e^2*x^10)
@test integrate(x^3*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(-1*(a+b*log(c*x^n))*(-1//10*e^-2*(d+e*x^2)^5+1//8*d*e^-2*(d+e*x^2)^4)+-1//100*b*n*e^-2*(d+e*x^2)^5+3//80*b*n*d^3*x^4+1//20*b*n*d^4*e^-1*x^2+1//40*b*n*d^5*e^-2*log(x)+1//60*b*e*n*d^2*x^6+1//320*b*d*n*e^2*x^8)
@test integrate(x*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(1//8*e^-1*(d+e*x^2)^4*(a+b*log(c*x^n))+-1//4*b*n*d^3*x^2+-1//64*b*n*e^3*x^8+-3//16*b*e*n*d^2*x^4+-1//8*b*n*d^4*e^-1*log(x)+-1//12*b*d*n*e^2*x^6)
@test integrate(x^-1*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(d^3*(a+b*log(c*x^n))*log(x)+1//6*e^3*x^6*(a+b*log(c*x^n))+-1//2*b*n*d^3*log(x)^2+-1//36*b*n*e^3*x^6+3//2*e*d^2*x^2*(a+b*log(c*x^n))+3//4*d*e^2*x^4*(a+b*log(c*x^n))+-3//4*b*e*n*d^2*x^2+-3//16*b*d*n*e^2*x^4)
@test integrate(x^-3*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(-1//2*d^3*x^-2*(a+b*log(c*x^n))+1//4*e^3*x^4*(a+b*log(c*x^n))+3*e*d^2*(a+b*log(c*x^n))*log(x)+-1//4*b*n*d^3*x^-2+-1//16*b*n*e^3*x^4+3//2*d*e^2*x^2*(a+b*log(c*x^n))+-3//2*b*e*n*d^2*log(x)^2+-3//4*b*d*n*e^2*x^2)
@test integrate(x^-5*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :((1/2)*e^3*x^2*(a+b*log(c*x^n))+-1//4*d^3*x^-4*(a+b*log(c*x^n))+3*d*e^2*(a+b*log(c*x^n))*log(x)+-3//2*e*d^2*x^-2*(a+b*log(c*x^n))+-1//4*b*n*e^3*x^2+-1//16*b*n*d^3*x^-4+-3//2*b*d*n*e^2*log(x)^2+-3//4*b*e*n*d^2*x^-2)
@test integrate(x^4*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(1//1155*(a+b*log(c*x^n))*(105*e^3*x^11+231*d^3*x^5+385*d*e^2*x^9+495*e*d^2*x^7)+-1//25*b*n*d^3*x^5+-1//121*b*n*e^3*x^11+-3//49*b*e*n*d^2*x^7+-1//27*b*d*n*e^2*x^9)
@test integrate(x^2*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//3*d^3*x^3+1//9*e^3*x^9+3//5*e*d^2*x^5+3//7*d*e^2*x^7)+-1//9*b*n*d^3*x^3+-1//81*b*n*e^3*x^9+-3//25*b*e*n*d^2*x^5+-3//49*b*d*n*e^2*x^7)
@test integrate((d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(x*d^3*(a+b*log(c*x^n))+1//7*e^3*x^7*(a+b*log(c*x^n))+e*d^2*x^3*(a+b*log(c*x^n))+-1*b*n*x*d^3+-1//49*b*n*e^3*x^7+3//5*d*e^2*x^5*(a+b*log(c*x^n))+-3//25*b*d*n*e^2*x^5+-1//3*b*e*n*d^2*x^3)
@test integrate(x^-2*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(-1*d^3*x^-1*(a+b*log(c*x^n))+1//5*e^3*x^5*(a+b*log(c*x^n))+d*e^2*x^3*(a+b*log(c*x^n))+-1*b*n*d^3*x^-1+3*e*x*d^2*(a+b*log(c*x^n))+-1//25*b*n*e^3*x^5+-3*b*e*n*x*d^2+-1//3*b*d*n*e^2*x^3)
@test integrate(x^-4*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(-1//3*d^3*x^-3*(a+b*log(c*x^n))+1//3*e^3*x^3*(a+b*log(c*x^n))+-3*e*d^2*x^-1*(a+b*log(c*x^n))+3*d*x*e^2*(a+b*log(c*x^n))+-1//9*b*n*d^3*x^-3+-1//9*b*n*e^3*x^3+-3*b*d*n*x*e^2+-3*b*e*n*d^2*x^-1)
@test integrate(x^-6*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(x*e^3*(a+b*log(c*x^n))+-1//5*d^3*x^-5*(a+b*log(c*x^n))+-1*b*n*x*e^3+-1*e*d^2*x^-3*(a+b*log(c*x^n))+-3*d*e^2*x^-1*(a+b*log(c*x^n))+-1//25*b*n*d^3*x^-5+-3*b*d*n*e^2*x^-1+-1//3*b*e*n*d^2*x^-3)
@test integrate(x^-8*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(-1*e^3*x^-1*(a+b*log(c*x^n))+-1//7*d^3*x^-7*(a+b*log(c*x^n))+-1*b*n*e^3*x^-1+-1*d*e^2*x^-3*(a+b*log(c*x^n))+-3//5*e*d^2*x^-5*(a+b*log(c*x^n))+-1//49*b*n*d^3*x^-7+-3//25*b*e*n*d^2*x^-5+-1//3*b*d*n*e^2*x^-3)
@test integrate(x^-10*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(-1//3*e^3*x^-3*(a+b*log(c*x^n))+-1//9*d^3*x^-9*(a+b*log(c*x^n))+-3//5*d*e^2*x^-5*(a+b*log(c*x^n))+-3//7*e*d^2*x^-7*(a+b*log(c*x^n))+-1//9*b*n*e^3*x^-3+-1//81*b*n*d^3*x^-9+-3//25*b*d*n*e^2*x^-5+-3//49*b*e*n*d^2*x^-7)
@test integrate(x^5*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(1//4*e^-1*x^4*(a+b*log(c*x^n))+(1/2)*d^2*e^-3*(a+b*log(c*x^n))*log(1+e*d^-1*x^2)+-1//2*d*e^-2*x^2*(a+b*log(c*x^n))+-1//16*b*n*e^-1*x^4+1//4*b*d*n*e^-2*x^2+1//4*b*n*d^2*e^-3*Polylogarithms.polylog(2,-1*e*d^-1*x^2))
@test integrate(x^3*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :((1/2)*e^-1*x^2*(a+b*log(c*x^n))+-1//2*d*e^-2*(a+b*log(c*x^n))*log(1+e*d^-1*x^2)+-1//4*b*n*e^-1*x^2+-1//4*b*d*n*e^-2*Polylogarithms.polylog(2,-1*e*d^-1*x^2))
@test integrate(x*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :((1/2)*e^-1*(a+b*log(c*x^n))*log(1+e*d^-1*x^2)+1//4*b*n*e^-1*Polylogarithms.polylog(2,-1*e*d^-1*x^2))
@test integrate(x^-1*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(-1//2*d^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^-2)+1//4*b*n*d^-1*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^-3*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(-1//2*d^-1*x^-2*(a+b*log(c*x^n))+(1/2)*e*d^-2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-2)+-1//4*b*n*d^-1*x^-2+-1//4*b*e*n*d^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^-5*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(-1//4*d^-1*x^-4*(a+b*log(c*x^n))+(1/2)*e*d^-2*x^-2*(a+b*log(c*x^n))+-1//2*d^-3*e^2*(a+b*log(c*x^n))*log(1+d*e^-1*x^-2)+-1//16*b*n*d^-1*x^-4+1//4*b*e*n*d^-2*x^-2+1//4*b*n*d^-3*e^2*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^4*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(1//3*e^-1*x^3*(a+b*log(c*x^n))+d^3//2*e^-5//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-1*a*d*x*e^-2+-1//9*b*n*e^-1*x^3+b*d*n*x*e^-2+-1*b*d*x*e^-2*log(c*x^n)+(1/2)*im*b*n*d^3//2*e^-5//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2))+-1//2*im*b*n*d^3//2*e^-5//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^2*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(a*x*e^-1+b*x*e^-1*log(c*x^n)+-1*b*n*x*e^-1+-1*d^(1/2)*e^-3//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+(1/2)*im*b*n*d^(1/2)*e^-3//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+-1//2*im*b*n*d^(1/2)*e^-3//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate((d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(d^-1//2*e^-1//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+(1/2)*im*b*n*d^-1//2*e^-1//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2))+-1//2*im*b*n*d^-1//2*e^-1//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(-1*d^-1*x^-1*(a+b*log(c*x^n))+-1*b*n*d^-1*x^-1+-1*d^-3//2*e^(1/2)*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+(1/2)*im*b*n*d^-3//2*e^(1/2)*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+-1//2*im*b*n*d^-3//2*e^(1/2)*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate(x^-4*(d+e*x^2)^-1*(a+b*log(c*x^n)), x) == :(-1//3*d^-1*x^-3*(a+b*log(c*x^n))+e*d^-2*x^-1*(a+b*log(c*x^n))+d^-5//2*e^3//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-1//9*b*n*d^-1*x^-3+b*e*n*d^-2*x^-1+(1/2)*im*b*n*d^-5//2*e^3//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2))+-1//2*im*b*n*d^-5//2*e^3//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^5*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :((1/2)*e^-2*x^2*(a+b*log(c*x^n))+-1*d*e^-3*(a+b*log(c*x^n))*log(1+e*d^-1*x^2)+-1//4*b*n*e^-2*x^2+(1/2)*d*e^-2*x^2*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//2*b*d*n*e^-3*Polylogarithms.polylog(2,-1*e*d^-1*x^2)+-1//4*b*d*n*e^-3*log(d+e*x^2))
@test integrate(x^3*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :((1/2)*e^-2*(a+b*log(c*x^n))*log(1+e*d^-1*x^2)+-1//2*e^-1*x^2*(d+e*x^2)^-1*(a+b*log(c*x^n))+1//4*b*n*e^-2*Polylogarithms.polylog(2,-1*e*d^-1*x^2)+1//4*b*n*e^-2*log(d+e*x^2))
@test integrate(x*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :((1/2)*d^-1*x^2*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//4*b*n*d^-1*e^-1*log(d+e*x^2))
@test integrate(x^-1*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :((1/2)*d^-1*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//4*d^-2*(2a+-1*b*n+2*b*log(c*x^n))*log(1+d*e^-1*x^-2)+1//4*b*n*d^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^-3*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :(-1//4*d^-2*x^-2*(4a+-1*b*n+4*b*log(c*x^n))+(1/2)*d^-1*x^-2*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//2*b*n*d^-2*x^-2+1//4*e*d^-3*(4a+-1*b*n+4*b*log(c*x^n))*log(1+d*e^-1*x^-2)+-1//2*b*e*n*d^-3*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^4*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :(a*x*e^-2+b*x*e^-2*log(c*x^n)+-1*b*n*x*e^-2+-3//2*d^(1/2)*e^-5//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+(1/2)*d*x*e^-2*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//2*b*n*d^(1/2)*e^-5//2*arctan(x*d^-1//2*e^(1/2))+-3//4*im*b*n*d^(1/2)*e^-5//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2))+3//4*im*b*n*d^(1/2)*e^-5//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^2*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :((1/2)*d^-1//2*e^-3//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-1//2*x*e^-1*(d+e*x^2)^-1*(a+b*log(c*x^n))+(1/2)*b*n*d^-1//2*e^-3//2*arctan(x*d^-1//2*e^(1/2))+-1//4*im*b*n*d^-1//2*e^-3//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+1//4*im*b*n*d^-1//2*e^-3//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate((d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :((1/2)*x*d^-1*(d+e*x^2)^-1*(a+b*log(c*x^n))+(1/2)*d^-3//2*e^-1//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-1//2*b*n*d^-3//2*e^-1//2*arctan(x*d^-1//2*e^(1/2))+-1//4*im*b*n*d^-3//2*e^-1//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+1//4*im*b*n*d^-3//2*e^-1//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :(-1//2*d^-2*x^-1*(3a+-1*b*n+3*b*log(c*x^n))+(1/2)*d^-1*x^-1*(d+e*x^2)^-1*(a+b*log(c*x^n))+-3//2*b*n*d^-2*x^-1+-1//2*d^-5//2*e^(1/2)*(3a+-1*b*n+3*b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-3//4*im*b*n*d^-5//2*e^(1/2)*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2))+3//4*im*b*n*d^-5//2*e^(1/2)*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^-4*(d+e*x^2)^-2*(a+b*log(c*x^n)), x) == :(-1//6*d^-2*x^-3*(5a+-1*b*n+5*b*log(c*x^n))+(1/2)*e*d^-3*x^-1*(5a+-1*b*n+5*b*log(c*x^n))+(1/2)*d^-1*x^-3*(d+e*x^2)^-1*(a+b*log(c*x^n))+(1/2)*d^-7//2*e^3//2*(5a+-1*b*n+5*b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-5//18*b*n*d^-2*x^-3+5//2*b*e*n*d^-3*x^-1+-5//4*im*b*n*d^-7//2*e^3//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+5//4*im*b*n*d^-7//2*e^3//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate(x^5*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :((1/2)*e^-3*(a+b*log(c*x^n))*log(1+e*d^-1*x^2)+-1*e^-2*x^2*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//4*d^2*e^-3*(d+e*x^2)^-2*(a+b*log(c*x^n))+1//4*b*n*e^-3*Polylogarithms.polylog(2,-1*e*d^-1*x^2)+1//4*b*n*e^-3*log(x)+3//8*b*n*e^-3*log(d+e*x^2)+1//8*b*d*n*e^-3*(d+e*x^2)^-1)
@test integrate(x^3*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//8*b*n*e^-2*(d+e*x^2)^-1+1//4*d^-1*x^4*(d+e*x^2)^-2*(a+b*log(c*x^n))+-1//8*b*n*d^-1*e^-2*log(d+e*x^2))
@test integrate(x*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//4*e^-1*(d+e*x^2)^-2*(a+b*log(c*x^n))+-1//8*b*n*d^-2*e^-1*log(d+e*x^2)+1//4*b*n*d^-2*e^-1*log(x)+1//8*b*n*d^-1*e^-1*(d+e*x^2)^-1)
@test integrate(x^-1*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//8*d^-3*(4a+-3*b*n+4*b*log(c*x^n))*log(1+d*e^-1*x^-2)+1//4*d^-1*(d+e*x^2)^-2*(a+b*log(c*x^n))+1//8*d^-2*(d+e*x^2)^-1*(4a+-1*b*n+4*b*log(c*x^n))+1//4*b*n*d^-3*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^-3*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//8*d^-3*x^-2*(12a+-5*b*n+12*b*log(c*x^n))+-3//4*b*n*d^-3*x^-2+1//4*d^-1*x^-2*(d+e*x^2)^-2*(a+b*log(c*x^n))+1//8*e*d^-4*(12a+-5*b*n+12*b*log(c*x^n))*log(1+d*e^-1*x^-2)+1//8*d^-2*x^-2*(d+e*x^2)^-1*(6a+-1*b*n+6*b*log(c*x^n))+-3//4*b*e*n*d^-4*Polylogarithms.polylog(2,-1*d*e^-1*x^-2))
@test integrate(x^4*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-5//8*x*e^-2*(d+e*x^2)^-1*(a+b*log(c*x^n))+3//8*d^-1//2*e^-5//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+(1/2)*b*n*d^-1//2*e^-5//2*arctan(x*d^-1//2*e^(1/2))+-1//8*b*n*x*e^-2*(d+e*x^2)^-1+1//4*d*x*e^-2*(d+e*x^2)^-2*(a+b*log(c*x^n))+-3//16*im*b*n*d^-1//2*e^-5//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+3//16*im*b*n*d^-1//2*e^-5//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate(x^2*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//4*x*e^-1*(d+e*x^2)^-2*(a+b*log(c*x^n))+1//8*d^-3//2*e^-3//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+1//8*x*d^-1*e^-1*(d+e*x^2)^-1*(a+b*log(c*x^n))+-1//16*im*b*n*d^-3//2*e^-3//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+1//8*b*n*x*d^-1*e^-1*(d+e*x^2)^-1+1//16*im*b*n*d^-3//2*e^-3//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate((d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(1//4*x*d^-1*(d+e*x^2)^-2*(a+b*log(c*x^n))+3//8*x*d^-2*(d+e*x^2)^-1*(a+b*log(c*x^n))+3//8*d^-5//2*e^-1//2*(a+b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+-1//2*b*n*d^-5//2*e^-1//2*arctan(x*d^-1//2*e^(1/2))+-1//8*b*n*x*d^-2*(d+e*x^2)^-1+-3//16*im*b*n*d^-5//2*e^-1//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+3//16*im*b*n*d^-5//2*e^-1//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate(x^-2*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//8*d^-3*x^-1*(15a+-8*b*n+15*b*log(c*x^n))+-15//8*b*n*d^-3*x^-1+-1//8*d^-7//2*e^(1/2)*(15a+-8*b*n+15*b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+1//4*d^-1*x^-1*(d+e*x^2)^-2*(a+b*log(c*x^n))+1//8*d^-2*x^-1*(d+e*x^2)^-1*(5a+-1*b*n+5*b*log(c*x^n))+-15//16*im*b*n*d^-7//2*e^(1/2)*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2))+15//16*im*b*n*d^-7//2*e^(1/2)*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2)))
@test integrate(x^-4*(d+e*x^2)^-3*(a+b*log(c*x^n)), x) == :(-1//24*d^-3*x^-3*(35a+-12*b*n+35*b*log(c*x^n))+-35//72*b*n*d^-3*x^-3+1//4*d^-1*x^-3*(d+e*x^2)^-2*(a+b*log(c*x^n))+1//8*e*d^-4*x^-1*(35a+-12*b*n+35*b*log(c*x^n))+1//8*d^-2*x^-3*(d+e*x^2)^-1*(7a+-1*b*n+7*b*log(c*x^n))+1//8*d^-9//2*e^3//2*(35a+-12*b*n+35*b*log(c*x^n))*arctan(x*d^-1//2*e^(1/2))+35//8*b*e*n*d^-4*x^-1+-35//16*im*b*n*d^-9//2*e^3//2*Polylogarithms.polylog(2,-1*im*x*d^-1//2*e^(1/2))+35//16*im*b*n*d^-9//2*e^3//2*Polylogarithms.polylog(2,im*x*d^-1//2*e^(1/2)))
@test integrate(x*(1+-1*c*x^2)^-1*log(c*x^2), x) == :((1/2)*c^-1*Polylogarithms.polylog(2,1+-1*c*x^2))
@test integrate(x*(c+-1*x^2)^-1*log(c^-1*x^2), x) == :((1/2)*Polylogarithms.polylog(2,1+-1*c^-1*x^2))
@test integrate((1+-1*x^2)^-1*log(x), x) == :((1/2)*Polylogarithms.polylog(2,-1x)+-1//2*Polylogarithms.polylog(2,x)+arctanh(x)*log(x))
@test integrate((1+x^2)^-1*log(x), x) == :(arctan(x)*log(x)+(1/2)*im*Polylogarithms.polylog(2,im*x)+-1//2*im*Polylogarithms.polylog(2,-1*im*x))
@test integrate((1+-1*e*x^2)^-1*(a+b*log(c*x)), x) == :(e^-1//2*(a+b*log(c*x))*arctanh(x*e^(1/2))+(1/2)*b*e^-1//2*Polylogarithms.polylog(2,-1*x*e^(1/2))+-1//2*b*e^-1//2*Polylogarithms.polylog(2,x*e^(1/2)))
@test integrate((1+-1*e*x^2)^-1*(a+b*log(c*x^n)), x) == :(e^-1//2*(a+b*log(c*x^n))*arctanh(x*e^(1/2))+(1/2)*b*n*e^-1//2*Polylogarithms.polylog(2,-1*x*e^(1/2))+-1//2*b*n*e^-1//2*Polylogarithms.polylog(2,x*e^(1/2)))
@test integrate((a+b*log(c*x^n))^2*(d+e*x^2)^-2, x) == :(-1//4*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^2*log(1+-1*x*e^(1/2)*(-1d)^-1//2)+1//4*x*(-1d)^-3//2*(a+b*log(c*x^n))^2*((-1d)^(1/2)+x*e^(1/2))^-1+1//4*x*(-1d)^-3//2*(a+b*log(c*x^n))^2*((-1d)^(1/2)+-1*x*e^(1/2))^-1+1//4*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^2*log(1+x*e^(1/2)*(-1d)^-1//2)+(1/2)*b^2*e^-1//2*n^2*(-1d)^-3//2*Polylogarithms.polylog(2,x*e^(1/2)*(-1d)^-1//2)+(1/2)*b^2*e^-1//2*n^2*(-1d)^-3//2*Polylogarithms.polylog(3,x*e^(1/2)*(-1d)^-1//2)+-1//2*b^2*e^-1//2*n^2*(-1d)^-3//2*Polylogarithms.polylog(2,-1*x*e^(1/2)*(-1d)^-1//2)+-1//2*b^2*e^-1//2*n^2*(-1d)^-3//2*Polylogarithms.polylog(3,-1*x*e^(1/2)*(-1d)^-1//2)+(1/2)*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*x*e^(1/2)*(-1d)^-1//2)+(1/2)*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))*log(1+-1*x*e^(1/2)*(-1d)^-1//2)+-1//2*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,x*e^(1/2)*(-1d)^-1//2)+-1//2*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))*log(1+x*e^(1/2)*(-1d)^-1//2))
@test integrate((a+b*log(c*x^n))^3*(d+e*x^2)^-2, x) == :(-1//4*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^3*log(1+-1*x*e^(1/2)*(-1d)^-1//2)+1//4*x*(-1d)^-3//2*(a+b*log(c*x^n))^3*((-1d)^(1/2)+x*e^(1/2))^-1+1//4*x*(-1d)^-3//2*(a+b*log(c*x^n))^3*((-1d)^(1/2)+-1*x*e^(1/2))^-1+1//4*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^3*log(1+x*e^(1/2)*(-1d)^-1//2)+-3//2*b^3*e^-1//2*n^3*(-1d)^-3//2*Polylogarithms.polylog(3,x*e^(1/2)*(-1d)^-1//2)+-3//2*b^3*e^-1//2*n^3*(-1d)^-3//2*Polylogarithms.polylog(4,x*e^(1/2)*(-1d)^-1//2)+3//2*b^3*e^-1//2*n^3*(-1d)^-3//2*Polylogarithms.polylog(3,-1*x*e^(1/2)*(-1d)^-1//2)+3//2*b^3*e^-1//2*n^3*(-1d)^-3//2*Polylogarithms.polylog(4,-1*x*e^(1/2)*(-1d)^-1//2)+-3//2*b^2*e^-1//2*n^2*(-1d)^-3//2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*x*e^(1/2)*(-1d)^-1//2)+-3//2*b^2*e^-1//2*n^2*(-1d)^-3//2*(a+b*log(c*x^n))*Polylogarithms.polylog(3,-1*x*e^(1/2)*(-1d)^-1//2)+-3//4*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^2*Polylogarithms.polylog(2,x*e^(1/2)*(-1d)^-1//2)+-3//4*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^2*log(1+x*e^(1/2)*(-1d)^-1//2)+3//2*b^2*e^-1//2*n^2*(-1d)^-3//2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,x*e^(1/2)*(-1d)^-1//2)+3//2*b^2*e^-1//2*n^2*(-1d)^-3//2*(a+b*log(c*x^n))*Polylogarithms.polylog(3,x*e^(1/2)*(-1d)^-1//2)+3//4*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^2*Polylogarithms.polylog(2,-1*x*e^(1/2)*(-1d)^-1//2)+3//4*b*n*e^-1//2*(-1d)^-3//2*(a+b*log(c*x^n))^2*log(1+-1*x*e^(1/2)*(-1d)^-1//2))
@test integrate(x^5*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(1//7*e^-3*(d+e*x^2)^7//2*(a+b*log(c*x^n))+-2//5*d*e^-3*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-1//49*b*n*e^-3*(d+e*x^2)^7//2+1//3*d^2*e^-3*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-8//105*b*n*d^3*e^-3*(d+e*x^2)^(1/2)+-8//315*b*n*d^2*e^-3*(d+e*x^2)^3//2+8//105*b*n*d^7//2*e^-3*arctanh(d^-1//2*(d+e*x^2)^(1/2))+9//175*b*d*n*e^-3*(d+e*x^2)^5//2)
@test integrate(x^3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(1//5*e^-2*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-1//3*d*e^-2*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1//25*b*n*e^-2*(d+e*x^2)^5//2+-2//15*b*n*d^5//2*e^-2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+2//15*b*n*d^2*e^-2*(d+e*x^2)^(1/2)+2//45*b*d*n*e^-2*(d+e*x^2)^3//2)
@test integrate(x*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(1//3*e^-1*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1//9*b*n*e^-1*(d+e*x^2)^3//2+-1//3*b*d*n*e^-1*(d+e*x^2)^(1/2)+1//3*b*n*d^3//2*e^-1*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*((d+e*x^2)^(1/2)+-1*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2)))+-1*b*n*(d+e*x^2)^(1/2)+b*n*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+(1/2)*b*n*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//2*b*n*d^(1/2)*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+-1*b*n*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^-3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(-1//2*x^-2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//2*e*d^-1//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1//4*b*n*x^-2*(d+e*x^2)^(1/2)+-1//4*b*e*n*d^-1//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+-1//4*b*e*n*d^-1//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+1//4*b*e*n*d^-1//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//2*b*e*n*d^-1//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^4*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(1//6*x^5*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//36*b*n*x^5*(d+e*x^2)^(1/2)+-1//16*x*d^2*e^-2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+1//24*d*e^-1*x^3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-5//288*b*d*n*e^-1*x^3*(d+e*x^2)^(1/2)+1//16*d^5//2*e^-5//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+7//192*b*n*x*d^2*e^-2*(d+e*x^2)^(1/2)+-1//32*b*n*d^5//2*e^-5//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+1//32*b*n*d^5//2*e^-5//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))^2+5//192*b*n*d^5//2*e^-5//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))+-1//16*b*n*d^5//2*e^-5//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(1//4*x^3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//16*b*n*x^3*(d+e*x^2)^(1/2)+1//8*d*x*e^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-3//32*b*d*n*x*e^-1*(d+e*x^2)^(1/2)+-1//8*d^3//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+-1//16*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))^2+-1//32*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))+1//16*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+1//8*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate((d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :((1/2)*x*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//4*b*n*x*(d+e*x^2)^(1/2)+-1//4*b*d*n*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+(1/2)*d^3//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+-1//4*b*n*d^3//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+1//4*b*n*d^3//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))^2+-1//2*b*n*d^3//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^-2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(-1*x^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1*b*n*x^-1*(d+e*x^2)^(1/2)+d^-1//2*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+b*n*d^-1//2*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))+(1/2)*b*n*d^-1//2*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))^2+-1//2*b*n*d^-1//2*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+-1*b*n*d^-1//2*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^-4*(d+e*x^2)^(1/2)*(a+b*log(c*x^n)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1//9*b*n*d^-1*x^-3*(d+e*x^2)^3//2+1//3*b*n*d^-1*e^3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//3*b*e*n*d^-1*x^-1*(d+e*x^2)^(1/2))
@test integrate(x^5*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(1//9*e^-3*(d+e*x^2)^9//2*(a+b*log(c*x^n))+-2//7*d*e^-3*(d+e*x^2)^7//2*(a+b*log(c*x^n))+-1//81*b*n*e^-3*(d+e*x^2)^9//2+1//5*d^2*e^-3*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-8//315*b*n*d^4*e^-3*(d+e*x^2)^(1/2)+-8//945*b*n*d^3*e^-3*(d+e*x^2)^3//2+-8//1575*b*n*d^2*e^-3*(d+e*x^2)^5//2+8//315*b*n*d^9//2*e^-3*arctanh(d^-1//2*(d+e*x^2)^(1/2))+11//441*b*d*n*e^-3*(d+e*x^2)^7//2)
@test integrate(x^3*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(1//7*e^-2*(d+e*x^2)^7//2*(a+b*log(c*x^n))+-1//5*d*e^-2*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-1//49*b*n*e^-2*(d+e*x^2)^7//2+-2//35*b*n*d^7//2*e^-2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+2//35*b*n*d^3*e^-2*(d+e*x^2)^(1/2)+2//105*b*n*d^2*e^-2*(d+e*x^2)^3//2+2//175*b*d*n*e^-2*(d+e*x^2)^5//2)
@test integrate(x*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(1//5*e^-1*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-1//25*b*n*e^-1*(d+e*x^2)^5//2+-1//5*b*n*d^2*e^-1*(d+e*x^2)^(1/2)+-1//15*b*d*n*e^-1*(d+e*x^2)^3//2+1//5*b*n*d^5//2*e^-1*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^-1*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(1//3*(d+e*x^2)^3//2+d*(d+e*x^2)^(1/2)+-1*d^3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2)))+-1//9*b*n*(d+e*x^2)^3//2+(1/2)*b*n*d^3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-4//3*b*d*n*(d+e*x^2)^(1/2)+-1//2*b*n*d^3//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+4//3*b*n*d^3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1*b*n*d^3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^-3*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(-1//2*x^-2*(d+e*x^2)^3//2*(a+b*log(c*x^n))+3//2*e*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1*b*e*n*(d+e*x^2)^(1/2)+-3//2*e*d^(1/2)*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-3//4*b*e*n*d^(1/2)*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+-1//4*b*d*n*x^-2*(d+e*x^2)^(1/2)+3//4*b*e*n*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+3//4*b*e*n*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-3//2*b*e*n*d^(1/2)*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^2*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(1//6*x^3*(d+e*x^2)^3//2*(a+b*log(c*x^n))+1//8*d*x^3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-23//288*b*d*n*x^3*(d+e*x^2)^(1/2)+-1//36*b*e*n*x^5*(d+e*x^2)^(1/2)+1//16*x*d^2*e^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-11//192*b*n*x*d^2*e^-1*(d+e*x^2)^(1/2)+-1//16*d^5//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+-1//32*b*n*d^5//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))^2+-1//192*b*n*d^5//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))+1//32*b*n*d^5//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+1//16*b*n*d^5//2*e^-3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate((d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(1//4*x*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1//16*b*n*x*(d+e*x^2)^3//2+3//8*d*x*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-9//32*b*d*n*x*(d+e*x^2)^(1/2)+-9//32*b*n*d^2*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+3//8*d^5//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+-3//16*b*n*d^5//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+3//16*b*n*d^5//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))^2+-3//8*b*n*d^5//2*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^-2*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(-1*x^-1*(d+e*x^2)^3//2*(a+b*log(c*x^n))+3//2*e*x*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1*b*d*n*x^-1*(d+e*x^2)^(1/2)+-1//4*b*e*n*x*(d+e*x^2)^(1/2)+3//2*d^(1/2)*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+-3//4*b*n*d^(1/2)*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+3//4*b*n*d^(1/2)*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))^2+3//4*b*n*d^(1/2)*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))+-3//2*b*n*d^(1/2)*e^(1/2)*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^-4*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(-1//3*x^-3*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1*e*x^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//9*b*n*x^-3*(d+e*x^2)^3//2+-4//3*b*e*n*x^-1*(d+e*x^2)^(1/2)+d^-1//2*e^3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+(1/2)*b*n*d^-1//2*e^3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))^2+-1//2*b*n*d^-1//2*e^3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+4//3*b*n*d^-1//2*e^3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))+-1*b*n*d^-1//2*e^3//2*(1+e*d^-1*x^2)^-1//2*(d+e*x^2)^(1/2)*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^-6*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(-1//5*d^-1*x^-5*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-1//25*b*n*d^-1*x^-5*(d+e*x^2)^5//2+1//5*b*n*d^-1*e^5//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//5*b*n*d^-1*e^2*x^-1*(d+e*x^2)^(1/2)+-1//15*b*e*n*d^-1*x^-3*(d+e*x^2)^3//2)
@test integrate(x^-8*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(-1//7*d^-1*x^-7*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-2//35*b*n*d^-2*e^7//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//49*b*n*d^-2*x^-7*(d+e*x^2)^7//2+2//35*e*d^-2*x^-5*(d+e*x^2)^5//2*(a+b*log(c*x^n))+2//35*b*n*d^-2*e^3*x^-1*(d+e*x^2)^(1/2)+2//105*b*n*d^-2*e^2*x^-3*(d+e*x^2)^3//2+2//175*b*e*n*d^-2*x^-5*(d+e*x^2)^5//2)
@test integrate(x^-10*(d+e*x^2)^3//2*(a+b*log(c*x^n)), x) == :(-1//9*d^-1*x^-9*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-8//315*d^-3*e^2*x^-5*(d+e*x^2)^5//2*(a+b*log(c*x^n))+-1//81*b*n*d^-2*x^-9*(d+e*x^2)^7//2+4//63*e*d^-2*x^-7*(d+e*x^2)^5//2*(a+b*log(c*x^n))+8//315*b*n*d^-3*e^9//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-8//315*b*n*d^-3*e^4*x^-1*(d+e*x^2)^(1/2)+-8//945*b*n*d^-3*e^3*x^-3*(d+e*x^2)^3//2+-8//1575*b*n*d^-3*e^2*x^-5*(d+e*x^2)^5//2+50//3969*b*e*n*d^-3*x^-7*(d+e*x^2)^7//2)
@test integrate(x*(4+x^2)^(1/2)*log(x), x) == :(-4//3*(4+x^2)^(1/2)+-1//9*(4+x^2)^3//2+8//3*arctanh((1/2)*(4+x^2)^(1/2))+1//3*(4+x^2)^3//2*log(x))
@test integrate(x^5*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(1//5*e^-3*(d+e*x^2)^5//2*(a+b*log(c*x^n))+d^2*e^-3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-2//3*d*e^-3*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1//25*b*n*e^-3*(d+e*x^2)^5//2+-8//15*b*n*d^2*e^-3*(d+e*x^2)^(1/2)+7//45*b*d*n*e^-3*(d+e*x^2)^3//2+8//15*b*n*d^5//2*e^-3*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^3*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(1//3*e^-2*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1*d*e^-2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//9*b*n*e^-2*(d+e*x^2)^3//2+-2//3*b*n*d^3//2*e^-2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+2//3*b*d*n*e^-2*(d+e*x^2)^(1/2))
@test integrate(x*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(e^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1*b*n*e^-1*(d+e*x^2)^(1/2)+b*n*d^(1/2)*e^-1*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(-1*d^-1//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^2)^(1/2))+(1/2)*b*n*d^-1//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//2*b*n*d^-1//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+-1*b*n*d^-1//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :((1/2)*e*d^-3//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1//2*d^-1*x^-2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//4*b*e*n*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//4*b*e*n*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1//4*b*n*d^-1*x^-2*(d+e*x^2)^(1/2)+1//4*b*e*n*d^-3//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+(1/2)*b*e*n*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^2*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :((1/2)*x*e^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//4*b*n*x*e^-1*(d+e*x^2)^(1/2)+-1//2*d^3//2*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+-1//4*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))^2+-1//4*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))+1//4*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+(1/2)*b*n*d^3//2*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate((d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(d^(1/2)*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+(1/2)*b*n*d^(1/2)*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))^2+-1//2*b*n*d^(1/2)*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+-1*b*n*d^(1/2)*e^-1//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(-1*d^-1*x^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+b*n*d^-1*e^(1/2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1*b*n*d^-1*x^-1*(d+e*x^2)^(1/2))
@test integrate(x^-4*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-2//3*b*n*d^-2*e^3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//9*b*n*d^-2*x^-3*(d+e*x^2)^3//2+2//3*e*d^-2*x^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+2//3*b*e*n*d^-2*x^-1*(d+e*x^2)^(1/2))
@test integrate(x^-6*(d+e*x^2)^-1//2*(a+b*log(c*x^n)), x) == :(-1//5*d^-1*x^-5*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-8//15*d^-3*e^2*x^-1*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//25*b*n*d^-2*x^-5*(d+e*x^2)^3//2+4//15*e*d^-2*x^-3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+8//15*b*n*d^-3*e^5//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-8//15*b*n*d^-3*e^2*x^-1*(d+e*x^2)^(1/2)+26//225*b*e*n*d^-3*x^-3*(d+e*x^2)^3//2)
@test integrate(x^7*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(1//5*e^-4*(d+e*x^2)^5//2*(a+b*log(c*x^n))+d^3*e^-4*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1*d*e^-4*(d+e*x^2)^3//2*(a+b*log(c*x^n))+3*d^2*e^-4*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//25*b*n*e^-4*(d+e*x^2)^5//2+-11//5*b*n*d^2*e^-4*(d+e*x^2)^(1/2)+4//15*b*d*n*e^-4*(d+e*x^2)^3//2+16//5*b*n*d^5//2*e^-4*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^5*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(1//3*e^-3*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-1*d^2*e^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-2*d*e^-3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1//9*b*n*e^-3*(d+e*x^2)^3//2+-8//3*b*n*d^3//2*e^-3*arctanh(d^-1//2*(d+e*x^2)^(1/2))+5//3*b*d*n*e^-3*(d+e*x^2)^(1/2))
@test integrate(x^3*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(e^-2*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+d*e^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1*b*n*e^-2*(d+e*x^2)^(1/2)+2*b*n*d^(1/2)*e^-2*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(-1*e^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1*b*n*d^-1//2*e^-1*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^-1*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(d^-1*(d+e*x^2)^-1//2+-1*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2)))+b*n*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+(1/2)*b*n*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//2*b*n*d^-3//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+-1*b*n*d^-3//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^-3*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(-3//2*e*d^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//2*d^-1*x^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+3//2*e*d^-5//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-5//4*b*e*n*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-3//4*b*e*n*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//4*b*n*d^-2*x^-2*(d+e*x^2)^(1/2)+3//4*b*e*n*d^-5//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+3//2*b*e*n*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^2*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(-1*x*e^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+d^(1/2)*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+b*n*d^(1/2)*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))+(1/2)*b*n*d^(1/2)*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))^2+-1//2*b*n*d^(1/2)*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+-1*b*n*d^(1/2)*e^-3//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate((d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(x*d^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1*b*n*d^-1*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2))
@test integrate(x^-2*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(-1*d^-1*x^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1*b*n*d^-2*x^-1*(d+e*x^2)^(1/2)+-2*e*x*d^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+2*b*n*d^-2*e^(1/2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2))
@test integrate(x^-4*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-8//3*b*n*d^-3*e^3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//9*b*n*d^-2*x^-3*(d+e*x^2)^(1/2)+4//3*e*d^-2*x^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+8//3*x*d^-3*e^2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+14//9*b*e*n*d^-3*x^-1*(d+e*x^2)^(1/2))
@test integrate(x^-6*(d+e*x^2)^-3//2*(a+b*log(c*x^n)), x) == :(-1//5*d^-1*x^-5*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-16//5*x*d^-4*e^3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-8//5*d^-3*e^2*x^-1*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//25*b*n*d^-2*x^-5*(d+e*x^2)^(1/2)+2//5*e*d^-2*x^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+16//5*b*n*d^-4*e^5//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-148//75*b*n*d^-4*e^2*x^-1*(d+e*x^2)^(1/2)+14//75*b*e*n*d^-3*x^-3*(d+e*x^2)^(1/2))
@test integrate(x^7*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(1//3*e^-4*(d+e*x^2)^3//2*(a+b*log(c*x^n))+-3*d*e^-4*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-3*d^2*e^-4*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//9*b*n*e^-4*(d+e*x^2)^3//2+1//3*d^3*e^-4*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-16//3*b*n*d^3//2*e^-4*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1//3*b*n*d^2*e^-4*(d+e*x^2)^-1//2+8//3*b*d*n*e^-4*(d+e*x^2)^(1/2))
@test integrate(x^5*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(e^-3*(d+e*x^2)^(1/2)*(a+b*log(c*x^n))+-1*b*n*e^-3*(d+e*x^2)^(1/2)+2*d*e^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//3*d^2*e^-3*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+1//3*b*d*n*e^-3*(d+e*x^2)^-1//2+8//3*b*n*d^(1/2)*e^-3*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x^3*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(-1*e^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//3*b*n*e^-2*(d+e*x^2)^-1//2+1//3*d*e^-2*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-2//3*b*n*d^-1//2*e^-2*arctanh(d^-1//2*(d+e*x^2)^(1/2)))
@test integrate(x*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(-1//3*e^-1*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-1//3*b*n*d^-3//2*e^-1*arctanh(d^-1//2*(d+e*x^2)^(1/2))+1//3*b*n*d^-1*e^-1*(d+e*x^2)^-1//2)
@test integrate(x^-1*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(d^-2*(d+e*x^2)^-1//2+-1*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+1//3*d^-1*(d+e*x^2)^-3//2)+(1/2)*b*n*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//2*b*n*d^-5//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+-1//3*b*n*d^-2*(d+e*x^2)^-1//2+4//3*b*n*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-1*b*n*d^-5//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^-3*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(-5//2*e*d^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-5//6*e*d^-2*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-1//2*d^-1*x^-2*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+5//2*e*d^-7//2*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-31//12*b*e*n*d^-7//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))+-5//4*b*e*n*d^-7//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))^2+-1//4*b*n*d^-3*x^-2*(d+e*x^2)^(1/2)+1//3*b*e*n*d^-3*(d+e*x^2)^-1//2+5//4*b*e*n*d^-7//2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1)+5//2*b*e*n*d^-7//2*arctanh(d^-1//2*(d+e*x^2)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^2)^(1/2))^-1))
@test integrate(x^4*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(-1*x*e^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//3*e^-1*x^3*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-1//3*b*n*x*e^-2*(d+e*x^2)^-1//2+d^(1/2)*e^-5//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*(a+b*log(c*x^n))*arcsinh(x*d^-1//2*e^(1/2))+(1/2)*b*n*d^(1/2)*e^-5//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))^2+-1//2*b*n*d^(1/2)*e^-5//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(x*d^-1//2*e^(1/2))))+4//3*b*n*d^(1/2)*e^-5//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))+-1*b*n*d^(1/2)*e^-5//2*(1+e*d^-1*x^2)^(1/2)*(d+e*x^2)^-1//2*arcsinh(x*d^-1//2*e^(1/2))*log(1+-1*exp(2*arcsinh(x*d^-1//2*e^(1/2)))))
@test integrate(x^2*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(1//3*d^-1*x^3*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-1//3*b*n*d^-1*e^-3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+1//3*b*n*x*d^-1*e^-1*(d+e*x^2)^-1//2)
@test integrate((d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(1//3*x*d^-1*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+2//3*x*d^-2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-2//3*b*n*d^-2*e^-1//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//3*b*n*x*d^-2*(d+e*x^2)^-1//2)
@test integrate(x^-2*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(-1*d^-1*x^-1*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-1*b*n*d^-2*x^-1*(d+e*x^2)^-1//2+-8//3*e*x*d^-3*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-4//3*e*x*d^-2*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+8//3*b*n*d^-3*e^(1/2)*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-2//3*b*e*n*x*d^-3*(d+e*x^2)^-1//2)
@test integrate(x^-4*(d+e*x^2)^-5//2*(a+b*log(c*x^n)), x) == :(-1//3*d^-1*x^-3*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+2*e*d^-2*x^-1*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+-16//3*b*n*d^-4*e^3//2*arctanh(x*e^(1/2)*(d+e*x^2)^-1//2)+-1//9*b*n*d^-3*x^-3*(d+e*x^2)^(1/2)+8//3*x*d^-3*e^2*(d+e*x^2)^-3//2*(a+b*log(c*x^n))+16//3*x*d^-4*e^2*(d+e*x^2)^-1//2*(a+b*log(c*x^n))+-1//3*b*n*x*d^-4*e^2*(d+e*x^2)^-1//2+23//9*b*e*n*d^-4*x^-1*(d+e*x^2)^(1/2))
@test integrate(x^3*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(1//3*e^-4*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)^2*(a+b*log(c*x^n))+-1*d^2*e^-4*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+-1//9*b*n*e^-4*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)^2+2//3*b*n*d^2*e^-4*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)+-2//3*b*n*d^4*e^-4*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2)))
@test integrate(x*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-1*e^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+b*n*e^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)+-1*b*n*d^2*e^-2*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2)))
@test integrate(x^-1*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-1*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))+(1/2)*b*n*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))^2+-1//2*b*n*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*Polylogarithms.polylog(2,-1*(1+-1*(1+-1*d^-2*e^2*x^2)^(1/2))^-1*(1+(1+-1*d^-2*e^2*x^2)^(1/2)))+-1*b*n*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))*log(2*(1+-1*(1+-1*d^-2*e^2*x^2)^(1/2))^-1))
@test integrate(x^-3*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-1//2*d^-2*x^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+-1//2*d^-2*e^2*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))+-1//4*b*n*d^-2*x^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)+-1//4*b*n*d^-2*e^2*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*Polylogarithms.polylog(2,-1*(1+-1*(1+-1*d^-2*e^2*x^2)^(1/2))^-1*(1+(1+-1*d^-2*e^2*x^2)^(1/2)))+1//4*b*n*d^-2*e^2*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))^2+1//4*b*n*d^-2*e^2*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))+-1//2*b*n*d^-2*e^2*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arctanh((1+-1*d^-2*e^2*x^2)^(1/2))*log(2*(1+-1*(1+-1*d^-2*e^2*x^2)^(1/2))^-1))
@test integrate(x^2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-1//2*x*e^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+(1/2)*d^3*e^-3*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*arcsin(e*x*d^-1)+1//4*b*n*x*e^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)+1//4*b*n*d^3*e^-3*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1)+-1//2*b*n*d^3*e^-3*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1)*log(1+-1*exp(2*im*arcsin(e*x*d^-1)))+1//4*im*b*n*d^3*e^-3*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1)^2+1//4*im*b*n*d^3*e^-3*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(e*x*d^-1))))
@test integrate((d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(d*e^-1*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*arcsin(e*x*d^-1)+(1/2)*im*b*d*n*e^-1*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1)^2+(1/2)*im*b*d*n*e^-1*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*Polylogarithms.polylog(2,exp(2*im*arcsin(e*x*d^-1)))+-1*b*d*n*e^-1*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1)*log(1+-1*exp(2*im*arcsin(e*x*d^-1))))
@test integrate(x^-2*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-1*d^-2*x^-1*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+-1*b*n*d^-2*x^-1*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)+-1*b*e*n*d^-1*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1))
@test integrate(x^-4*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n)), x) == :(-1//3*d^-2*x^-3*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+-2//3*d^-4*e^2*x^-1*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(a+b*log(c*x^n))*(d^2+-1*e^2*x^2)+-1//9*b*n*d^-4*x^-3*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)^2+-2//3*b*n*d^-4*e^2*x^-1*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*(d^2+-1*e^2*x^2)+-2//3*b*n*d^-3*e^3*(1+-1*d^-2*e^2*x^2)^(1/2)*(d+e*x)^-1//2*(d+-1*e*x)^-1//2*arcsin(e*x*d^-1))
@test integrate(x*(-1+x^2)^-1//2*log(x), x) == :(-1*(-1+x^2)^(1/2)+(-1+x^2)^(1/2)*log(x)+arctan((-1+x^2)^(1/2)))
@test integrate((f*x)^m*(d+e*x^2)^3*(a+b*log(c*x^n)), x) == :(d^3*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e^3*f^-7*(f*x)^(7+m)*(7+m)^-1*(a+b*log(c*x^n))+-1*b*n*d^3*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*n*e^3*f^-7*(f*x)^(7+m)*(7+m)^-2+3*d*e^2*f^-5*(f*x)^(5+m)*(5+m)^-1*(a+b*log(c*x^n))+3*e*d^2*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*f^-5*(f*x)^(5+m)*(5+m)^-2+-3*b*e*n*d^2*f^-3*(f*x)^(3+m)*(3+m)^-2)
@test integrate((f*x)^m*(d+e*x^2)^2*(a+b*log(c*x^n)), x) == :(d^2*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e^2*f^-5*(f*x)^(5+m)*(5+m)^-1*(a+b*log(c*x^n))+-1*b*n*d^2*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*n*e^2*f^-5*(f*x)^(5+m)*(5+m)^-2+2*d*e*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*f^-3*(f*x)^(3+m)*(3+m)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n))*(d+e*x^2), x) == :(d*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e*f^-3*(f*x)^(3+m)*(3+m)^-1*(a+b*log(c*x^n))+-1*b*d*n*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*e*n*f^-3*(f*x)^(3+m)*(3+m)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n)), x) == :(f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+-1*b*n*f^-1*(f*x)^(1+m)*(1+m)^-2)
@test integrate(x^3*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(1//4*d^-1*x^4*(a+b*log(c*x^n))+d^-5*e^4*(a+b*log(c*x^n))*log(1+d*x*e^-1)+(1/2)*d^-3*e^2*x^2*(a+b*log(c*x^n))+-1*a*x*d^-4*e^3+-1//3*e*d^-2*x^3*(a+b*log(c*x^n))+-1//16*b*n*d^-1*x^4+b*n*x*d^-4*e^3+b*n*d^-5*e^4*Polylogarithms.polylog(2,-1*d*x*e^-1)+-1*b*x*d^-4*e^3*log(c*x^n)+-1//4*b*n*d^-3*e^2*x^2+1//9*b*e*n*d^-2*x^3)
@test integrate(x^2*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(1//3*d^-1*x^3*(a+b*log(c*x^n))+a*x*d^-3*e^2+-1*d^-4*e^3*(a+b*log(c*x^n))*log(1+d*x*e^-1)+-1//2*e*d^-2*x^2*(a+b*log(c*x^n))+-1//9*b*n*d^-1*x^3+b*x*d^-3*e^2*log(c*x^n)+-1*b*n*x*d^-3*e^2+-1*b*n*d^-4*e^3*Polylogarithms.polylog(2,-1*d*x*e^-1)+1//4*b*e*n*d^-2*x^2)
@test integrate(x*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :((1/2)*d^-1*x^2*(a+b*log(c*x^n))+d^-3*e^2*(a+b*log(c*x^n))*log(1+d*x*e^-1)+-1*a*e*x*d^-2+-1//4*b*n*d^-1*x^2+b*e*n*x*d^-2+b*n*d^-3*e^2*Polylogarithms.polylog(2,-1*d*x*e^-1)+-1*b*e*x*d^-2*log(c*x^n))
@test integrate((d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(a*x*d^-1+b*x*d^-1*log(c*x^n)+-1*b*n*x*d^-1+-1*e*d^-2*(a+b*log(c*x^n))*log(1+d*x*e^-1)+-1*b*e*n*d^-2*Polylogarithms.polylog(2,-1*d*x*e^-1))
@test integrate(x^-1*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(d^-1*(a+b*log(c*x^n))*log(1+d*x*e^-1)+b*n*d^-1*Polylogarithms.polylog(2,-1*d*x*e^-1))
@test integrate(x^-2*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(-1*e^-1*(a+b*log(c*x^n))*log(1+e*d^-1*x^-1)+b*n*e^-1*Polylogarithms.polylog(2,-1*e*d^-1*x^-1))
@test integrate(x^-3*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(-1*e^-1*x^-1*(a+b*log(c*x^n))+d*e^-2*(a+b*log(c*x^n))*log(1+d*x*e^-1)+-1*b*n*e^-1*x^-1+b*d*n*e^-2*Polylogarithms.polylog(2,-1*d*x*e^-1)+-1//2*d*b^-1*e^-2*n^-1*(a+b*log(c*x^n))^2)
@test integrate(x^-4*(d+e*x^-1)^-1*(a+b*log(c*x^n)), x) == :(-1//2*e^-1*x^-2*(a+b*log(c*x^n))+d*e^-2*x^-1*(a+b*log(c*x^n))+-1*d^2*e^-3*(a+b*log(c*x^n))*log(1+d*x*e^-1)+-1//4*b*n*e^-1*x^-2+b*d*n*e^-2*x^-1+(1/2)*b^-1*d^2*e^-3*n^-1*(a+b*log(c*x^n))^2+-1*b*n*d^2*e^-3*Polylogarithms.polylog(2,-1*d*x*e^-1))
@test integrate(x^3*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(-1//16*b*d^-1*x^4+1//4*d^-1*x^4*(a+b*log(c*x))+b*x*d^-4*e^3+b*d^-5*e^4*Polylogarithms.polylog(2,-1*d*x*e^-1)+d^-5*e^4*(a+b*log(c*x))*log(1+d*x*e^-1)+(1/2)*d^-3*e^2*x^2*(a+b*log(c*x))+-1*a*x*d^-4*e^3+-1//3*e*d^-2*x^3*(a+b*log(c*x))+-1//4*b*d^-3*e^2*x^2+1//9*b*e*d^-2*x^3+-1*b*x*d^-4*e^3*log(c*x))
@test integrate(x^2*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(-1//9*b*d^-1*x^3+1//3*d^-1*x^3*(a+b*log(c*x))+a*x*d^-3*e^2+-1*b*x*d^-3*e^2+-1*b*d^-4*e^3*Polylogarithms.polylog(2,-1*d*x*e^-1)+-1*d^-4*e^3*(a+b*log(c*x))*log(1+d*x*e^-1)+-1//2*e*d^-2*x^2*(a+b*log(c*x))+1//4*b*e*d^-2*x^2+b*x*d^-3*e^2*log(c*x))
@test integrate(x*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :((1/2)*d^-1*x^2*(a+b*log(c*x))+-1//4*b*d^-1*x^2+b*e*x*d^-2+b*d^-3*e^2*Polylogarithms.polylog(2,-1*d*x*e^-1)+d^-3*e^2*(a+b*log(c*x))*log(1+d*x*e^-1)+-1*a*e*x*d^-2+-1*b*e*x*d^-2*log(c*x))
@test integrate((d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(a*x*d^-1+-1*b*x*d^-1+b*x*d^-1*log(c*x)+-1*b*e*d^-2*Polylogarithms.polylog(2,-1*d*x*e^-1)+-1*e*d^-2*(a+b*log(c*x))*log(1+d*x*e^-1))
@test integrate(x^-1*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(b*d^-1*Polylogarithms.polylog(2,-1*d*x*e^-1)+d^-1*(a+b*log(c*x))*log(1+d*x*e^-1))
@test integrate(x^-2*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(b*e^-1*Polylogarithms.polylog(2,-1*e*d^-1*x^-1)+-1*e^-1*(a+b*log(c*x))*log(1+e*d^-1*x^-1))
@test integrate(x^-3*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(-1*b*e^-1*x^-1+-1*e^-1*x^-1*(a+b*log(c*x))+b*d*e^-2*Polylogarithms.polylog(2,-1*d*x*e^-1)+d*e^-2*(a+b*log(c*x))*log(1+d*x*e^-1)+-1//2*d*b^-1*e^-2*(a+b*log(c*x))^2)
@test integrate(x^-4*(d+e*x^-1)^-1*(a+b*log(c*x)), x) == :(-1//2*e^-1*x^-2*(a+b*log(c*x))+-1//4*b*e^-1*x^-2+b*d*e^-2*x^-1+d*e^-2*x^-1*(a+b*log(c*x))+(1/2)*b^-1*d^2*e^-3*(a+b*log(c*x))^2+-1*b*d^2*e^-3*Polylogarithms.polylog(2,-1*d*x*e^-1)+-1*d^2*e^-3*(a+b*log(c*x))*log(1+d*x*e^-1))
@test integrate(x^(-1+n)*(1+-1*e*x^n)^-1*log(e*x^n), x) == :(e^-1*n^-1*Polylogarithms.polylog(2,1+-1*e*x^n))
@test integrate(x^(-1+n)*(d+-1*x^n)^-1*log(d^-1*x^n), x) == :(n^-1*Polylogarithms.polylog(2,1+-1*d^-1*x^n))
@test integrate(x^(-1+n)*(d+e*x^n)^-1*log(-1*e*d^-1*x^n), x) == :(-1*e^-1*n^-1*Polylogarithms.polylog(2,1+e*d^-1*x^n))
@test integrate((-1*x^2+a*x)^-1*log(a*x^-1), x) == :(a^-1*Polylogarithms.polylog(2,1+-1*a*x^-1))
@test integrate((-1*x^3+a*x)^-1*log(a*x^-2), x) == :((1/2)*a^-1*Polylogarithms.polylog(2,1+-1*a*x^-2))
@test integrate((-1*x^n+a*x)^-1*log(a*x^(1+-1n)), x) == :(-1*a^-1*(1+-1n)^-1*Polylogarithms.polylog(2,1+-1*a*x^(1+-1n)))
@test integrate((f*x)^(-1+m)*(d+e*x^m)^3*(a+b*log(c*x^n)), x) == :(-1*b*n*x*d^3*m^-2*(f*x)^(-1+m)+-1//16*b*n*e^3*m^-2*x^(1+3m)*(f*x)^(-1+m)+1//4*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^4*(a+b*log(c*x^n))+-3//4*b*e*n*d^2*m^-2*x^(1+m)*(f*x)^(-1+m)+-1//3*b*d*n*e^2*m^-2*x^(1+2m)*(f*x)^(-1+m)+-1//4*b*n*d^4*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*log(x))
@test integrate((f*x)^(-1+m)*(d+e*x^m)^2*(a+b*log(c*x^n)), x) == :(-1*b*n*x*d^2*m^-2*(f*x)^(-1+m)+-1//9*b*n*e^2*m^-2*x^(1+2m)*(f*x)^(-1+m)+1//3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^3*(a+b*log(c*x^n))+-1//2*b*d*e*n*m^-2*x^(1+m)*(f*x)^(-1+m)+-1//3*b*n*d^3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*log(x))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n)), x) == :(f^-1*m^-1*(f*x)^m*(a+b*log(c*x^n))+-1*b*n*f^-1*m^-2*(f*x)^m)
@test integrate((f*x)^(-1+m)*(d+e*x^m)^-1*(a+b*log(c*x^n)), x) == :(e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+e*d^-1*x^m)+b*n*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*Polylogarithms.polylog(2,-1*e*d^-1*x^m))
@test integrate((f*x)^(-1+m)*(d+e*x^m)^-2*(a+b*log(c*x^n)), x) == :(d^-1*f^-1*m^-1*(f*x)^m*(d+e*x^m)^-1*(a+b*log(c*x^n))+-1*b*n*d^-1*e^-1*f^-1*m^-2*x^(-1m)*(f*x)^m*log(d+e*x^m))
@test integrate((f*x)^(-1+m)*(d+e*x^m)^-3*(a+b*log(c*x^n)), x) == :(-1//2*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-2*(a+b*log(c*x^n))+(1/2)*b*n*d^-1*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-1+(1/2)*b*n*d^-2*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*log(x)+-1//2*b*n*d^-2*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*log(d+e*x^m))
@test integrate((f*x)^(-1+m)*(d+e*x^m)^-4*(a+b*log(c*x^n)), x) == :(-1//3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-3*(a+b*log(c*x^n))+-1//3*b*n*d^-3*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*log(d+e*x^m)+1//3*b*n*d^-3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*log(x)+1//3*b*n*d^-2*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-1+1//6*b*n*d^-1*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-2)
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^3, x) == :(2*x*b^2*d^3*m^-3*n^2*(f*x)^(-1+m)+1//4*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^4+1//32*b^2*e^3*m^-3*n^2*x^(1+3m)*(f*x)^(-1+m)+-2*b*n*x*d^3*m^-2*(f*x)^(-1+m)*(a+b*log(c*x^n))+-1//8*b*n*e^3*m^-2*x^(1+3m)*(f*x)^(-1+m)*(a+b*log(c*x^n))+2//9*d*b^2*e^2*m^-3*n^2*x^(1+2m)*(f*x)^(-1+m)+3//4*e*b^2*d^2*m^-3*n^2*x^(1+m)*(f*x)^(-1+m)+-3//2*b*e*n*d^2*m^-2*x^(1+m)*(f*x)^(-1+m)*(a+b*log(c*x^n))+-2//3*b*d*n*e^2*m^-2*x^(1+2m)*(f*x)^(-1+m)*(a+b*log(c*x^n))+1//4*b^2*d^4*e^-1*m^-1*n^2*x^(1+-1m)*(f*x)^(-1+m)*log(x)^2+-1//2*b*n*d^4*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(x))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^2, x) == :(2*x*b^2*d^2*m^-3*n^2*(f*x)^(-1+m)+1//3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^3+2//27*b^2*e^2*m^-3*n^2*x^(1+2m)*(f*x)^(-1+m)+(1/2)*d*e*b^2*m^-3*n^2*x^(1+m)*(f*x)^(-1+m)+-2*b*n*x*d^2*m^-2*(f*x)^(-1+m)*(a+b*log(c*x^n))+-2//9*b*n*e^2*m^-2*x^(1+2m)*(f*x)^(-1+m)*(a+b*log(c*x^n))+-1*b*d*e*n*m^-2*x^(1+m)*(f*x)^(-1+m)*(a+b*log(c*x^n))+1//3*b^2*d^3*e^-1*m^-1*n^2*x^(1+-1m)*(f*x)^(-1+m)*log(x)^2+-2//3*b*n*d^3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(x))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m), x) == :((1/2)*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^2+2*d*x*b^2*m^-3*n^2*(f*x)^(-1+m)+1//4*e*b^2*m^-3*n^2*x^(1+m)*(f*x)^(-1+m)+-2*b*d*n*x*m^-2*(f*x)^(-1+m)*(a+b*log(c*x^n))+-1//2*b*e*n*m^-2*x^(1+m)*(f*x)^(-1+m)*(a+b*log(c*x^n))+(1/2)*b^2*d^2*e^-1*m^-1*n^2*x^(1+-1m)*(f*x)^(-1+m)*log(x)^2+-1*b*n*d^2*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(x))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2, x) == :(f^-1*m^-1*(f*x)^m*(a+b*log(c*x^n))^2+2*b^2*f^-1*m^-3*n^2*(f*x)^m+-2*b*n*f^-1*m^-2*(f*x)^m*(a+b*log(c*x^n)))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-1, x) == :(e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*log(1+e*d^-1*x^m)+-2*b^2*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*Polylogarithms.polylog(3,-1*e*d^-1*x^m)+2*b*n*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*e*d^-1*x^m))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-2, x) == :(-1*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-1+2*b^2*d^-1*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1m))+-2*b*n*d^-1*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1m)))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-3, x) == :(-1//2*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-2+b^2*d^-2*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1m))+b^2*d^-2*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*log(d+e*x^m)+-1*b*n*x*d^-2*m^-2*(f*x)^(-1+m)*(d+e*x^m)^-1*(a+b*log(c*x^n))+-1*b*n*d^-2*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1m)))
@test integrate((f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-4, x) == :(-1//3*e^-1*m^-1*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))^2*(d+e*x^m)^-3+b^2*d^-3*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*log(d+e*x^m)+-2//3*b*n*x*d^-3*m^-2*(f*x)^(-1+m)*(d+e*x^m)^-1*(a+b*log(c*x^n))+-1//3*b^2*d^-3*e^-1*m^-2*n^2*x^(1+-1m)*(f*x)^(-1+m)*log(x)+-1//3*b^2*d^-2*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-1+2//3*b^2*d^-3*e^-1*m^-3*n^2*x^(1+-1m)*(f*x)^(-1+m)*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1m))+-2//3*b*n*d^-3*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1m))+1//3*b*n*d^-1*e^-1*m^-2*x^(1+-1m)*(f*x)^(-1+m)*(d+e*x^m)^-2*(a+b*log(c*x^n)))
@test integrate(x^5*(a+b*log(c*x^n))*(d+e*x^r), x) == :(1//6*(a+b*log(c*x^n))*(d*x^6+6*e*x^(6+r)*(6+r)^-1)+-1//36*b*d*n*x^6+-1*b*e*n*x^(6+r)*(6+r)^-2)
@test integrate(x^3*(a+b*log(c*x^n))*(d+e*x^r), x) == :(1//4*(a+b*log(c*x^n))*(d*x^4+4*e*x^(4+r)*(4+r)^-1)+-1//16*b*d*n*x^4+-1*b*e*n*x^(4+r)*(4+r)^-2)
@test integrate(x*(a+b*log(c*x^n))*(d+e*x^r), x) == :((1/2)*(a+b*log(c*x^n))*(d*x^2+2*e*x^(2+r)*(2+r)^-1)+-1//4*b*d*n*x^2+-1*b*e*n*x^(2+r)*(2+r)^-2)
@test integrate(x^-1*(a+b*log(c*x^n))*(d+e*x^r), x) == :(e*r^-1*x^r*(a+b*log(c*x^n))+(1/2)*d*b^-1*n^-1*(a+b*log(c*x^n))^2+-1*b*e*n*r^-2*x^r)
@test integrate(x^-3*(a+b*log(c*x^n))*(d+e*x^r), x) == :(-1//2*d*x^-2*(a+b*log(c*x^n))+-1*e*x^(-2+r)*(2+-1r)^-1*(a+b*log(c*x^n))+-1//4*b*d*n*x^-2+-1*b*e*n*x^(-2+r)*(2+-1r)^-2)
@test integrate(x^-5*(a+b*log(c*x^n))*(d+e*x^r), x) == :(-1//4*d*x^-4*(a+b*log(c*x^n))+-1*e*x^(-4+r)*(4+-1r)^-1*(a+b*log(c*x^n))+-1//16*b*d*n*x^-4+-1*b*e*n*x^(-4+r)*(4+-1r)^-2)
@test integrate(x^4*(a+b*log(c*x^n))*(d+e*x^r), x) == :(1//5*(a+b*log(c*x^n))*(d*x^5+5*e*x^(5+r)*(5+r)^-1)+-1//25*b*d*n*x^5+-1*b*e*n*x^(5+r)*(5+r)^-2)
@test integrate(x^2*(a+b*log(c*x^n))*(d+e*x^r), x) == :(1//3*(a+b*log(c*x^n))*(d*x^3+3*e*x^(3+r)*(3+r)^-1)+-1//9*b*d*n*x^3+-1*b*e*n*x^(3+r)*(3+r)^-2)
@test integrate((a+b*log(c*x^n))*(d+e*x^r), x) == :(d*x*(a+b*log(c*x^n))+e*x^(1+r)*(1+r)^-1*(a+b*log(c*x^n))+-1*b*d*n*x+-1*b*e*n*x^(1+r)*(1+r)^-2)
@test integrate(x^-2*(a+b*log(c*x^n))*(d+e*x^r), x) == :(-1*d*x^-1*(a+b*log(c*x^n))+-1*b*d*n*x^-1+-1*e*x^(-1+r)*(1+-1r)^-1*(a+b*log(c*x^n))+-1*b*e*n*x^(-1+r)*(1+-1r)^-2)
@test integrate(x^-4*(a+b*log(c*x^n))*(d+e*x^r), x) == :(-1//3*d*x^-3*(a+b*log(c*x^n))+-1*e*x^(-3+r)*(3+-1r)^-1*(a+b*log(c*x^n))+-1//9*b*d*n*x^-3+-1*b*e*n*x^(-3+r)*(3+-1r)^-2)
@test integrate(x^-6*(a+b*log(c*x^n))*(d+e*x^r), x) == :(-1//5*d*x^-5*(a+b*log(c*x^n))+-1*e*x^(-5+r)*(5+-1r)^-1*(a+b*log(c*x^n))+-1//25*b*d*n*x^-5+-1*b*e*n*x^(-5+r)*(5+-1r)^-2)
@test integrate(x^5*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(1//6*(a+b*log(c*x^n))*(d^2*x^6+3*e^2*x^(6+2r)*(3+r)^-1+12*d*e*x^(6+r)*(6+r)^-1)+-1//36*b*n*d^2*x^6+-1//4*b*n*e^2*x^(6+2r)*(3+r)^-2+-2*b*d*e*n*x^(6+r)*(6+r)^-2)
@test integrate(x^3*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(1//4*(a+b*log(c*x^n))*(d^2*x^4+2*e^2*x^(4+2r)*(2+r)^-1+8*d*e*x^(4+r)*(4+r)^-1)+-1//16*b*n*d^2*x^4+-1//4*b*n*e^2*x^(4+2r)*(2+r)^-2+-2*b*d*e*n*x^(4+r)*(4+r)^-2)
@test integrate(x*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :((1/2)*(a+b*log(c*x^n))*(d^2*x^2+e^2*x^(2+2r)*(1+r)^-1+4*d*e*x^(2+r)*(2+r)^-1)+-1//4*b*n*d^2*x^2+-1//4*b*n*e^2*x^(2+2r)*(1+r)^-2+-2*b*d*e*n*x^(2+r)*(2+r)^-2)
@test integrate(x^-1*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(d^2*(a+b*log(c*x^n))*log(x)+(1/2)*e^2*r^-1*x^(2r)*(a+b*log(c*x^n))+-1//2*b*n*d^2*log(x)^2+2*d*e*r^-1*x^r*(a+b*log(c*x^n))+-1//4*b*n*e^2*r^-2*x^(2r)+-2*b*d*e*n*r^-2*x^r)
@test integrate(x^-3*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(-1//2*d^2*x^-2*(a+b*log(c*x^n))+-1*e^2*x^(-2+2r)*(2+-2r)^-1*(a+b*log(c*x^n))+-1//4*b*n*d^2*x^-2+-2*d*e*x^(-2+r)*(2+-1r)^-1*(a+b*log(c*x^n))+-1//4*b*n*e^2*x^(-2+2r)*(1+-1r)^-2+-2*b*d*e*n*x^(-2+r)*(2+-1r)^-2)
@test integrate(x^-5*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(-1//4*d^2*x^-4*(a+b*log(c*x^n))+-1*e^2*x^(-4+2r)*(4+-2r)^-1*(a+b*log(c*x^n))+-1//16*b*n*d^2*x^-4+-2*d*e*x^(-4+r)*(4+-1r)^-1*(a+b*log(c*x^n))+-1//4*b*n*e^2*x^(-4+2r)*(2+-1r)^-2+-2*b*d*e*n*x^(-4+r)*(4+-1r)^-2)
@test integrate(x^4*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(1//5*(a+b*log(c*x^n))*(d^2*x^5+5*e^2*x^(5+2r)*(5+2r)^-1+10*d*e*x^(5+r)*(5+r)^-1)+-1//25*b*n*d^2*x^5+-1*b*n*e^2*x^(5+2r)*(5+2r)^-2+-2*b*d*e*n*x^(5+r)*(5+r)^-2)
@test integrate(x^2*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(1//3*(a+b*log(c*x^n))*(d^2*x^3+3*e^2*x^(3+2r)*(3+2r)^-1+6*d*e*x^(3+r)*(3+r)^-1)+-1//9*b*n*d^2*x^3+-1*b*n*e^2*x^(3+2r)*(3+2r)^-2+-2*b*d*e*n*x^(3+r)*(3+r)^-2)
@test integrate((d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(x*d^2*(a+b*log(c*x^n))+e^2*x^(1+2r)*(1+2r)^-1*(a+b*log(c*x^n))+-1*b*n*x*d^2+-1*b*n*e^2*x^(1+2r)*(1+2r)^-2+2*d*e*x^(1+r)*(1+r)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*x^(1+r)*(1+r)^-2)
@test integrate(x^-2*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(-1*d^2*x^-1*(a+b*log(c*x^n))+-1*b*n*d^2*x^-1+-1*e^2*x^(-1+2r)*(1+-2r)^-1*(a+b*log(c*x^n))+-1*b*n*e^2*x^(-1+2r)*(1+-2r)^-2+-2*d*e*x^(-1+r)*(1+-1r)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*x^(-1+r)*(1+-1r)^-2)
@test integrate(x^-4*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(-1//3*d^2*x^-3*(a+b*log(c*x^n))+-1*e^2*x^(-3+2r)*(3+-2r)^-1*(a+b*log(c*x^n))+-1//9*b*n*d^2*x^-3+-1*b*n*e^2*x^(-3+2r)*(3+-2r)^-2+-2*d*e*x^(-3+r)*(3+-1r)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*x^(-3+r)*(3+-1r)^-2)
@test integrate(x^-6*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(-1//5*d^2*x^-5*(a+b*log(c*x^n))+-1*e^2*x^(-5+2r)*(5+-2r)^-1*(a+b*log(c*x^n))+-1//25*b*n*d^2*x^-5+-1*b*n*e^2*x^(-5+2r)*(5+-2r)^-2+-2*d*e*x^(-5+r)*(5+-1r)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*x^(-5+r)*(5+-1r)^-2)
@test integrate(x^-8*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(-1//7*d^2*x^-7*(a+b*log(c*x^n))+-1*e^2*x^(-7+2r)*(7+-2r)^-1*(a+b*log(c*x^n))+-1//49*b*n*d^2*x^-7+-1*b*n*e^2*x^(-7+2r)*(7+-2r)^-2+-2*d*e*x^(-7+r)*(7+-1r)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*x^(-7+r)*(7+-1r)^-2)
@test integrate(x^5*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(1//6*(a+b*log(c*x^n))*(d^3*x^6+2*e^3*x^(6+3r)*(2+r)^-1+9*d*e^2*x^(6+2r)*(3+r)^-1+18*e*d^2*x^(6+r)*(6+r)^-1)+-1//36*b*n*d^3*x^6+-1//9*b*n*e^3*x^(6+3r)*(2+r)^-2+-3*b*e*n*d^2*x^(6+r)*(6+r)^-2+-3//4*b*d*n*e^2*x^(6+2r)*(3+r)^-2)
@test integrate(x^3*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(1//4*(a+b*log(c*x^n))*(d^3*x^4+4*e^3*x^(4+3r)*(4+3r)^-1+6*d*e^2*x^(4+2r)*(2+r)^-1+12*e*d^2*x^(4+r)*(4+r)^-1)+-1//16*b*n*d^3*x^4+-1*b*n*e^3*x^(4+3r)*(4+3r)^-2+-3*b*e*n*d^2*x^(4+r)*(4+r)^-2+-3//4*b*d*n*e^2*x^(4+2r)*(2+r)^-2)
@test integrate(x*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :((1/2)*(a+b*log(c*x^n))*(d^3*x^2+2*e^3*x^(2+3r)*(2+3r)^-1+3*d*e^2*x^(2+2r)*(1+r)^-1+6*e*d^2*x^(2+r)*(2+r)^-1)+-1//4*b*n*d^3*x^2+-1*b*n*e^3*x^(2+3r)*(2+3r)^-2+-3*b*e*n*d^2*x^(2+r)*(2+r)^-2+-3//4*b*d*n*e^2*x^(2+2r)*(1+r)^-2)
@test integrate(x^-1*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(d^3*(a+b*log(c*x^n))*log(x)+-1//2*b*n*d^3*log(x)^2+1//3*e^3*r^-1*x^(3r)*(a+b*log(c*x^n))+3*e*d^2*r^-1*x^r*(a+b*log(c*x^n))+-1//9*b*n*e^3*r^-2*x^(3r)+3//2*d*e^2*r^-1*x^(2r)*(a+b*log(c*x^n))+-3*b*e*n*d^2*r^-2*x^r+-3//4*b*d*n*e^2*r^-2*x^(2r))
@test integrate(x^-3*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1//2*d^3*x^-2*(a+b*log(c*x^n))+-1*e^3*x^(-2+3r)*(2+-3r)^-1*(a+b*log(c*x^n))+-1//4*b*n*d^3*x^-2+-1*b*n*e^3*x^(-2+3r)*(2+-3r)^-2+-3*d*e^2*x^(-2+2r)*(2+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-2+r)*(2+-1r)^-1*(a+b*log(c*x^n))+-3*b*e*n*d^2*x^(-2+r)*(2+-1r)^-2+-3//4*b*d*n*e^2*x^(-2+2r)*(1+-1r)^-2)
@test integrate(x^-5*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1//4*d^3*x^-4*(a+b*log(c*x^n))+-1*e^3*x^(-4+3r)*(4+-3r)^-1*(a+b*log(c*x^n))+-1//16*b*n*d^3*x^-4+-1*b*n*e^3*x^(-4+3r)*(4+-3r)^-2+-3*d*e^2*x^(-4+2r)*(4+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-4+r)*(4+-1r)^-1*(a+b*log(c*x^n))+-3*b*e*n*d^2*x^(-4+r)*(4+-1r)^-2+-3//4*b*d*n*e^2*x^(-4+2r)*(2+-1r)^-2)
@test integrate(x^4*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(1//5*(a+b*log(c*x^n))*(d^3*x^5+5*e^3*x^(5+3r)*(5+3r)^-1+15*d*e^2*x^(5+2r)*(5+2r)^-1+15*e*d^2*x^(5+r)*(5+r)^-1)+-1//25*b*n*d^3*x^5+-1*b*n*e^3*x^(5+3r)*(5+3r)^-2+-3*b*d*n*e^2*x^(5+2r)*(5+2r)^-2+-3*b*e*n*d^2*x^(5+r)*(5+r)^-2)
@test integrate(x^2*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(1//3*(a+b*log(c*x^n))*(d^3*x^3+e^3*x^(3+3r)*(1+r)^-1+9*d*e^2*x^(3+2r)*(3+2r)^-1+9*e*d^2*x^(3+r)*(3+r)^-1)+-1//9*b*n*d^3*x^3+-1//9*b*n*e^3*x^(3+3r)*(1+r)^-2+-3*b*d*n*e^2*x^(3+2r)*(3+2r)^-2+-3*b*e*n*d^2*x^(3+r)*(3+r)^-2)
@test integrate((d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(x*d^3*(a+b*log(c*x^n))+e^3*x^(1+3r)*(1+3r)^-1*(a+b*log(c*x^n))+-1*b*n*x*d^3+-1*b*n*e^3*x^(1+3r)*(1+3r)^-2+3*d*e^2*x^(1+2r)*(1+2r)^-1*(a+b*log(c*x^n))+3*e*d^2*x^(1+r)*(1+r)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*x^(1+2r)*(1+2r)^-2+-3*b*e*n*d^2*x^(1+r)*(1+r)^-2)
@test integrate(x^-2*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1*d^3*x^-1*(a+b*log(c*x^n))+-1*b*n*d^3*x^-1+-1*e^3*x^(-1+3r)*(1+-3r)^-1*(a+b*log(c*x^n))+-1*b*n*e^3*x^(-1+3r)*(1+-3r)^-2+-3*d*e^2*x^(-1+2r)*(1+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-1+r)*(1+-1r)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*x^(-1+2r)*(1+-2r)^-2+-3*b*e*n*d^2*x^(-1+r)*(1+-1r)^-2)
@test integrate(x^-4*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1//3*d^3*x^-3*(a+b*log(c*x^n))+-1*e^3*x^(-3+3r)*(3+-3r)^-1*(a+b*log(c*x^n))+-1//9*b*n*d^3*x^-3+-3*d*e^2*x^(-3+2r)*(3+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-3+r)*(3+-1r)^-1*(a+b*log(c*x^n))+-1//9*b*n*e^3*x^(-3+3r)*(1+-1r)^-2+-3*b*d*n*e^2*x^(-3+2r)*(3+-2r)^-2+-3*b*e*n*d^2*x^(-3+r)*(3+-1r)^-2)
@test integrate(x^-6*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1//5*d^3*x^-5*(a+b*log(c*x^n))+-1*e^3*x^(-5+3r)*(5+-3r)^-1*(a+b*log(c*x^n))+-1//25*b*n*d^3*x^-5+-1*b*n*e^3*x^(-5+3r)*(5+-3r)^-2+-3*d*e^2*x^(-5+2r)*(5+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-5+r)*(5+-1r)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*x^(-5+2r)*(5+-2r)^-2+-3*b*e*n*d^2*x^(-5+r)*(5+-1r)^-2)
@test integrate(x^-8*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1//7*d^3*x^-7*(a+b*log(c*x^n))+-1*e^3*x^(-7+3r)*(7+-3r)^-1*(a+b*log(c*x^n))+-1//49*b*n*d^3*x^-7+-1*b*n*e^3*x^(-7+3r)*(7+-3r)^-2+-3*d*e^2*x^(-7+2r)*(7+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-7+r)*(7+-1r)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*x^(-7+2r)*(7+-2r)^-2+-3*b*e*n*d^2*x^(-7+r)*(7+-1r)^-2)
@test integrate(x^-10*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(-1//9*d^3*x^-9*(a+b*log(c*x^n))+-1*e^3*x^(-9+3r)*(9+-3r)^-1*(a+b*log(c*x^n))+-1//81*b*n*d^3*x^-9+-3*d*e^2*x^(-9+2r)*(9+-2r)^-1*(a+b*log(c*x^n))+-3*e*d^2*x^(-9+r)*(9+-1r)^-1*(a+b*log(c*x^n))+-1//9*b*n*e^3*x^(-9+3r)*(3+-1r)^-2+-3*b*d*n*e^2*x^(-9+2r)*(9+-2r)^-2+-3*b*e*n*d^2*x^(-9+r)*(9+-1r)^-2)
@test integrate(x^-1*(d+e*x^r)^-1*(a+b*log(c*x^n)), x) == :(-1*d^-1*r^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r))+b*n*d^-1*r^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r)))
@test integrate(x^-1*(d+e*x^r)^-2*(a+b*log(c*x^n)), x) == :(-1*d^-2*r^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r))+b*n*d^-2*r^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+b*n*d^-2*r^-2*log(d+e*x^r)+-1*e*d^-2*r^-1*x^r*(d+e*x^r)^-1*(a+b*log(c*x^n)))
@test integrate(x^-1*(c+-1*x^(-1n))^-1*(a+b*log(c*x^n)), x) == :(a*c^-1*n^-1*log(1+-1*c*x^n)+-1*b*c^-1*n^-1*Polylogarithms.polylog(2,1+-1*c*x^n))
@test integrate(x^-1*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(d^3*(a+b*log(c*x^n))*log(x)+-1//2*b*n*d^3*log(x)^2+1//3*e^3*r^-1*x^(3r)*(a+b*log(c*x^n))+3*e*d^2*r^-1*x^r*(a+b*log(c*x^n))+-1//9*b*n*e^3*r^-2*x^(3r)+3//2*d*e^2*r^-1*x^(2r)*(a+b*log(c*x^n))+-3*b*e*n*d^2*r^-2*x^r+-3//4*b*d*n*e^2*r^-2*x^(2r))
@test integrate(x^-1*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(d^2*(a+b*log(c*x^n))*log(x)+(1/2)*e^2*r^-1*x^(2r)*(a+b*log(c*x^n))+-1//2*b*n*d^2*log(x)^2+2*d*e*r^-1*x^r*(a+b*log(c*x^n))+-1//4*b*n*e^2*r^-2*x^(2r)+-2*b*d*e*n*r^-2*x^r)
@test integrate(x^-1*(a+b*log(c*x^n))*(d+e*x^r), x) == :(e*r^-1*x^r*(a+b*log(c*x^n))+(1/2)*d*b^-1*n^-1*(a+b*log(c*x^n))^2+-1*b*e*n*r^-2*x^r)
@test integrate(x^-1*(d+e*x^r)^-1*(a+b*log(c*x^n)), x) == :(-1*d^-1*r^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r))+b*n*d^-1*r^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r)))
@test integrate(x^-1*(d+e*x^r)^-2*(a+b*log(c*x^n)), x) == :(-1*d^-2*r^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r))+b*n*d^-2*r^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+b*n*d^-2*r^-2*log(d+e*x^r)+-1*e*d^-2*r^-1*x^r*(d+e*x^r)^-1*(a+b*log(c*x^n)))
@test integrate(x^-1*(d+e*x^r)^-3*(a+b*log(c*x^n)), x) == :((1/2)*d^-1*r^-1*(d+e*x^r)^-2*(a+b*log(c*x^n))+-1*d^-3*r^-1*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r))+b*n*d^-3*r^-2*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+-1//2*b*n*d^-3*r^-1*log(x)+-1//2*b*n*d^-2*r^-2*(d+e*x^r)^-1+3//2*b*n*d^-3*r^-2*log(d+e*x^r)+-1*e*d^-3*r^-1*x^r*(d+e*x^r)^-1*(a+b*log(c*x^n)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^3, x) == :(1//3*b^-1*d^3*n^-1*(a+b*log(c*x^n))^3+1//3*e^3*r^-1*x^(3r)*(a+b*log(c*x^n))^2+3*e*d^2*r^-1*x^r*(a+b*log(c*x^n))^2+2//27*b^2*e^3*n^2*r^-3*x^(3r)+3//2*d*e^2*r^-1*x^(2r)*(a+b*log(c*x^n))^2+6*e*b^2*d^2*n^2*r^-3*x^r+-2//9*b*n*e^3*r^-2*x^(3r)*(a+b*log(c*x^n))+3//4*d*b^2*e^2*n^2*r^-3*x^(2r)+-6*b*e*n*d^2*r^-2*x^r*(a+b*log(c*x^n))+-3//2*b*d*n*e^2*r^-2*x^(2r)*(a+b*log(c*x^n)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^2, x) == :((1/2)*e^2*r^-1*x^(2r)*(a+b*log(c*x^n))^2+1//3*b^-1*d^2*n^-1*(a+b*log(c*x^n))^3+2*d*e*r^-1*x^r*(a+b*log(c*x^n))^2+1//4*b^2*e^2*n^2*r^-3*x^(2r)+4*d*e*b^2*n^2*r^-3*x^r+-1//2*b*n*e^2*r^-2*x^(2r)*(a+b*log(c*x^n))+-4*b*d*e*n*r^-2*x^r*(a+b*log(c*x^n)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x^r), x) == :(e*r^-1*x^r*(a+b*log(c*x^n))^2+1//3*d*b^-1*n^-1*(a+b*log(c*x^n))^3+2*e*b^2*n^2*r^-3*x^r+-2*b*e*n*r^-2*x^r*(a+b*log(c*x^n)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^-1, x) == :(-1*d^-1*r^-1*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^(-1r))+2*b^2*d^-1*n^2*r^-3*Polylogarithms.polylog(3,-1*d*e^-1*x^(-1r))+2*b*n*d^-1*r^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^-2, x) == :(d^-1*r^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^-1+-1*d^-2*r^-1*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^(-1r))+-2*b^2*d^-2*n^2*r^-3*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+2*b^2*d^-2*n^2*r^-3*Polylogarithms.polylog(3,-1*d*e^-1*x^(-1r))+2*b*n*d^-2*r^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+2*b*n*d^-2*r^-2*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r)))
@test integrate(x^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^-3, x) == :(d^-2*r^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^-1+(1/2)*d^-1*r^-1*(a+b*log(c*x^n))^2*(d+e*x^r)^-2+-1*d^-3*r^-1*(a+b*log(c*x^n))^2*log(1+d*e^-1*x^(-1r))+-1*b^2*d^-3*n^2*r^-3*log(d+e*x^r)+-3*b^2*d^-3*n^2*r^-3*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+2*b^2*d^-3*n^2*r^-3*Polylogarithms.polylog(3,-1*d*e^-1*x^(-1r))+2*b*n*d^-3*r^-2*(a+b*log(c*x^n))*Polylogarithms.polylog(2,-1*d*e^-1*x^(-1r))+3*b*n*d^-3*r^-2*(a+b*log(c*x^n))*log(1+d*e^-1*x^(-1r))+b*e*n*d^-3*r^-2*x^r*(d+e*x^r)^-1*(a+b*log(c*x^n)))
@test integrate(x^-1*(d+e*x^r)^5//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(2//5*r^-1*(d+e*x^r)^5//2+-2*d^5//2*r^-1*arctanh(d^-1//2*(d+e*x^r)^(1/2))+2*d^2*r^-1*(d+e*x^r)^(1/2)+2//3*d*r^-1*(d+e*x^r)^3//2)+-4//25*b*n*r^-2*(d+e*x^r)^5//2+-2*b*n*d^5//2*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^5//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+-92//15*b*n*d^2*r^-2*(d+e*x^r)^(1/2)+-32//45*b*d*n*r^-2*(d+e*x^r)^3//2+92//15*b*n*d^5//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-4*b*n*d^5//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate(x^-1*(d+e*x^r)^3//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(2//3*r^-1*(d+e*x^r)^3//2+-2*d^3//2*r^-1*arctanh(d^-1//2*(d+e*x^r)^(1/2))+2*d*r^-1*(d+e*x^r)^(1/2))+-4//9*b*n*r^-2*(d+e*x^r)^3//2+-2*b*n*d^3//2*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^3//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+-16//3*b*d*n*r^-2*(d+e*x^r)^(1/2)+16//3*b*n*d^3//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-4*b*n*d^3//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate(x^-1*(d+e*x^r)^(1/2)*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(2*r^-1*(d+e*x^r)^(1/2)+-2*d^(1/2)*r^-1*arctanh(d^-1//2*(d+e*x^r)^(1/2)))+-4*b*n*r^-2*(d+e*x^r)^(1/2)+-2*b*n*d^(1/2)*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^(1/2)*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+4*b*n*d^(1/2)*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-4*b*n*d^(1/2)*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate(x^-1*(d+e*x^r)^-1//2*(a+b*log(c*x^n)), x) == :(-2*d^-1//2*r^-1*(a+b*log(c*x^n))*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-2*b*n*d^-1//2*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^-1//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+-4*b*n*d^-1//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate(x^-1*(d+e*x^r)^-3//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(-2*d^-3//2*r^-1*arctanh(d^-1//2*(d+e*x^r)^(1/2))+2*d^-1*r^-1*(d+e*x^r)^-1//2)+-2*b*n*d^-3//2*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^-3//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+4*b*n*d^-3//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-4*b*n*d^-3//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate(x^-1*(d+e*x^r)^-5//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(-2*d^-5//2*r^-1*arctanh(d^-1//2*(d+e*x^r)^(1/2))+2*d^-2*r^-1*(d+e*x^r)^-1//2+2//3*d^-1*r^-1*(d+e*x^r)^-3//2)+-2*b*n*d^-5//2*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^-5//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+-4//3*b*n*d^-2*r^-2*(d+e*x^r)^-1//2+16//3*b*n*d^-5//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-4*b*n*d^-5//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate(x^-1*(d+e*x^r)^-7//2*(a+b*log(c*x^n)), x) == :((a+b*log(c*x^n))*(-2*d^-7//2*r^-1*arctanh(d^-1//2*(d+e*x^r)^(1/2))+2*d^-3*r^-1*(d+e*x^r)^-1//2+2//3*d^-2*r^-1*(d+e*x^r)^-3//2+2//5*d^-1*r^-1*(d+e*x^r)^-5//2)+-2*b*n*d^-7//2*r^-2*Polylogarithms.polylog(2,1+-2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1)+2*b*n*d^-7//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))^2+-32//15*b*n*d^-3*r^-2*(d+e*x^r)^-1//2+-4//15*b*n*d^-2*r^-2*(d+e*x^r)^-3//2+92//15*b*n*d^-7//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))+-4*b*n*d^-7//2*r^-2*arctanh(d^-1//2*(d+e*x^r)^(1/2))*log(2*d^(1/2)*(d^(1/2)+-1*(d+e*x^r)^(1/2))^-1))
@test integrate((f*x)^m*(d+e*x^r)^3*(a+b*log(c*x^n)), x) == :(d^3*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e^3*x^(1+3r)*(f*x)^m*(1+m+3r)^-1*(a+b*log(c*x^n))+-1*b*n*d^3*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*n*e^3*x^(1+3r)*(f*x)^m*(1+m+3r)^-2+3*d*e^2*x^(1+2r)*(f*x)^m*(1+m+2r)^-1*(a+b*log(c*x^n))+3*e*d^2*x^(1+r)*(f*x)^m*(1+m+r)^-1*(a+b*log(c*x^n))+-3*b*d*n*e^2*x^(1+2r)*(f*x)^m*(1+m+2r)^-2+-3*b*e*n*d^2*x^(1+r)*(f*x)^m*(1+m+r)^-2)
@test integrate((f*x)^m*(d+e*x^r)^2*(a+b*log(c*x^n)), x) == :(d^2*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e^2*x^(1+2r)*(f*x)^m*(1+m+2r)^-1*(a+b*log(c*x^n))+-1*b*n*d^2*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*n*e^2*x^(1+2r)*(f*x)^m*(1+m+2r)^-2+2*d*e*x^(1+r)*(f*x)^m*(1+m+r)^-1*(a+b*log(c*x^n))+-2*b*d*e*n*x^(1+r)*(f*x)^m*(1+m+r)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n))*(d+e*x^r), x) == :(d*f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+e*x^(1+r)*(f*x)^m*(1+m+r)^-1*(a+b*log(c*x^n))+-1*b*d*n*f^-1*(f*x)^(1+m)*(1+m)^-2+-1*b*e*n*x^(1+r)*(f*x)^m*(1+m+r)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n)), x) == :(f^-1*(f*x)^(1+m)*(1+m)^-1*(a+b*log(c*x^n))+-1*b*n*f^-1*(f*x)^(1+m)*(1+m)^-2)
@test integrate((f*x)^m*(a+b*log(c*x^n))^p*(d+e*x^r)^3, x) == :(d^3*f^-1*(c*x^n)^(-1*n^-1*(1+m))*(f*x)^(1+m)*(-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))^(-1p)*(1+m)^-1*(a+b*log(c*x^n))^p*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))*exp(-1*a*b^-1*n^-1*(1+m))+e^3*x^(1+3r)*(c*x^n)^(-1*n^-1*(1+m+3r))*(f*x)^m*(-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+3r))^(-1p)*(a+b*log(c*x^n))^p*(1+m+3r)^-1*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+3r))*exp(-1*a*b^-1*n^-1*(1+m+3r))+3*d*e^2*x^(1+2r)*(c*x^n)^(-1*n^-1*(1+m+2r))*(f*x)^m*(-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+2r))^(-1p)*(a+b*log(c*x^n))^p*(1+m+2r)^-1*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+2r))*exp(-1*a*b^-1*n^-1*(1+m+2r))+3*e*d^2*x^(1+r)*(c*x^n)^(-1*n^-1*(1+m+r))*(f*x)^m*(-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+r))^(-1p)*(a+b*log(c*x^n))^p*(1+m+r)^-1*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+r))*exp(-1*a*b^-1*n^-1*(1+m+r)))
@test integrate((f*x)^m*(a+b*log(c*x^n))^p*(d+e*x^r)^2, x) == :(d^2*f^-1*(c*x^n)^(-1*n^-1*(1+m))*(f*x)^(1+m)*(-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))^(-1p)*(1+m)^-1*(a+b*log(c*x^n))^p*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))*exp(-1*a*b^-1*n^-1*(1+m))+e^2*x^(1+2r)*(c*x^n)^(-1*n^-1*(1+m+2r))*(f*x)^m*(-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+2r))^(-1p)*(a+b*log(c*x^n))^p*(1+m+2r)^-1*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+2r))*exp(-1*a*b^-1*n^-1*(1+m+2r))+2*d*e*x^(1+r)*(c*x^n)^(-1*n^-1*(1+m+r))*(f*x)^m*(-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+r))^(-1p)*(a+b*log(c*x^n))^p*(1+m+r)^-1*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+r))*exp(-1*a*b^-1*n^-1*(1+m+r)))
@test integrate((f*x)^m*(a+b*log(c*x^n))^p*(d+e*x^r), x) == :(d*f^-1*(c*x^n)^(-1*n^-1*(1+m))*(f*x)^(1+m)*(-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))^(-1p)*(1+m)^-1*(a+b*log(c*x^n))^p*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))*exp(-1*a*b^-1*n^-1*(1+m))+e*x^(1+r)*(c*x^n)^(-1*n^-1*(1+m+r))*(f*x)^m*(-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+r))^(-1p)*(a+b*log(c*x^n))^p*(1+m+r)^-1*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(a+b*log(c*x^n))*(1+m+r))*exp(-1*a*b^-1*n^-1*(1+m+r)))
@test integrate((f*x)^m*(a+b*log(c*x^n))^p, x) == :(f^-1*(c*x^n)^(-1*n^-1*(1+m))*(f*x)^(1+m)*(-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))^(-1p)*(1+m)^-1*(a+b*log(c*x^n))^p*SpecialFunctions.gamma(1+p,-1*b^-1*n^-1*(1+m)*(a+b*log(c*x^n)))*exp(-1*a*b^-1*n^-1*(1+m)))
@test integrate((d+e*x)^-3*(a+b*log(c*x^n))*(f+g*x), x) == :(-1*(d+e*x)^-2*(f+g*x)^2*(-2*d*g+2*e*f)^-1*(a+b*log(c*x^n))+(1/2)*b*n*d^-1*e^-2*(d+e*x)^-1*(e*f+-1*d*g)+(1/2)*b*n*d^-2*f^2*(e*f+-1*d*g)^-1*log(x)+-1//2*b*n*d^-2*e^-2*(d*g+e*f)*log(d+e*x))
@test integrate((a+b*log(c*x^n))^2*(d+e*x)^-3*(f+g*x), x) == :((1/2)*d^-2*f^2*(a+b*log(c*x^n))^2*(e*f+-1*d*g)^-1+-1*(a+b*log(c*x^n))^2*(d+e*x)^-2*(f+g*x)^2*(-2*d*g+2*e*f)^-1+b^2*d^-2*e^-2*n^2*(e*f+-1*d*g)*log(d+e*x)+-1*b^2*d^-2*e^-2*n^2*(d*g+e*f)*Polylogarithms.polylog(2,-1*e*x*d^-1)+-1*b*n*d^-2*e^-2*(a+b*log(c*x^n))*(d*g+e*f)*log(1+e*x*d^-1)+-1*b*n*x*d^-2*e^-1*(d+e*x)^-1*(a+b*log(c*x^n))*(e*f+-1*d*g))
@test integrate((a+b*log(c*x^n))^3*(d+e*x)^-3*(f+g*x), x) == :((1/2)*d^-2*f^2*(a+b*log(c*x^n))^3*(e*f+-1*d*g)^-1+-1*(a+b*log(c*x^n))^3*(d+e*x)^-2*(f+g*x)^2*(-2*d*g+2*e*f)^-1+3*b^3*d^-2*e^-2*n^3*(d*g+e*f)*Polylogarithms.polylog(3,-1*e*x*d^-1)+3*b^3*d^-2*e^-2*n^3*(e*f+-1*d*g)*Polylogarithms.polylog(2,-1*e*x*d^-1)+-3*b^2*d^-2*e^-2*n^2*(a+b*log(c*x^n))*(d*g+e*f)*Polylogarithms.polylog(2,-1*e*x*d^-1)+3*b^2*d^-2*e^-2*n^2*(a+b*log(c*x^n))*(e*f+-1*d*g)*log(1+e*x*d^-1)+-3//2*b*n*d^-2*e^-2*(a+b*log(c*x^n))^2*(d*g+e*f)*log(1+e*x*d^-1)+-3//2*b*n*x*d^-2*e^-1*(a+b*log(c*x^n))^2*(d+e*x)^-1*(e*f+-1*d*g))

max_stars_repo_path: test/3 Logarithms/3.1.4 (f x)^m (d+e x^r)^q (a+b log(c x^n))^p.jl