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

@test integrate(x^4*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(1//5*d*x^5*(a+b*arcsinh(c*x))+-2//35*b*d*c^-5*(1+c^2*x^2)^(1/2)+-1//49*b*d*c^-5*(1+c^2*x^2)^7//2+-1//105*b*d*c^-5*(1+c^2*x^2)^3//2+1//7*d*c^2*x^7*(a+b*arcsinh(c*x))+8//175*b*d*c^-5*(1+c^2*x^2)^5//2)
@test integrate(x^3*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(1//4*d*x^4*(a+b*arcsinh(c*x))+-1//24*b*d*c^-4*arcsinh(c*x)+1//6*d*c^2*x^6*(a+b*arcsinh(c*x))+-1//36*b*c*d*x^5*(1+c^2*x^2)^(1/2)+-1//36*b*d*c^-1*x^3*(1+c^2*x^2)^(1/2)+1//24*b*d*x*c^-3*(1+c^2*x^2)^(1/2))
@test integrate(x^2*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(1//3*d*x^3*(a+b*arcsinh(c*x))+-1//25*b*d*c^-3*(1+c^2*x^2)^5//2+1//5*d*c^2*x^5*(a+b*arcsinh(c*x))+1//45*b*d*c^-3*(1+c^2*x^2)^3//2+2//15*b*d*c^-3*(1+c^2*x^2)^(1/2))
@test integrate(x*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(-3//32*b*d*c^-2*arcsinh(c*x)+1//4*d*c^-2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))+-3//32*b*d*x*c^-1*(1+c^2*x^2)^(1/2)+-1//16*b*d*x*c^-1*(1+c^2*x^2)^3//2)
@test integrate((a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(d*x*(a+b*arcsinh(c*x))+-2//3*b*d*c^-1*(1+c^2*x^2)^(1/2)+-1//9*b*d*c^-1*(1+c^2*x^2)^3//2+1//3*d*c^2*x^3*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(d*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*b*d*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*d*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1//2*d*b^-1*(a+b*arcsinh(c*x))^2+-1//4*b*d*arcsinh(c*x)+-1//4*b*c*d*x*(1+c^2*x^2)^(1/2))
@test integrate(x^-2*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(-1*d*x^-1*(a+b*arcsinh(c*x))+d*x*c^2*(a+b*arcsinh(c*x))+-1*b*c*d*(1+c^2*x^2)^(1/2)+-1*b*c*d*arctanh((1+c^2*x^2)^(1/2)))
@test integrate(x^-3*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(d*c^2*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*b*d*c^2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*b*d*c^2*arcsinh(c*x)+-1//2*d*b^-1*c^2*(a+b*arcsinh(c*x))^2+-1//2*d*x^-2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1//2*b*c*d*x^-1*(1+c^2*x^2)^(1/2))
@test integrate(x^-4*(a+b*arcsinh(c*x))*(d+d*c^2*x^2), x) == :(-1//3*d*x^-3*(a+b*arcsinh(c*x))+-1*d*c^2*x^-1*(a+b*arcsinh(c*x))+-5//6*b*d*c^3*arctanh((1+c^2*x^2)^(1/2))+-1//6*b*c*d*x^-2*(1+c^2*x^2)^(1/2))
@test integrate(x^4*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(1//5*d^2*x^5*(a+b*arcsinh(c*x))+-8//315*b*c^-5*d^2*(1+c^2*x^2)^(1/2)+-4//945*b*c^-5*d^2*(1+c^2*x^2)^3//2+-1//81*b*c^-5*d^2*(1+c^2*x^2)^9//2+-1//525*b*c^-5*d^2*(1+c^2*x^2)^5//2+1//9*c^4*d^2*x^9*(a+b*arcsinh(c*x))+2//7*c^2*d^2*x^7*(a+b*arcsinh(c*x))+10//441*b*c^-5*d^2*(1+c^2*x^2)^7//2)
@test integrate(x^3*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(1//4*d^2*x^4*(a+b*arcsinh(c*x))+-73//3072*b*c^-4*d^2*arcsinh(c*x)+1//3*c^2*d^2*x^6*(a+b*arcsinh(c*x))+1//8*c^4*d^2*x^8*(a+b*arcsinh(c*x))+-73//4608*b*c^-1*d^2*x^3*(1+c^2*x^2)^(1/2)+-43//1152*b*c*d^2*x^5*(1+c^2*x^2)^(1/2)+-1//64*b*c^3*d^2*x^7*(1+c^2*x^2)^(1/2)+73//3072*b*x*c^-3*d^2*(1+c^2*x^2)^(1/2))
@test integrate(x^2*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(1//3*d^2*x^3*(a+b*arcsinh(c*x))+-1//49*b*c^-3*d^2*(1+c^2*x^2)^7//2+1//7*c^4*d^2*x^7*(a+b*arcsinh(c*x))+1//175*b*c^-3*d^2*(1+c^2*x^2)^5//2+2//5*c^2*d^2*x^5*(a+b*arcsinh(c*x))+4//315*b*c^-3*d^2*(1+c^2*x^2)^3//2+8//105*b*c^-3*d^2*(1+c^2*x^2)^(1/2))
@test integrate(x*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(-5//96*b*c^-2*d^2*arcsinh(c*x)+1//6*c^-2*d^2*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))+-5//96*b*x*c^-1*d^2*(1+c^2*x^2)^(1/2)+-5//144*b*x*c^-1*d^2*(1+c^2*x^2)^3//2+-1//36*b*x*c^-1*d^2*(1+c^2*x^2)^5//2)
@test integrate((d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(x*d^2*(a+b*arcsinh(c*x))+-8//15*b*c^-1*d^2*(1+c^2*x^2)^(1/2)+-4//45*b*c^-1*d^2*(1+c^2*x^2)^3//2+-1//25*b*c^-1*d^2*(1+c^2*x^2)^5//2+1//5*c^4*d^2*x^5*(a+b*arcsinh(c*x))+2//3*c^2*d^2*x^3*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(d^2*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*b*d^2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-11//32*b*d^2*arcsinh(c*x)+-1//2*b^-1*d^2*(a+b*arcsinh(c*x))^2+1//4*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))+-11//32*b*c*x*d^2*(1+c^2*x^2)^(1/2)+-1//16*b*c*x*d^2*(1+c^2*x^2)^3//2)
@test integrate(x^-2*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(-1*d^2*x^-1*(a+b*arcsinh(c*x))+-1*b*c*d^2*arctanh((1+c^2*x^2)^(1/2))+2*x*c^2*d^2*(a+b*arcsinh(c*x))+-5//3*b*c*d^2*(1+c^2*x^2)^(1/2)+-1//9*b*c*d^2*(1+c^2*x^2)^3//2+1//3*c^4*d^2*x^3*(a+b*arcsinh(c*x)))
@test integrate(x^-3*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(b*c^2*d^2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+c^2*d^2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1*b^-1*c^2*d^2*(a+b*arcsinh(c*x))^2+2*c^2*d^2*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+-1//2*d^2*x^-2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))+1//4*b*c^2*d^2*arcsinh(c*x)+-1//2*b*c*d^2*x^-1*(1+c^2*x^2)^3//2+1//4*b*x*c^3*d^2*(1+c^2*x^2)^(1/2))
@test integrate(x^-4*(d+d*c^2*x^2)^2*(a+b*arcsinh(c*x)), x) == :(-1//3*d^2*x^-3*(a+b*arcsinh(c*x))+x*c^4*d^2*(a+b*arcsinh(c*x))+-1*b*c^3*d^2*(1+c^2*x^2)^(1/2)+-2*c^2*d^2*x^-1*(a+b*arcsinh(c*x))+-11//6*b*c^3*d^2*arctanh((1+c^2*x^2)^(1/2))+-1//6*b*c*d^2*x^-2*(1+c^2*x^2)^(1/2))
@test integrate(x^4*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(1//5*d^3*x^5*(a+b*arcsinh(c*x))+-16//1155*b*c^-5*d^3*(1+c^2*x^2)^(1/2)+-8//3465*b*c^-5*d^3*(1+c^2*x^2)^3//2+-2//1925*b*c^-5*d^3*(1+c^2*x^2)^5//2+-1//121*b*c^-5*d^3*(1+c^2*x^2)^11//2+-1//1617*b*c^-5*d^3*(1+c^2*x^2)^7//2+1//3*c^4*d^3*x^9*(a+b*arcsinh(c*x))+1//11*c^6*d^3*x^11*(a+b*arcsinh(c*x))+3//7*c^2*d^3*x^7*(a+b*arcsinh(c*x))+4//297*b*c^-5*d^3*(1+c^2*x^2)^9//2)
@test integrate(x^3*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(-1//8*c^-4*d^3*(1+c^2*x^2)^4*(a+b*arcsinh(c*x))+1//10*c^-4*d^3*(1+c^2*x^2)^5*(a+b*arcsinh(c*x))+49//5120*b*c^-4*d^3*arcsinh(c*x)+-1//100*b*x*c^-3*d^3*(1+c^2*x^2)^9//2+7//1600*b*x*c^-3*d^3*(1+c^2*x^2)^7//2+49//5120*b*x*c^-3*d^3*(1+c^2*x^2)^(1/2)+49//7680*b*x*c^-3*d^3*(1+c^2*x^2)^3//2+49//9600*b*x*c^-3*d^3*(1+c^2*x^2)^5//2)
@test integrate(x^2*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(1//3*d^3*x^3*(a+b*arcsinh(c*x))+-1//81*b*c^-3*d^3*(1+c^2*x^2)^9//2+1//9*c^6*d^3*x^9*(a+b*arcsinh(c*x))+1//441*b*c^-3*d^3*(1+c^2*x^2)^7//2+2//525*b*c^-3*d^3*(1+c^2*x^2)^5//2+3//5*c^2*d^3*x^5*(a+b*arcsinh(c*x))+3//7*c^4*d^3*x^7*(a+b*arcsinh(c*x))+8//945*b*c^-3*d^3*(1+c^2*x^2)^3//2+16//315*b*c^-3*d^3*(1+c^2*x^2)^(1/2))
@test integrate(x*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(-35//1024*b*c^-2*d^3*arcsinh(c*x)+1//8*c^-2*d^3*(1+c^2*x^2)^4*(a+b*arcsinh(c*x))+-35//1024*b*x*c^-1*d^3*(1+c^2*x^2)^(1/2)+-35//1536*b*x*c^-1*d^3*(1+c^2*x^2)^3//2+-7//384*b*x*c^-1*d^3*(1+c^2*x^2)^5//2+-1//64*b*x*c^-1*d^3*(1+c^2*x^2)^7//2)
@test integrate((d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(x*d^3*(a+b*arcsinh(c*x))+c^2*d^3*x^3*(a+b*arcsinh(c*x))+-16//35*b*c^-1*d^3*(1+c^2*x^2)^(1/2)+-8//105*b*c^-1*d^3*(1+c^2*x^2)^3//2+-6//175*b*c^-1*d^3*(1+c^2*x^2)^5//2+-1//49*b*c^-1*d^3*(1+c^2*x^2)^7//2+1//7*c^6*d^3*x^7*(a+b*arcsinh(c*x))+3//5*c^4*d^3*x^5*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(d^3*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*b*d^3*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-19//48*b*d^3*arcsinh(c*x)+-1//2*b^-1*d^3*(a+b*arcsinh(c*x))^2+1//4*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))+1//6*d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))+-19//48*b*c*x*d^3*(1+c^2*x^2)^(1/2)+-7//72*b*c*x*d^3*(1+c^2*x^2)^3//2+-1//36*b*c*x*d^3*(1+c^2*x^2)^5//2)
@test integrate(x^-2*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(-1*d^3*x^-1*(a+b*arcsinh(c*x))+c^4*d^3*x^3*(a+b*arcsinh(c*x))+-1*b*c*d^3*arctanh((1+c^2*x^2)^(1/2))+3*x*c^2*d^3*(a+b*arcsinh(c*x))+-11//5*b*c*d^3*(1+c^2*x^2)^(1/2)+-1//5*b*c*d^3*(1+c^2*x^2)^3//2+-1//25*b*c*d^3*(1+c^2*x^2)^5//2+1//5*c^6*d^3*x^5*(a+b*arcsinh(c*x)))
@test integrate(x^-3*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(3*c^2*d^3*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+-3//2*b^-1*c^2*d^3*(a+b*arcsinh(c*x))^2+-3//32*b*c^2*d^3*arcsinh(c*x)+-1//2*d^3*x^-2*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))+3//2*b*c^2*d^3*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+3//2*c^2*d^3*(1+c^2*x^2)*(a+b*arcsinh(c*x))+3//4*c^2*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))+-3//32*b*x*c^3*d^3*(1+c^2*x^2)^(1/2)+-1//2*b*c*d^3*x^-1*(1+c^2*x^2)^5//2+7//16*b*x*c^3*d^3*(1+c^2*x^2)^3//2)
@test integrate(x^-4*(d+d*c^2*x^2)^3*(a+b*arcsinh(c*x)), x) == :(-1//3*d^3*x^-3*(a+b*arcsinh(c*x))+-3*c^2*d^3*x^-1*(a+b*arcsinh(c*x))+3*x*c^4*d^3*(a+b*arcsinh(c*x))+-17//6*b*c^3*d^3*arctanh((1+c^2*x^2)^(1/2))+-8//3*b*c^3*d^3*(1+c^2*x^2)^(1/2)+-1//9*b*c^3*d^3*(1+c^2*x^2)^3//2+1//3*c^6*d^3*x^3*(a+b*arcsinh(c*x))+-1//6*b*c*d^3*x^-2*(1+c^2*x^2)^(1/2))
@test integrate(x^4*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(c^-5*d^-1*(2a+2*b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-1*x*c^-4*d^-1*(a+b*arcsinh(c*x))+-1//9*b*c^-5*d^-1*(1+c^2*x^2)^3//2+1//3*c^-2*d^-1*x^3*(a+b*arcsinh(c*x))+4//3*b*c^-5*d^-1*(1+c^2*x^2)^(1/2)+im*b*c^-5*d^-1*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1*im*b*c^-5*d^-1*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^3*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :((1/2)*b^-1*c^-4*d^-1*(a+b*arcsinh(c*x))^2+(1/2)*c^-2*d^-1*x^2*(a+b*arcsinh(c*x))+-1*c^-4*d^-1*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//2*b*c^-4*d^-1*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+1//4*b*c^-4*d^-1*arcsinh(c*x)+-1//4*b*x*c^-3*d^-1*(1+c^2*x^2)^(1/2))
@test integrate(x^2*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(x*c^-2*d^-1*(a+b*arcsinh(c*x))+-1*b*c^-3*d^-1*(1+c^2*x^2)^(1/2)+-1*c^-3*d^-1*(2a+2*b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+im*b*c^-3*d^-1*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1*im*b*c^-3*d^-1*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(c^-2*d^-1*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+(1/2)*b*c^-2*d^-1*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//2*b^-1*c^-2*d^-1*(a+b*arcsinh(c*x))^2)
@test integrate((d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(c^-1*d^-1*(2a+2*b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+im*b*c^-1*d^-1*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1*im*b*c^-1*d^-1*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-1*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(d^-1*(-2a+-2*b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+(1/2)*b*d^-1*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1//2*b*d^-1*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x))))
@test integrate(x^-2*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(-1*d^-1*x^-1*(a+b*arcsinh(c*x))+-1*b*c*d^-1*arctanh((1+c^2*x^2)^(1/2))+-2*c*d^-1*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+im*b*c*d^-1*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1*im*b*c*d^-1*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^-3*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(-1//2*d^-1*x^-2*(a+b*arcsinh(c*x))+(1/2)*b*c^2*d^-1*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+2*c^2*d^-1*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+-1//2*b*c^2*d^-1*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1//2*b*c*d^-1*x^-1*(1+c^2*x^2)^(1/2))
@test integrate(x^-4*(d+d*c^2*x^2)^-1*(a+b*arcsinh(c*x)), x) == :(-1//3*d^-1*x^-3*(a+b*arcsinh(c*x))+c^2*d^-1*x^-1*(a+b*arcsinh(c*x))+2*c^3*d^-1*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+7//6*b*c^3*d^-1*arctanh((1+c^2*x^2)^(1/2))+im*b*c^3*d^-1*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1*im*b*c^3*d^-1*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//6*b*c*d^-1*x^-2*(1+c^2*x^2)^(1/2))
@test integrate(x^4*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :((1/2)*b*c^-5*d^-2*(1+c^2*x^2)^-1//2+-1*b*c^-5*d^-2*(1+c^2*x^2)^(1/2)+-1*c^-5*d^-2*(3a+3*b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+3//2*x*c^-4*d^-2*(a+b*arcsinh(c*x))+-3//2*im*b*c^-5*d^-2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//2*c^-2*d^-2*x^3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+3//2*im*b*c^-5*d^-2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^3*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(c^-4*d^-2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+(1/2)*b*c^-4*d^-2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+(1/2)*b*c^-4*d^-2*arcsinh(c*x)+-1//2*b^-1*c^-4*d^-2*(a+b*arcsinh(c*x))^2+-1//2*b*x*c^-3*d^-2*(1+c^2*x^2)^-1//2+-1//2*c^-2*d^-2*x^2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x)))
@test integrate(x^2*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(c^-3*d^-2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-1//2*b*c^-3*d^-2*(1+c^2*x^2)^-1//2+(1/2)*im*b*c^-3*d^-2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//2*im*b*c^-3*d^-2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//2*x*c^-2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x)))
@test integrate(x*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(-1//2*c^-2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+(1/2)*b*x*c^-1*d^-2*(1+c^2*x^2)^-1//2)
@test integrate((d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(c^-1*d^-2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+(1/2)*b*c^-1*d^-2*(1+c^2*x^2)^-1//2+(1/2)*x*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+(1/2)*im*b*c^-1*d^-2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//2*im*b*c^-1*d^-2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-1*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :((1/2)*b*d^-2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-1*d^-2*(2a+2*b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+-1//2*b*d^-2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//2*b*c*x*d^-2*(1+c^2*x^2)^-1//2)
@test integrate(x^-2*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(-1*b*c*d^-2*arctanh((1+c^2*x^2)^(1/2))+-1*d^-2*x^-1*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-3*c*d^-2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-1//2*b*c*d^-2*(1+c^2*x^2)^-1//2+-3//2*im*b*c*d^-2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-3//2*x*c^2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+3//2*im*b*c*d^-2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-3*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(b*c^2*d^-2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1*b*c^2*d^-2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*c^2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+4*c^2*d^-2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+-1//2*d^-2*x^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-1//2*b*c*d^-2*x^-1*(1+c^2*x^2)^-1//2)
@test integrate(x^-4*(d+d*c^2*x^2)^-2*(a+b*arcsinh(c*x)), x) == :(5*c^3*d^-2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-1//3*d^-2*x^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+1//3*b*c^3*d^-2*(1+c^2*x^2)^-1//2+13//6*b*c^3*d^-2*arctanh((1+c^2*x^2)^(1/2))+-5//2*im*b*c^3*d^-2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//6*b*c*d^-2*x^-2*(1+c^2*x^2)^-1//2+5//2*im*b*c^3*d^-2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+5//2*x*c^4*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+5//3*c^2*d^-2*x^-1*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x)))
@test integrate(x^4*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(-5//8*b*c^-5*d^-3*(1+c^2*x^2)^-1//2+1//4*c^-5*d^-3*(3a+3*b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+1//12*b*c^-5*d^-3*(1+c^2*x^2)^-3//2+-3//8*im*b*c^-5*d^-3*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-3//8*x*c^-4*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-1//4*c^-2*d^-3*x^3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+3//8*im*b*c^-5*d^-3*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^3*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(-1//4*b*c^-4*d^-3*arcsinh(c*x)+1//4*d^-3*x^4*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+1//4*b*x*c^-3*d^-3*(1+c^2*x^2)^-1//2+1//12*b*c^-1*d^-3*x^3*(1+c^2*x^2)^-3//2)
@test integrate(x^2*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(-1//12*b*c^-3*d^-3*(1+c^2*x^2)^-3//2+1//4*c^-3*d^-3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+1//8*b*c^-3*d^-3*(1+c^2*x^2)^-1//2+-1//4*x*c^-2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+-1//8*im*b*c^-3*d^-3*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+1//8*im*b*c^-3*d^-3*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+1//8*x*c^-2*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x)))
@test integrate(x*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(-1//4*c^-2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+1//6*b*x*c^-1*d^-3*(1+c^2*x^2)^-1//2+1//12*b*x*c^-1*d^-3*(1+c^2*x^2)^-3//2)
@test integrate((d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(1//4*x*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+1//4*c^-1*d^-3*(3a+3*b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+1//12*b*c^-1*d^-3*(1+c^2*x^2)^-3//2+3//8*b*c^-1*d^-3*(1+c^2*x^2)^-1//2+3//8*x*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-3//8*im*b*c^-1*d^-3*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+3//8*im*b*c^-1*d^-3*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^-1*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :((1/2)*b*d^-3*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-1*d^-3*(2a+2*b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+-1//2*b*d^-3*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+1//4*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+-2//3*b*c*x*d^-3*(1+c^2*x^2)^-1//2+-1//12*b*c*x*d^-3*(1+c^2*x^2)^-3//2)
@test integrate(x^-2*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(-1*b*c*d^-3*arctanh((1+c^2*x^2)^(1/2))+-1*d^-3*x^-1*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+-15//4*c*d^-3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-7//8*b*c*d^-3*(1+c^2*x^2)^-1//2+-1//12*b*c*d^-3*(1+c^2*x^2)^-3//2+-15//8*im*b*c*d^-3*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-15//8*x*c^2*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-5//4*x*c^2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+15//8*im*b*c*d^-3*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-3*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(6*c^2*d^-3*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+-3//2*b*c^2*d^-3*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-3//2*c^2*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+-3//4*c^2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+-1//2*d^-3*x^-2*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+3//2*b*c^2*d^-3*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-5//12*b*x*c^3*d^-3*(1+c^2*x^2)^-3//2+-1//2*b*c*d^-3*x^-1*(1+c^2*x^2)^-3//2+2//3*b*x*c^3*d^-3*(1+c^2*x^2)^-1//2)
@test integrate(x^-4*(d+d*c^2*x^2)^-3*(a+b*arcsinh(c*x)), x) == :(-1//3*d^-3*x^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+-1//12*b*c^3*d^-3*(1+c^2*x^2)^-3//2+19//6*b*c^3*d^-3*arctanh((1+c^2*x^2)^(1/2))+29//24*b*c^3*d^-3*(1+c^2*x^2)^-1//2+35//4*c^3*d^-3*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-35//8*im*b*c^3*d^-3*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//6*b*c*d^-3*x^-2*(1+c^2*x^2)^-3//2+7//3*c^2*d^-3*x^-1*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))+35//8*im*b*c^3*d^-3*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+35//8*x*c^4*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))+35//12*x*c^4*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x)))
@test integrate(x^3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :(-1//3*c^-4*d^-1*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+1//5*c^-4*d^-2*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-1//25*b*c*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//45*b*c^-1*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+2//15*b*x*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :(1//4*x^3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//8*x*c^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//16*b*c*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//16*b*c^-1*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//16*b^-1*c^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :(1//3*c^-2*d^-1*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1//3*b*x*c^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//9*b*c*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate((d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :((1/2)*x*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//4*b*c*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+1//4*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :((d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-1*b*c*x*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :(-1*x^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*c*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*log(x)+(1/2)*c*b^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :(-1//2*x^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+(1/2)*b*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-1//2*b*c*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//2*b*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x))))
@test integrate(x^-4*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)), x) == :(-1//3*d^-1*x^-3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1//6*b*c*x^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+1//3*b*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(-1//5*c^-4*d^-1*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+1//7*c^-4*d^-2*(d+d*c^2*x^2)^7//2*(a+b*arcsinh(c*x))+-8//175*b*c*d*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//49*b*d*c^3*x^7*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//105*b*d*c^-1*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+2//35*b*d*x*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^2*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(1//6*x^3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+1//8*d*x^3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//16*d*x*c^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-7//96*b*c*d*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//32*b*d*c^-1*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//32*d*b^-1*c^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1//36*b*d*c^3*x^6*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(1//5*c^-2*d^-1*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-2//15*b*c*d*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//5*b*d*x*c^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//25*b*d*c^3*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate((d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(1//4*x*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+3//8*d*x*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-5//16*b*c*d*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//16*b*d*c^3*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+3//16*d*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(1//3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+d*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-4//3*b*c*d*x*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//9*b*d*c^3*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-2*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(-1*x^-1*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+3//2*d*x*c^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*c*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*log(x)+-1//4*b*d*c^3*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+3//4*c*d*b^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(-1//2*x^-2*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+3//2*d*c^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*b*d*x*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-3*d*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-3//2*b*d*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1//2*b*c*d*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+3//2*b*d*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-4*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x)), x) == :(-1//3*x^-3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1*d*c^2*x^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+(1/2)*d*b^-1*c^3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1//6*b*c*d*x^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+4//3*b*d*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*log(x))
@test integrate(x^3*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(-1//7*c^-4*d^-1*(d+d*c^2*x^2)^7//2*(a+b*arcsinh(c*x))+1//9*c^-4*d^-2*(d+d*c^2*x^2)^9//2*(a+b*arcsinh(c*x))+-19//441*b*c^3*d^2*x^7*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//21*b*c*d^2*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//81*b*c^5*d^2*x^9*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//189*b*c^-1*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+2//63*b*x*c^-3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^2*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(1//8*x^3*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+5//48*d*x^3*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+5//64*d^2*x^3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+5//128*x*c^-2*d^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-59//768*b*c*d^2*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-17//288*b*c^3*d^2*x^6*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-5//256*b*c^-1*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-5//256*b^-1*c^-3*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1//64*b*c^5*d^2*x^8*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(1//7*c^-2*d^-1*(d+d*c^2*x^2)^7//2*(a+b*arcsinh(c*x))+-3//35*b*c^3*d^2*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//7*b*c*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//7*b*x*c^-1*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//49*b*c^5*d^2*x^7*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate((d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(1//6*x*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+5//16*x*d^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+5//24*d*x*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1//36*b*c^-1*d^2*(1+c^2*x^2)^5//2*(d+d*c^2*x^2)^(1/2)+-25//96*b*c*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-5//96*b*c^3*d^2*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+5//32*b^-1*c^-1*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-1*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(1//5*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+d^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//3*d*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+b*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-23//15*b*c*x*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-11//45*b*c^3*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//25*b*c^5*d^2*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-2*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(-1*x^-1*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+5//4*d*x*c^2*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+15//8*x*c^2*d^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*c*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*log(x)+-9//16*b*c^3*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//16*b*c^5*d^2*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+15//16*c*b^-1*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2))
@test integrate(x^-3*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(-1//2*x^-2*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+5//2*c^2*d^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+5//6*d*c^2*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-5*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-7//3*b*x*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-5//2*b*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1//2*b*c*d^2*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//9*b*c^5*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+5//2*b*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-4*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x)), x) == :(-1//3*x^-3*(d+d*c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-5//3*d*c^2*x^-1*(d+d*c^2*x^2)^3//2*(a+b*arcsinh(c*x))+5//2*x*c^4*d^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//4*b*c^5*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-1//6*b*c*d^2*x^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+5//4*b^-1*c^3*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+7//3*b*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*log(x))
@test integrate((1+x^2)^(1/2)*arcsinh(x), x) == :(-1//4*x^2+1//4*arcsinh(x)^2+(1/2)*x*(1+x^2)^(1/2)*arcsinh(x))
@test integrate(x^5*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(8//15*c^-6*d^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-8//15*b*x*c^-5*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-4//15*c^-4*d^-1*x^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//25*b*c^-1*x^5*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+1//5*c^-2*d^-1*x^4*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+4//45*b*c^-3*x^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate(x^4*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(-3//8*x*c^-4*d^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//16*b*c^-1*x^4*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+1//4*c^-2*d^-1*x^3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+3//16*b*c^-3*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+3//16*b^-1*c^-5*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2)
@test integrate(x^3*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(-2//3*c^-4*d^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//9*b*c^-1*x^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+2//3*b*x*c^-3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate(x^2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :((1/2)*x*c^-2*d^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//4*b*c^-1*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-1//4*b^-1*c^-3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2)
@test integrate(x*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(c^-2*d^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*b*x*c^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate((d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :((1/2)*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2)
@test integrate(x^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(b*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x))))
@test integrate(x^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(-1*d^-1*x^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*c*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(x))
@test integrate(x^-3*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(-1//2*d^-1*x^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+(1/2)*b*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1//2*b*c*x^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-1//2*b*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-4*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)), x) == :(-1//3*d^-1*x^-3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//3*b*c^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(x)+-1//6*b*c*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+2//3*c^2*d^-1*x^-1*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^5*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-8//3*c^-6*d^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*c^-2*d^-1*x^4*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+4//3*c^-4*d^-2*x^2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+b*c^-6*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x)+-1//9*b*c^-3*d^-1*x^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+5//3*b*x*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate(x^4*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-1*c^-2*d^-1*x^3*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+3//2*x*c^-4*d^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-3//4*b^-1*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//2*b*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2)+-1//4*b*c^-3*d^-1*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate(x^3*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(2*c^-4*d^-2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*c^-2*d^-1*x^2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1*b*x*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-1*b*c^-4*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x))
@test integrate(x^2*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-1*x*c^-2*d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+(1/2)*b*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2)+(1/2)*b^-1*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2)
@test integrate(x*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-1*c^-2*d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+b*c^-2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x))
@test integrate((d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(x*d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//2*b*c^-1*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2))
@test integrate(x^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+b*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1*b*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x)+-2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x))))
@test integrate(x^-2*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-1*d^-1*x^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-2*x*c^2*d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+b*c*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(x)+(1/2)*b*c*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2))
@test integrate(x^-3*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-3//2*c^2*d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//2*d^-1*x^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+b*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x)+3*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-3//2*b*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1//2*b*c*d^-1*x^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+3//2*b*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x))))
@test integrate(x^-4*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x)), x) == :(-1//3*d^-1*x^-3*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+4//3*c^2*d^-1*x^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+8//3*x*c^4*d^-1*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-5//3*b*c^3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(x)+-1//2*b*c^3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2)+-1//6*b*c*d^-1*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate(x^6*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-5//3*c^-4*d^-2*x^3*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//3*c^-2*d^-1*x^5*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-1//6*b*c^-7*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+5//2*x*c^-6*d^-3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-7//6*b*c^-7*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2)+-5//4*b^-1*c^-7*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//4*b*c^-5*d^-2*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate(x^5*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(8//3*c^-6*d^-3*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-4//3*c^-4*d^-2*x^2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//3*c^-2*d^-1*x^4*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-11//6*b*c^-6*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x)+-5//6*b*x*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-1//6*b*c^-3*d^-2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2)
@test integrate(x^4*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-1*x*c^-4*d^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//3*c^-2*d^-1*x^3*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+1//6*b*c^-5*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+(1/2)*b^-1*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+2//3*b*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2))
@test integrate(x^3*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-1//3*c^-4*d^-2*(d+d*c^2*x^2)^-1//2*(2a+2*b*arcsinh(c*x))+-1//3*c^-2*d^-1*x^2*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-1//6*b*x*c^-3*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+5//6*b*c^-4*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x))
@test integrate(x^2*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(1//3*d^-1*x^3*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-1//6*b*c^-3*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+-1//6*b*c^-3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2))
@test integrate(x*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-1//3*c^-2*d^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+1//6*b*x*c^-1*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+1//6*b*c^-2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x))
@test integrate((d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(1//3*x*d^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+2//3*x*d^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+1//6*b*c^-1*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+-1//3*b*c^-1*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2))
@test integrate(x^-1*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(d^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+1//3*d^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+b*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-7//6*b*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x)+-1//6*b*c*x*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2)
@test integrate(x^-2*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-1*d^-1*x^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-8//3*x*c^2*d^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-4//3*x*c^2*d^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-1//6*b*c*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+b*c*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(x)+5//6*b*c*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2))
@test integrate(x^-3*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-5//2*c^2*d^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-5//6*c^2*d^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-1//2*d^-1*x^-2*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+5*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-5//2*b*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-3//4*b*c*d^-2*x^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+1//4*b*c*d^-2*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+5//2*b*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+5//12*b*x*c^3*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+13//6*b*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctan(c*x))
@test integrate(x^-4*(d+d*c^2*x^2)^-5//2*(a+b*arcsinh(c*x)), x) == :(-1//3*d^-1*x^-3*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+2*c^2*d^-1*x^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+1//6*b*c^3*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2+8//3*x*c^4*d^-1*(d+d*c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+16//3*x*c^4*d^-2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-8//3*b*c^3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(x)+-4//3*b*c^3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*log(1+c^2*x^2)+-1//6*b*c*d^-2*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2)
@test integrate((c+c*a^2*x^2)^-7//2*arcsinh(a*x), x) == :(1//5*x*c^-1*(c+c*a^2*x^2)^-5//2*arcsinh(a*x)+1//20*a^-1*c^-3*(1+a^2*x^2)^-3//2*(c+c*a^2*x^2)^-1//2+2//15*a^-1*c^-3*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^-1//2+4//15*x*c^-2*(c+c*a^2*x^2)^-3//2*arcsinh(a*x)+8//15*x*c^-3*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)+-4//15*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*log(1+a^2*x^2))
@test integrate(x^4*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :(-1//16*a^-1*x^4+3//16*a^-5*arcsinh(a*x)^2+3//16*a^-3*x^2+-3//8*x*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)+1//4*a^-2*x^3*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x^3*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :(-1//9*a^-1*x^3+2//3*x*a^-3+-2//3*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)+1//3*a^-2*x^2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x^2*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :(-1//4*a^-1*x^2+-1//4*a^-3*arcsinh(a*x)^2+(1/2)*x*a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :(-1*x*a^-1+a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate((1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :((1/2)*a^-1*arcsinh(a*x)^2)
@test integrate(x^-1*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :(-1*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x)))+-2*arcsinh(a*x)*arctanh(exp(arcsinh(a*x)))+Polylogarithms.polylog(2,exp(arcsinh(a*x))))
@test integrate(x^-2*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :(a*log(x)+-1*x^-1*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x^-3*(1+a^2*x^2)^-1//2*arcsinh(a*x), x) == :((1/2)*a^2*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x)))+-1//2*a*x^-1+-1//2*a^2*Polylogarithms.polylog(2,exp(arcsinh(a*x)))+a^2*arcsinh(a*x)*arctanh(exp(arcsinh(a*x)))+-1//2*x^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(2//35*d*x^5*(a+b*arcsinh(c*x))^2+38//6125*d*b^2*x^5+-152//11025*d*b^2*c^-2*x^3+1//7*d*x^5*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+2//343*d*b^2*c^2*x^7+304//3675*d*x*b^2*c^-4+-32//525*b*d*c^-5*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//21*b*d*c^-5*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-2//49*b*d*c^-5*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x))+4//35*b*d*c^-5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-4//175*b*d*c^-1*x^4*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+16//525*b*d*c^-3*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(-1//24*d*c^-4*(a+b*arcsinh(c*x))^2+1//12*d*x^4*(a+b*arcsinh(c*x))^2+1//72*d*b^2*x^4+-1//24*d*b^2*c^-2*x^2+1//6*d*x^4*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+1//108*d*b^2*c^2*x^6+-1//18*b*c*d*x^5*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//18*b*d*c^-1*x^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//12*b*d*x*c^-3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(2//15*d*x^3*(a+b*arcsinh(c*x))^2+26//675*d*b^2*x^3+-52//225*d*x*b^2*c^-2+1//5*d*x^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+2//125*d*b^2*c^2*x^5+-2//25*b*d*c^-3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+2//15*b*d*c^-3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+8//45*b*d*c^-3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-4//45*b*d*c^-1*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(-3//32*d*c^-2*(a+b*arcsinh(c*x))^2+5//32*d*b^2*x^2+1//4*d*c^-2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1//32*d*b^2*c^2*x^4+-3//16*b*d*x*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//8*b*d*x*c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(2//3*d*x*(a+b*arcsinh(c*x))^2+14//9*d*x*b^2+1//3*d*x*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+2//27*d*b^2*c^2*x^3+-4//3*b*d*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//9*b*d*c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(-1//4*d*(a+b*arcsinh(c*x))^2+d*(a+b*arcsinh(c*x))^2*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*d*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1//2*d*b^2*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-1//3*d*b^-1*(a+b*arcsinh(c*x))^3+b*d*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+1//4*d*b^2*c^2*x^2+-1//2*b*c*d*x*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(-1*d*x^-1*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-2*c*d*b^2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*c*d*b^2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+2*d*x*b^2*c^2+2*d*x*c^2*(a+b*arcsinh(c*x))^2+-4*b*c*d*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-2*b*c*d*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :((1/2)*d*c^2*(a+b*arcsinh(c*x))^2+d*b^2*c^2*log(x)+d*c^2*(a+b*arcsinh(c*x))^2*log(1+-1*exp(2*arcsinh(c*x)))+-1//2*d*b^2*c^2*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-1//2*d*x^-2*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1//3*d*b^-1*c^2*(a+b*arcsinh(c*x))^3+b*d*c^2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*b*c*d*x^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2), x) == :(-5//3*d*b^2*c^3*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2//3*d*c^2*x^-1*(a+b*arcsinh(c*x))^2+-1//3*d*b^2*c^2*x^-1+-1//3*d*x^-3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+5//3*d*b^2*c^3*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-10//3*b*d*c^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-1//3*b*c*d*x^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(8//315*d^2*x^5*(a+b*arcsinh(c*x))^2+526//165375*b^2*d^2*x^5+-2104//297675*b^2*c^-2*d^2*x^3+1//9*d^2*x^5*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+2//729*b^2*c^4*d^2*x^9+4//63*d^2*x^5*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+212//27783*b^2*c^2*d^2*x^7+4208//99225*x*b^2*c^-4*d^2+-128//4725*b*c^-5*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-8//189*b*c^-5*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-2//81*b*c^-5*d^2*(1+c^2*x^2)^9//2*(a+b*arcsinh(c*x))+2//315*b*c^-5*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+20//441*b*c^-5*d^2*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x))+-16//1575*b*c^-1*d^2*x^4*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+64//4725*b*c^-3*d^2*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(-73//3072*c^-4*d^2*(a+b*arcsinh(c*x))^2+1//24*d^2*x^4*(a+b*arcsinh(c*x))^2+73//9216*b^2*d^2*x^4+-73//3072*b^2*c^-2*d^2*x^2+1//8*d^2*x^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1//12*d^2*x^4*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+1//256*b^2*c^4*d^2*x^8+43//3456*b^2*c^2*d^2*x^6+-73//2304*b*c^-1*d^2*x^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-25//576*b*c*d^2*x^5*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//32*b*c*d^2*x^5*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+73//1536*b*x*c^-3*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(8//105*d^2*x^3*(a+b*arcsinh(c*x))^2+818//33075*b^2*d^2*x^3+-1636//11025*x*b^2*c^-2*d^2+1//7*d^2*x^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+2//343*b^2*c^4*d^2*x^7+4//35*d^2*x^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+136//6125*b^2*c^2*d^2*x^5+-2//49*b*c^-3*d^2*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x))+2//175*b*c^-3*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+8//105*b*c^-3*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+32//315*b*c^-3*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-16//315*b*c^-1*d^2*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(-5//96*c^-2*d^2*(a+b*arcsinh(c*x))^2+25//288*b^2*d^2*x^2+1//6*c^-2*d^2*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+1//108*b^2*c^-2*d^2*(1+c^2*x^2)^3+5//288*b^2*c^2*d^2*x^4+-5//48*b*x*c^-1*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-5//72*b*x*c^-1*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1//18*b*x*c^-1*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(8//15*x*d^2*(a+b*arcsinh(c*x))^2+298//225*x*b^2*d^2+1//5*x*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+2//125*b^2*c^4*d^2*x^5+4//15*x*d^2*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+76//675*b^2*c^2*d^2*x^3+-16//15*b*c^-1*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-8//45*b*c^-1*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-2//25*b*c^-1*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(-11//32*d^2*(a+b*arcsinh(c*x))^2+d^2*(a+b*arcsinh(c*x))^2*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*d^2*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1//2*b^2*d^2*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-1//3*b^-1*d^2*(a+b*arcsinh(c*x))^3+1//4*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+b*d^2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+1//32*b^2*c^4*d^2*x^4+13//32*b^2*c^2*d^2*x^2+-11//16*b*c*x*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//8*b*c*x*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(-1*d^2*x^-1*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+-2*c*b^2*d^2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*c*b^2*d^2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+2//27*b^2*c^4*d^2*x^3+8//3*x*c^2*d^2*(a+b*arcsinh(c*x))^2+32//9*x*b^2*c^2*d^2+-4*b*c*d^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-10//3*b*c*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//9*b*c*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+4//3*x*c^2*d^2*(a+b*arcsinh(c*x))^2*(1+c^2*x^2))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(1//4*c^2*d^2*(a+b*arcsinh(c*x))^2+b^2*c^2*d^2*log(x)+c^2*d^2*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1*b^2*c^2*d^2*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+2*c^2*d^2*(a+b*arcsinh(c*x))^2*log(1+-1*exp(2*arcsinh(c*x)))+-2//3*b^-1*c^2*d^2*(a+b*arcsinh(c*x))^3+-1//2*d^2*x^-2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1//4*b^2*c^4*d^2*x^2+2*b*c^2*d^2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*b*x*c^3*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*b*c*d^2*x^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^2, x) == :(2*x*b^2*c^4*d^2+-11//3*b^2*c^3*d^2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1//3*b^2*c^2*d^2*x^-1+-1//3*d^2*x^-3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+8//3*x*c^4*d^2*(a+b*arcsinh(c*x))^2+11//3*b^2*c^3*d^2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-22//3*b*c^3*d^2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-5//3*b*c^3*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-4//3*c^2*d^2*x^-1*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1//3*b*c*d^2*x^-2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(16//1155*d^3*x^5*(a+b*arcsinh(c*x))^2+12622//6670125*b^2*d^3*x^5+-50488//12006225*b^2*c^-2*d^3*x^3+1//11*d^3*x^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+2//33*d^3*x^5*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+2//1331*b^2*c^6*d^3*x^11+8//231*d^3*x^5*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+182//29403*b^2*c^4*d^3*x^9+9410//1120581*b^2*c^2*d^3*x^7+100976//4002075*x*b^2*c^-4*d^3+-256//17325*b*c^-5*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-16//693*b*c^-5*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-2//121*b*c^-5*d^3*(1+c^2*x^2)^11//2*(a+b*arcsinh(c*x))+-2//1617*b*c^-5*d^3*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x))+4//1155*b*c^-5*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+8//297*b*c^-5*d^3*(1+c^2*x^2)^9//2*(a+b*arcsinh(c*x))+-32//5775*b*c^-1*d^3*x^4*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+128//17325*b*c^-3*d^3*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(-79//5120*c^-4*d^3*(a+b*arcsinh(c*x))^2+1//40*d^3*x^4*(a+b*arcsinh(c*x))^2+79//15360*b^2*d^3*x^4+-79//5120*b^2*c^-2*d^3*x^2+1//10*d^3*x^4*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+1//20*d^3*x^4*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+1//500*b^2*c^6*d^3*x^10+3//40*d^3*x^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+57//6400*b^2*c^4*d^3*x^8+401//28800*b^2*c^2*d^3*x^6+-79//3840*b*c^-1*d^3*x^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-31//960*b*c*d^3*x^5*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//32*b*c*d^3*x^5*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1//50*b*c*d^3*x^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+79//2560*b*x*c^-3*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(16//315*d^3*x^3*(a+b*arcsinh(c*x))^2+5258//297675*b^2*d^3*x^3+-10516//99225*x*b^2*c^-2*d^3+1//9*d^3*x^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+2//21*d^3*x^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+2//729*b^2*c^6*d^3*x^9+8//105*d^3*x^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+374//27783*b^2*c^4*d^3*x^7+4198//165375*b^2*c^2*d^3*x^5+-2//81*b*c^-3*d^3*(1+c^2*x^2)^9//2*(a+b*arcsinh(c*x))+2//441*b*c^-3*d^3*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x))+4//525*b*c^-3*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+16//315*b*c^-3*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+64//945*b*c^-3*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-32//945*b*c^-1*d^3*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(-35//1024*c^-2*d^3*(a+b*arcsinh(c*x))^2+175//3072*b^2*d^3*x^2+1//8*c^-2*d^3*(1+c^2*x^2)^4*(a+b*arcsinh(c*x))^2+1//256*b^2*c^-2*d^3*(1+c^2*x^2)^4+7//1152*b^2*c^-2*d^3*(1+c^2*x^2)^3+35//3072*b^2*c^2*d^3*x^4+-35//512*b*x*c^-1*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-35//768*b*x*c^-1*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-7//192*b*x*c^-1*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-1//32*b*x*c^-1*d^3*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(16//35*x*d^3*(a+b*arcsinh(c*x))^2+4322//3675*x*b^2*d^3+1//7*x*d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+2//343*b^2*c^6*d^3*x^7+6//35*x*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+8//35*x*d^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+234//6125*b^2*c^4*d^3*x^5+1514//11025*b^2*c^2*d^3*x^3+-32//35*b*c^-1*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-16//105*b*c^-1*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-12//175*b*c^-1*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-2//49*b*c^-1*d^3*(1+c^2*x^2)^7//2*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(-19//48*d^3*(a+b*arcsinh(c*x))^2+d^3*(a+b*arcsinh(c*x))^2*log(1+-1*exp(2*arcsinh(c*x)))+(1/2)*d^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1//2*b^2*d^3*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-1//3*b^-1*d^3*(a+b*arcsinh(c*x))^3+1//4*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+1//6*d^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+1//108*b^2*d^3*(1+c^2*x^2)^3+b*d^3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+7//144*b^2*c^4*d^3*x^4+71//144*b^2*c^2*d^3*x^2+-19//24*b*c*x*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-7//36*b*c*x*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-1//18*b*c*x*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(-1*d^3*x^-1*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+-2*c*b^2*d^3*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*c*b^2*d^3*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+2//125*b^2*c^6*d^3*x^5+14//75*b^2*c^4*d^3*x^3+16//5*x*c^2*d^3*(a+b*arcsinh(c*x))^2+122//25*x*b^2*c^2*d^3+-4*b*c*d^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-22//5*b*c*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//5*b*c*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+-2//25*b*c*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+6//5*x*c^2*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+8//5*x*c^2*d^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(-3//32*c^2*d^3*(a+b*arcsinh(c*x))^2+b^2*c^2*d^3*log(x)+-1*b^-1*c^2*d^3*(a+b*arcsinh(c*x))^3+3*c^2*d^3*(a+b*arcsinh(c*x))^2*log(1+-1*exp(2*arcsinh(c*x)))+-3//2*b^2*c^2*d^3*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-1//2*d^3*x^-2*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+1//32*b^2*c^6*d^3*x^4+3//2*c^2*d^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+3//4*c^2*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+21//32*b^2*c^4*d^3*x^2+3*b*c^2*d^3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*b*c*d^3*x^-1*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))+-3//16*b*x*c^3*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+7//8*b*x*c^3*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3, x) == :(-17//3*b^2*c^3*d^3*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1//3*b^2*c^2*d^3*x^-1+-1//3*d^3*x^-3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2+2//27*b^2*c^6*d^3*x^3+16//3*x*c^4*d^3*(a+b*arcsinh(c*x))^2+17//3*b^2*c^3*d^3*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+50//9*x*b^2*c^4*d^3+-5*b*c^3*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2*c^2*d^3*x^-1*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2+-34//3*b*c^3*d^3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+1//9*b*c^3*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))+8//3*x*c^4*d^3*(a+b*arcsinh(c*x))^2*(1+c^2*x^2)+-1//3*b*c*d^3*x^-2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(-1*x*c^-4*d^-1*(a+b*arcsinh(c*x))^2+2*c^-5*d^-1*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-22//9*x*b^2*c^-4*d^-1+1//3*c^-2*d^-1*x^3*(a+b*arcsinh(c*x))^2+2//27*b^2*c^-2*d^-1*x^3+-2*im*b^2*c^-5*d^-1*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+2*im*b^2*c^-5*d^-1*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+22//9*b*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2*im*b*c^-5*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*im*b*c^-5*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-2//9*b*c^-3*d^-1*x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(1//4*c^-4*d^-1*(a+b*arcsinh(c*x))^2+(1/2)*b^2*c^-4*d^-1*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+(1/2)*c^-2*d^-1*x^2*(a+b*arcsinh(c*x))^2+-1*c^-4*d^-1*(a+b*arcsinh(c*x))^2*log(1+exp(2*arcsinh(c*x)))+1//3*b^-1*c^-4*d^-1*(a+b*arcsinh(c*x))^3+1//4*b^2*c^-2*d^-1*x^2+-1*b*c^-4*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//2*b*x*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(x*c^-2*d^-1*(a+b*arcsinh(c*x))^2+-2*c^-3*d^-1*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+2*x*b^2*c^-2*d^-1+-2*im*b^2*c^-3*d^-1*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+-2*b*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+2*im*b^2*c^-3*d^-1*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-2*im*b*c^-3*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+2*im*b*c^-3*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(c^-2*d^-1*(a+b*arcsinh(c*x))^2*log(1+exp(2*arcsinh(c*x)))+-1//2*b^2*c^-2*d^-1*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+-1//3*b^-1*c^-2*d^-1*(a+b*arcsinh(c*x))^3+b*c^-2*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(2*c^-1*d^-1*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-2*im*b^2*c^-1*d^-1*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+2*im*b^2*c^-1*d^-1*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+-2*im*b*c^-1*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*im*b*c^-1*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :((1/2)*b^2*d^-1*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+-2*d^-1*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))+-1//2*b^2*d^-1*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+b*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*b*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x))))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(-1*d^-1*x^-1*(a+b*arcsinh(c*x))^2+-2*c*b^2*d^-1*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*c*d^-1*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+2*c*b^2*d^-1*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-4*b*c*d^-1*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-2*im*c*b^2*d^-1*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+2*im*c*b^2*d^-1*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-2*im*b*c*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+2*im*b*c*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(-1//2*d^-1*x^-2*(a+b*arcsinh(c*x))^2+b^2*c^2*d^-1*log(x)+(1/2)*b^2*c^2*d^-1*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+2*c^2*d^-1*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))+-1//2*b^2*c^2*d^-1*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+b*c^2*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1*b*c^2*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*b*c*d^-1*x^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1, x) == :(-1//3*d^-1*x^-3*(a+b*arcsinh(c*x))^2+c^2*d^-1*x^-1*(a+b*arcsinh(c*x))^2+2*c^3*d^-1*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-7//3*b^2*c^3*d^-1*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1//3*b^2*c^2*d^-1*x^-1+7//3*b^2*c^3*d^-1*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-2*im*b^2*c^3*d^-1*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+2*im*b^2*c^3*d^-1*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+14//3*b*c^3*d^-1*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-2*im*b*c^3*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*im*b*c^3*d^-1*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//3*b*c*d^-1*x^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(-1*b^2*c^-5*d^-2*arctan(c*x)+-3*c^-5*d^-2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+2*x*b^2*c^-4*d^-2+3//2*x*c^-4*d^-2*(a+b*arcsinh(c*x))^2+b*c^-5*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-3*im*b^2*c^-5*d^-2*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+-2*b*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+3*im*b^2*c^-5*d^-2*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-1//2*c^-2*d^-2*x^3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-3*im*b*c^-5*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+3*im*b*c^-5*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :((1/2)*c^-4*d^-2*(a+b*arcsinh(c*x))^2+c^-4*d^-2*(a+b*arcsinh(c*x))^2*log(1+exp(2*arcsinh(c*x)))+(1/2)*b^2*c^-4*d^-2*log(1+c^2*x^2)+-1//2*b^2*c^-4*d^-2*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+-1//3*b^-1*c^-4*d^-2*(a+b*arcsinh(c*x))^3+b*c^-4*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//2*c^-2*d^-2*x^2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-1*b*x*c^-3*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(b^2*c^-3*d^-2*arctan(c*x)+c^-3*d^-2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+im*b^2*c^-3*d^-2*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+-1*im*b^2*c^-3*d^-2*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-1*b*c^-3*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//2*x*c^-2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+im*b*c^-3*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1*im*b*c^-3*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(-1//2*b^2*c^-2*d^-2*log(1+c^2*x^2)+-1//2*c^-2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+b*x*c^-1*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(c^-1*d^-2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+(1/2)*x*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-1*b^2*c^-1*d^-2*arctan(c*x)+im*b^2*c^-1*d^-2*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+b*c^-1*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1*im*b^2*c^-1*d^-2*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+im*b*c^-1*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1*im*b*c^-1*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :((1/2)*b^2*d^-2*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+(1/2)*b^2*d^-2*log(1+c^2*x^2)+(1/2)*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-2*d^-2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))+-1//2*b^2*d^-2*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+b*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*b*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1*b*c*x*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(c*b^2*d^-2*arctan(c*x)+-1*d^-2*x^-1*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-3*c*d^-2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-2*c*b^2*d^-2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*c*b^2*d^-2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*c*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-4*b*c*d^-2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-3*im*c*b^2*d^-2*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+3*im*c*b^2*d^-2*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-3//2*x*c^2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-3*im*b*c*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+3*im*b*c*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(b^2*c^2*d^-2*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+b^2*c^2*d^-2*log(x)+-1*b^2*c^2*d^-2*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+-1*c^2*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+4*c^2*d^-2*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))+-1//2*b^2*c^2*d^-2*log(1+c^2*x^2)+-1//2*d^-2*x^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-2*b*c^2*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+2*b*c^2*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1*b*c*d^-2*x^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-2, x) == :(-1*b^2*c^3*d^-2*arctan(c*x)+5*c^3*d^-2*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-13//3*b^2*c^3*d^-2*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1//3*b^2*c^2*d^-2*x^-1+-1//3*d^-2*x^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+13//3*b^2*c^3*d^-2*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-5*im*b^2*c^3*d^-2*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+5*im*b^2*c^3*d^-2*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+2//3*b*c^3*d^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+5//2*x*c^4*d^-2*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+5//3*c^2*d^-2*x^-1*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+26//3*b*c^3*d^-2*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-5*im*b*c^3*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+5*im*b*c^3*d^-2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//3*b*c*d^-2*x^-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(3//4*c^-5*d^-3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+7//6*b^2*c^-5*d^-3*arctan(c*x)+-5//4*b*c^-5*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-3//4*im*b^2*c^-5*d^-3*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-3//8*x*c^-4*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-1//4*c^-2*d^-3*x^3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+-1//12*x*b^2*c^-4*d^-3*(1+c^2*x^2)^-1+1//6*b*c^-5*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+3//4*im*b^2*c^-5*d^-3*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+-3//4*im*b*c^-5*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+3//4*im*b*c^-5*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(-1//4*c^-4*d^-3*(a+b*arcsinh(c*x))^2+-1//3*b^2*c^-4*d^-3*log(1+c^2*x^2)+-1//12*b^2*c^-4*d^-3*(1+c^2*x^2)^-1+1//4*d^-3*x^4*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+(1/2)*b*x*c^-3*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+1//6*b*c^-1*d^-3*x^3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(-1//6*b^2*c^-3*d^-3*arctan(c*x)+1//4*c^-3*d^-3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-1//4*im*b^2*c^-3*d^-3*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-1//4*x*c^-2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+-1//6*b*c^-3*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+1//4*im*b^2*c^-3*d^-3*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+1//4*b*c^-3*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+1//8*x*c^-2*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+1//12*x*b^2*c^-2*d^-3*(1+c^2*x^2)^-1+-1//4*im*b*c^-3*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+1//4*im*b*c^-3*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(-1//4*c^-2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+-1//6*b^2*c^-2*d^-3*log(1+c^2*x^2)+1//12*b^2*c^-2*d^-3*(1+c^2*x^2)^-1+1//3*b*x*c^-1*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+1//6*b*x*c^-1*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(-5//6*b^2*c^-1*d^-3*arctan(c*x)+-1//12*x*b^2*d^-3*(1+c^2*x^2)^-1+1//4*x*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+3//4*c^-1*d^-3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+3//8*x*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-3//4*im*b^2*c^-1*d^-3*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+1//6*b*c^-1*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+3//4*im*b^2*c^-1*d^-3*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+3//4*b*c^-1*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-3//4*im*b*c^-1*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+3//4*im*b*c^-1*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :((1/2)*b^2*d^-3*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+(1/2)*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-2*d^-3*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))+-1//2*b^2*d^-3*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-1//12*b^2*d^-3*(1+c^2*x^2)^-1+1//4*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+2//3*b^2*d^-3*log(1+c^2*x^2)+b*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1*b*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-4//3*b*c*x*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1//6*b*c*x*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(-1*d^-3*x^-1*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+-2*c*b^2*d^-3*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*c*b^2*d^-3*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-15//4*c*d^-3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+11//6*c*b^2*d^-3*arctan(c*x)+-4*b*c*d^-3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-15//4*im*c*b^2*d^-3*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+-15//8*x*c^2*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-7//4*b*c*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-5//4*x*c^2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+-1//6*b*c*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+1//12*x*b^2*c^2*d^-3*(1+c^2*x^2)^-1+15//4*im*c*b^2*d^-3*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-15//4*im*b*c*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+15//4*im*b*c*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(b^2*c^2*d^-3*log(x)+6*c^2*d^-3*(a+b*arcsinh(c*x))^2*arctanh(exp(2*arcsinh(c*x)))+-7//6*b^2*c^2*d^-3*log(1+c^2*x^2)+-3//2*b^2*c^2*d^-3*Polylogarithms.polylog(3,-1*exp(2*arcsinh(c*x)))+-3//2*c^2*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+-3//4*c^2*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+-1//2*d^-3*x^-2*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+1//12*b^2*c^2*d^-3*(1+c^2*x^2)^-1+3//2*b^2*c^2*d^-3*Polylogarithms.polylog(3,exp(2*arcsinh(c*x)))+-3*b*c^2*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+3*b*c^2*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1*b*c*d^-3*x^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+-5//6*b*x*c^3*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+4//3*b*x*c^3*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3, x) == :(-19//3*b^2*c^3*d^-3*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-17//6*b^2*c^3*d^-3*arctan(c*x)+-1//2*b^2*c^2*d^-3*x^-1+-1//3*d^-3*x^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+19//3*b^2*c^3*d^-3*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+35//4*c^3*d^-3*(a+b*arcsinh(c*x))^2*arctan(exp(arcsinh(c*x)))+-35//4*im*b^2*c^3*d^-3*Polylogarithms.polylog(3,im*exp(arcsinh(c*x)))+-1//6*b*c^3*d^-3*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+1//6*b^2*c^2*d^-3*x^-1*(1+c^2*x^2)^-1+1//12*x*b^2*c^4*d^-3*(1+c^2*x^2)^-1+7//3*c^2*d^-3*x^-1*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+29//12*b*c^3*d^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+35//4*im*b^2*c^3*d^-3*Polylogarithms.polylog(3,-1*im*exp(arcsinh(c*x)))+35//8*x*c^4*d^-3*(1+c^2*x^2)^-1*(a+b*arcsinh(c*x))^2+35//12*x*c^4*d^-3*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2+38//3*b*c^3*d^-3*(a+b*arcsinh(c*x))*arctanh(exp(arcsinh(c*x)))+-35//4*im*b*c^3*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//3*b*c*d^-3*x^-2*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))+35//4*im*b*c^3*d^-3*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,im*exp(arcsinh(c*x))))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :(-52//225*b^2*c^-4*(d+d*c^2*x^2)^(1/2)+-2//15*c^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//5*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-26//675*b^2*c^-4*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+1//15*c^-2*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2//125*b^2*c^-4*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+-2//25*b*c*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//45*b*c^-1*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+4//15*a*b*x*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+4//15*x*b^2*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :(1//4*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//32*b^2*x^3*(d+d*c^2*x^2)^(1/2)+1//8*x*c^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//64*x*b^2*c^-2*(d+d*c^2*x^2)^(1/2)+-1//24*b^-1*c^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+-1//64*b^2*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-1//8*b*c*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//8*b*c^-1*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :(4//9*b^2*c^-2*(d+d*c^2*x^2)^(1/2)+1//3*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+2//27*b^2*c^-2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-2//3*b*x*c^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//9*b*c*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :((1/2)*x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//4*x*b^2*(d+d*c^2*x^2)^(1/2)+-1//4*b^2*c^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+1//6*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+-1//2*b*c*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2*b^2*(d+d*c^2*x^2)^(1/2)+-2*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)*arctanh(exp(arcsinh(c*x)))+2*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-2*b*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*b*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-2*a*b*c*x*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-2*c*x*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :(-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1*c*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+c*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+1//3*c*b^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+2*b*c*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :(-1//2*x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+b^2*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-1*b^2*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-1*b^2*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arctanh((1+c^2*x^2)^(1/2))+-1*c^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)*arctanh(exp(arcsinh(c*x)))+b*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-1*b*c*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*b*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x))))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2), x) == :(-1//3*b^2*c^2*x^-1*(d+d*c^2*x^2)^(1/2)+-1//3*c^3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1//3*d^-1*x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+1//3*b^2*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+1//3*b^2*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-1//3*b*c*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+2//3*b*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x))))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(1//7*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+-304//3675*d*b^2*c^-4*(d+d*c^2*x^2)^(1/2)+-2//35*d*c^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+3//35*d*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-152//11025*d*b^2*c^-4*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-38//6125*d*b^2*c^-4*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+1//35*d*c^-2*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2//343*d*b^2*c^-4*(1+c^2*x^2)^3*(d+d*c^2*x^2)^(1/2)+-16//175*b*c*d*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//49*b*d*c^3*x^7*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//105*b*d*c^-1*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+4//35*a*b*d*x*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+4//35*d*x*b^2*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(1//6*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+1//8*d*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+43//1728*d*b^2*x^3*(d+d*c^2*x^2)^(1/2)+-7//1152*d*x*b^2*c^-2*(d+d*c^2*x^2)^(1/2)+1//16*d*x*c^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//108*d*b^2*c^2*x^5*(d+d*c^2*x^2)^(1/2)+-1//48*d*b^-1*c^-3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+7//1152*d*b^2*c^-3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-7//48*b*c*d*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//16*b*d*c^-1*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//18*b*d*c^3*x^6*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(1//5*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+16//75*d*b^2*c^-2*(d+d*c^2*x^2)^(1/2)+2//125*d*b^2*c^-2*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+8//225*d*b^2*c^-2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-4//15*b*c*d*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//5*b*d*x*c^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//25*b*d*c^3*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(1//4*x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+3//8*d*x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+15//64*d*x*b^2*(d+d*c^2*x^2)^(1/2)+1//32*d*x*b^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-9//64*d*b^2*c^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-1//8*b*d*c^-1*(1+c^2*x^2)^3//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//8*d*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+-3//8*b*c*d*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(1//3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+d*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+22//9*d*b^2*(d+d*c^2*x^2)^(1/2)+2//27*d*b^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-2*d*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-2*d*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)*arctanh(exp(arcsinh(c*x)))+2*d*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-2*b*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*b*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-2*a*b*c*d*x*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-2*c*d*x*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-2//3*b*c*d*x*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//9*b*d*c^3*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+-1*c*d*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//4*d*x*b^2*c^2*(d+d*c^2*x^2)^(1/2)+3//2*d*x*c^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+b*c*d*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+c*d*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+(1/2)*c*d*b^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+-5//4*c*d*b^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+2*b*c*d*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+-3//2*b*d*c^3*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(-1//2*x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+2*d*b^2*c^2*(d+d*c^2*x^2)^(1/2)+3//2*d*c^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1*d*b^2*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arctanh((1+c^2*x^2)^(1/2))+-3*d*b^2*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-3*d*c^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)*arctanh(exp(arcsinh(c*x)))+3*d*b^2*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+b*d*x*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1*b*c*d*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-3*a*b*d*x*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-3*b*d*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-3*d*x*b^2*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+3*b*d*c^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2, x) == :(-1//3*x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+-1*d*c^2*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-4//3*d*c^3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1//3*d*b^2*c^2*x^-1*(d+d*c^2*x^2)^(1/2)+1//3*d*b^-1*c^3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+1//3*d*b^2*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+4//3*d*b^2*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1//3*b*c*d*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+8//3*b*d*c^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x))))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(1//9*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+-160//3969*b^2*c^-4*d^2*(d+d*c^2*x^2)^(1/2)+-2//63*c^-4*d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//21*d^2*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+5//63*d*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+-80//11907*b^2*c^-4*d^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-50//27783*b^2*c^-4*d^2*(1+c^2*x^2)^3*(d+d*c^2*x^2)^(1/2)+-4//1323*b^2*c^-4*d^2*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+1//63*c^-2*d^2*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2//729*b^2*c^-4*d^2*(1+c^2*x^2)^4*(d+d*c^2*x^2)^(1/2)+-38//441*b*c^3*d^2*x^7*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//21*b*c*d^2*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//81*b*c^5*d^2*x^9*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//189*b*c^-1*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+4//63*a*b*x*c^-3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+4//63*x*b^2*c^-3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(1//8*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+5//48*d*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+5//64*d^2*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1079//55296*b^2*d^2*x^3*(d+d*c^2*x^2)^(1/2)+-359//36864*x*b^2*c^-2*d^2*(d+d*c^2*x^2)^(1/2)+1//256*b^2*c^4*d^2*x^7*(d+d*c^2*x^2)^(1/2)+5//128*x*c^-2*d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+209//13824*b^2*c^2*d^2*x^5*(d+d*c^2*x^2)^(1/2)+-5//384*b^-1*c^-3*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+359//36864*b^2*c^-3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-59//384*b*c*d^2*x^4*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-17//144*b*c^3*d^2*x^6*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-5//128*b*c^-1*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//32*b*c^5*d^2*x^8*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(1//7*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^7//2+32//245*b^2*c^-2*d^2*(d+d*c^2*x^2)^(1/2)+2//343*b^2*c^-2*d^2*(1+c^2*x^2)^3*(d+d*c^2*x^2)^(1/2)+12//1225*b^2*c^-2*d^2*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+16//735*b^2*c^-2*d^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-6//35*b*c^3*d^2*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//7*b*c*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//7*b*x*c^-1*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//49*b*c^5*d^2*x^7*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(1//6*x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+5//16*x*d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+5//24*d*x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+245//1152*x*b^2*d^2*(d+d*c^2*x^2)^(1/2)+1//108*x*b^2*d^2*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+65//1728*x*b^2*d^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-115//1152*b^2*c^-1*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-5//48*b*c^-1*d^2*(1+c^2*x^2)^3//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//18*b*c^-1*d^2*(1+c^2*x^2)^5//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+5//48*b^-1*c^-1*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+-5//16*b*c*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(1//5*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//3*d*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+598//225*b^2*d^2*(d+d*c^2*x^2)^(1/2)+2//125*b^2*d^2*(1+c^2*x^2)^2*(d+d*c^2*x^2)^(1/2)+74//675*b^2*d^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-2*b^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-2*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)*arctanh(exp(arcsinh(c*x)))+2*b^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-2*b*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*b*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-2*a*b*c*x*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-2*c*x*b^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-22//45*b*c^3*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-16//15*b*c*x*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-2//25*b*c^5*d^2*x^5*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+-1*c*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+5//4*d*x*c^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+15//8*x*c^2*d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+31//64*x*b^2*c^2*d^2*(d+d*c^2*x^2)^(1/2)+b*c*d^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+c*b^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-89//64*c*b^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-1//8*b*c*d^2*(1+c^2*x^2)^3//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//32*x*b^2*c^2*d^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+5//8*c*b^-1*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+2*b*c*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+-15//8*b*c^3*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(-1//2*x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+5//2*c^2*d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+5//6*d*c^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+40//9*b^2*c^2*d^2*(d+d*c^2*x^2)^(1/2)+2//27*b^2*c^2*d^2*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+-1*b^2*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arctanh((1+c^2*x^2)^(1/2))+-5*b^2*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-5*c^2*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)*arctanh(exp(arcsinh(c*x)))+5*b^2*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-1*b*c*d^2*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-5*a*b*x*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)+-5*b*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-5*x*b^2*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+5*b*c^2*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-2//9*b*c^5*d^2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+1//3*b*x*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2, x) == :(-1//3*x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^5//2+-7//3*c^3*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-5//3*d*c^2*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^3//2+5//2*x*c^4*d^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+7//12*x*b^2*c^4*d^2*(d+d*c^2*x^2)^(1/2)+-23//12*b^2*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*arcsinh(c*x)+-1//3*b^2*c^2*d^2*x^-1*(d+d*c^2*x^2)^(1/2)*(1+c^2*x^2)+5//6*b^-1*c^3*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^(1/2)+7//3*b*c^3*d^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+7//3*b^2*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-5//2*b*c^5*d^2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+-1//3*b*c*d^2*x^-2*(1+c^2*x^2)^3//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))+14//3*b*c^3*d^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x))))
@test integrate(x^4*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(1//8*a^-5*arcsinh(a*x)^3+15//64*a^-5*arcsinh(a*x)+-15//64*x*a^-4*(1+a^2*x^2)^(1/2)+-1//8*a^-1*x^4*arcsinh(a*x)+1//32*a^-2*x^3*(1+a^2*x^2)^(1/2)+3//8*a^-3*x^2*arcsinh(a*x)+-3//8*x*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+1//4*a^-2*x^3*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate(x^3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(-14//9*a^-4*(1+a^2*x^2)^(1/2)+2//27*a^-4*(1+a^2*x^2)^3//2+-2//3*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+-2//9*a^-1*x^3*arcsinh(a*x)+4//3*x*a^-3*arcsinh(a*x)+1//3*a^-2*x^2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate(x^2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(-1//4*a^-3*arcsinh(a*x)+-1//6*a^-3*arcsinh(a*x)^3+-1//2*a^-1*x^2*arcsinh(a*x)+1//4*x*a^-2*(1+a^2*x^2)^(1/2)+(1/2)*x*a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate(x*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(2*a^-2*(1+a^2*x^2)^(1/2)+a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+-2*x*a^-1*arcsinh(a*x))
@test integrate((1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(1//3*a^-1*arcsinh(a*x)^3)
@test integrate(x^-1*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(-2*Polylogarithms.polylog(3,exp(arcsinh(a*x)))+2*Polylogarithms.polylog(3,-1*exp(arcsinh(a*x)))+-2*arcsinh(a*x)^2*arctanh(exp(arcsinh(a*x)))+-2*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x)))*arcsinh(a*x)+2*Polylogarithms.polylog(2,exp(arcsinh(a*x)))*arcsinh(a*x))
@test integrate(x^-2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(a*Polylogarithms.polylog(2,exp(2*arcsinh(a*x)))+-1*a*arcsinh(a*x)^2+-1*x^-1*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+2*a*arcsinh(a*x)*log(1+-1*exp(2*arcsinh(a*x))))
@test integrate(x^-3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2, x) == :(a^2*Polylogarithms.polylog(3,exp(arcsinh(a*x)))+-1*a^2*Polylogarithms.polylog(3,-1*exp(arcsinh(a*x)))+-1*a^2*arctanh((1+a^2*x^2)^(1/2))+a^2*arcsinh(a*x)^2*arctanh(exp(arcsinh(a*x)))+a^2*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x)))*arcsinh(a*x)+-1*a*x^-1*arcsinh(a*x)+-1*a^2*Polylogarithms.polylog(2,exp(arcsinh(a*x)))*arcsinh(a*x)+-1//2*x^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate(x^5*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-76//675*b^2*c^-6*(1+c^2*x^2)^2*(d+d*c^2*x^2)^-1//2+2//125*b^2*c^-6*(1+c^2*x^2)^3*(d+d*c^2*x^2)^-1//2+8//15*c^-6*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+298//225*b^2*c^-6*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-4//15*c^-4*d^-1*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//5*c^-2*d^-1*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-16//15*a*b*x*c^-5*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-16//15*x*b^2*c^-5*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+-2//25*b*c^-1*x^5*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+8//45*b*c^-3*x^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-15//64*x*b^2*c^-4*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-3//8*x*c^-4*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//4*c^-2*d^-1*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+1//8*b^-1*c^-5*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^-1//2+1//32*b^2*c^-2*x^3*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+15//64*b^2*c^-5*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+-1//8*b*c^-1*x^4*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+3//8*b*c^-3*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-14//9*b^2*c^-4*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-2//3*c^-4*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2//27*b^2*c^-4*(1+c^2*x^2)^2*(d+d*c^2*x^2)^-1//2+1//3*c^-2*d^-1*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-2//9*b*c^-1*x^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+4//3*a*b*x*c^-3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+4//3*x*b^2*c^-3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :((1/2)*x*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1//4*b^2*c^-3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+-1//6*b^-1*c^-3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^-1//2+1//4*x*b^2*c^-2*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-1//2*b*c^-1*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2*b^2*c^-2*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-2*a*b*x*c^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-2*x*b^2*c^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(1//3*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^-1//2)
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-2*b^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2*arctanh(exp(arcsinh(c*x)))+2*b^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-2*b*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*b*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-1*c*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1*d^-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+c*b^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+2*b*c*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-1//2*d^-1*x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+b^2*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+c^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2*arctanh(exp(arcsinh(c*x)))+-1*b^2*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-1*b^2*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctanh((1+c^2*x^2)^(1/2))+b*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-1*b*c*x^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-1*b*c^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2, x) == :(-1//3*d^-1*x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2//3*c^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-2//3*b^2*c^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1//3*b^2*c^2*x^-1*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+2//3*c^2*d^-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-4//3*b*c^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+-1*exp(2*arcsinh(c*x)))+-1//3*b*c*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^5*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(-8//3*c^-6*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1*c^-2*d^-1*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-32//9*b^2*c^-6*d^-1*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+2//27*b^2*c^-6*d^-1*(1+c^2*x^2)^2*(d+d*c^2*x^2)^-1//2+4//3*c^-4*d^-2*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-2*im*b^2*c^-6*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-2*b*x*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+2*im*b^2*c^-6*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+4*b*c^-6*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-2//9*b*c^-3*d^-1*x^3*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+16//3*a*b*x*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+16//3*x*b^2*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(c^-5*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1*c^-2*d^-1*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+3//2*x*c^-4*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1*b^2*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//2*b^-1*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^-1//2+-1//4*b^2*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+1//4*x*b^2*c^-4*d^-1*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-2*b*c^-5*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//2*b*c^-3*d^-1*x^2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(2*c^-4*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+-1*c^-2*d^-1*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+2*b^2*c^-4*d^-1*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-4*a*b*x*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-4*b*c^-4*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-4*x*b^2*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+-2*im*b^2*c^-4*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+2*im*b^2*c^-4*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*b*x*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(-1*x*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+b^2*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+1//3*b^-1*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^-1//2+2*b*c^-3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(-1*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-2*im*b^2*c^-2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*im*b^2*c^-2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+4*b*c^-2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(x*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+c^-1*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1*b^2*c^-1*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-2*b*c^-1*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-2*b^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-2*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2*arctanh(exp(arcsinh(c*x)))+2*b^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-4*b*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-2*im*b^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-2*b*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*im*b^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*b*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x))))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(-1*d^-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-2*c*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-2*x*c^2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+c*b^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+c*b^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-4*b*c*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+4*b*c*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(-3//2*c^2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//2*d^-1*x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1*b^2*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctanh((1+c^2*x^2)^(1/2))+-3*b^2*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+3*b^2*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+3*c^2*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2*arctanh(exp(arcsinh(c*x)))+-1*b*c*d^-1*x^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-3*b*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-2*im*b^2*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*im*b^2*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+3*b*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+4*b*c^2*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2, x) == :(-1//3*d^-1*x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+4//3*c^2*d^-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+8//3*x*c^4*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+8//3*c^3*d^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1*b^2*c^3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-5//3*b^2*c^3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1//3*b^2*c^2*d^-1*x^-1*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-16//3*b*c^3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//3*b*c*d^-1*x^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+20//3*b*c^3*d^-1*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x))))
@test integrate(x^5*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(1//3*b^2*c^-6*d^-2*(d+d*c^2*x^2)^-1//2+8//3*c^-6*d^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^(1/2)+2*b^2*c^-6*d^-2*(d+d*c^2*x^2)^-1//2*(1+c^2*x^2)+-4//3*c^-4*d^-2*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//3*c^-2*d^-1*x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+-22//3*b*c^-6*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-16//3*a*b*x*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2+-16//3*x*b^2*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+-11//3*im*b^2*c^-6*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//3*b*c^-3*d^-2*x^3*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+11//3*im*b^2*c^-6*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+11//3*b*x*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-1*x*c^-4*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-4//3*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//3*x*b^2*c^-4*d^-2*(d+d*c^2*x^2)^-1//2+-1//3*c^-2*d^-1*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+1//3*b^-1*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+d*c^2*x^2)^-1//2+1//3*b^2*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+4//3*b^2*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//3*b*c^-3*d^-2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+8//3*b*c^-5*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate(x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-2//3*c^-4*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//3*b^2*c^-4*d^-2*(d+d*c^2*x^2)^-1//2+-1//3*c^-2*d^-1*x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+-5//3*im*b^2*c^-4*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//3*b*x*c^-3*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+5//3*im*b^2*c^-4*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+10//3*b*c^-4*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate(x^2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(1//3*d^-1*x^3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+1//3*x*b^2*c^-2*d^-2*(d+d*c^2*x^2)^-1//2+1//3*c^-3*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//3*b^2*c^-3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//3*b^2*c^-3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arcsinh(c*x)+-2//3*b*c^-3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+1//3*b*c^-1*d^-2*x^2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-1//3*c^-2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+1//3*b^2*c^-2*d^-2*(d+d*c^2*x^2)^-1//2+-1//3*im*b^2*c^-2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+1//3*im*b^2*c^-2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+1//3*b*x*c^-1*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+2//3*b*c^-2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-1//3*x*b^2*d^-2*(d+d*c^2*x^2)^-1//2+1//3*x*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+2//3*x*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+2//3*c^-1*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-2//3*b^2*c^-1*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+1//3*b*c^-1*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-4//3*b*c^-1*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate(x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-1//3*b^2*d^-2*(d+d*c^2*x^2)^-1//2+1//3*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+-2*b^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+-2*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2*arctanh(exp(arcsinh(c*x)))+2*b^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+-2*b*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+2*b*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+-14//3*b*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x)))+-7//3*im*b^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+7//3*im*b^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//3*b*c*x*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x)))
@test integrate(x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-1*d^-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+-8//3*c*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-8//3*x*c^2*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-4//3*x*c^2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+1//3*x*b^2*c^2*d^-2*(d+d*c^2*x^2)^-1//2+c*b^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-1//3*b*c*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+5//3*c*b^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-4*b*c*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x)))+16//3*b*c*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate(x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-5//2*c^2*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-5//6*c^2*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+-1//2*d^-1*x^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+1//3*b^2*c^2*d^-2*(d+d*c^2*x^2)^-1//2+-1*b^2*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*arctanh((1+c^2*x^2)^(1/2))+-5*b^2*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(arcsinh(c*x)))+5*b^2*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(3,exp(arcsinh(c*x)))+5*c^2*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2*arctanh(exp(arcsinh(c*x)))+-1*b*c*d^-2*x^-1*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+-5*b*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,exp(arcsinh(c*x)))+5*b*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*Polylogarithms.polylog(2,-1*exp(arcsinh(c*x)))+-13//3*im*b^2*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-2//3*b*x*c^3*d^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+13//3*im*b^2*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+26//3*b*c^2*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate(x^-4*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-5//2, x) == :(-1//3*d^-1*x^-3*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+2*c^2*d^-1*x^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+-2//3*x*b^2*c^4*d^-2*(d+d*c^2*x^2)^-1//2+-1//3*b^2*c^2*d^-2*x^-1*(d+d*c^2*x^2)^-1//2+8//3*x*c^4*d^-1*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-3//2+16//3*x*c^4*d^-2*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+16//3*c^3*d^-2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+d*c^2*x^2)^-1//2+-8//3*b^2*c^3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-8//3*b^2*c^3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*Polylogarithms.polylog(2,exp(2*arcsinh(c*x)))+-32//3*b*c^3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//3*b*c*d^-2*x^-2*(1+c^2*x^2)^-1//2*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))+32//3*b*c^3*d^-2*(1+c^2*x^2)^(1/2)*(d+d*c^2*x^2)^-1//2*(a+b*arcsinh(c*x))*arctanh(exp(2*arcsinh(c*x))))
@test integrate((c+c*a^2*x^2)^-7//2*arcsinh(a*x)^2, x) == :(-1//3*x*c^-3*(c+c*a^2*x^2)^-1//2+-1//30*x*c^-3*(1+a^2*x^2)^-1*(c+c*a^2*x^2)^-1//2+1//5*x*c^-1*(c+c*a^2*x^2)^-5//2*arcsinh(a*x)^2+4//15*x*c^-2*(c+c*a^2*x^2)^-3//2*arcsinh(a*x)^2+8//15*x*c^-3*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2+-8//15*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(a*x)))+1//10*a^-1*c^-3*(1+a^2*x^2)^-3//2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)+4//15*a^-1*c^-3*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)+8//15*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2+-16//15*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)*log(1+exp(2*arcsinh(a*x))))
@test integrate((c+c*a^2*x^2)^3*arcsinh(a*x)^3, x) == :(-413312//128625*a^-1*c^3*(1+a^2*x^2)^(1/2)+-30256//385875*a^-1*c^3*(1+a^2*x^2)^3//2+-2664//214375*a^-1*c^3*(1+a^2*x^2)^5//2+-6//2401*a^-1*c^3*(1+a^2*x^2)^7//2+16//35*x*c^3*arcsinh(a*x)^3+4322//1225*x*c^3*arcsinh(a*x)+-48//35*a^-1*c^3*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+-18//175*a^-1*c^3*(1+a^2*x^2)^5//2*arcsinh(a*x)^2+-8//35*a^-1*c^3*(1+a^2*x^2)^3//2*arcsinh(a*x)^2+-3//49*a^-1*c^3*(1+a^2*x^2)^7//2*arcsinh(a*x)^2+1//7*x*c^3*(1+a^2*x^2)^3*arcsinh(a*x)^3+6//35*x*c^3*(1+a^2*x^2)^2*arcsinh(a*x)^3+6//343*a^6*c^3*x^7*arcsinh(a*x)+8//35*x*c^3*arcsinh(a*x)^3*(1+a^2*x^2)+702//6125*a^4*c^3*x^5*arcsinh(a*x)+1514//3675*a^2*c^3*x^3*arcsinh(a*x))
@test integrate((c+c*a^2*x^2)^2*arcsinh(a*x)^3, x) == :(-4144//1125*a^-1*c^2*(1+a^2*x^2)^(1/2)+-272//3375*a^-1*c^2*(1+a^2*x^2)^3//2+-6//625*a^-1*c^2*(1+a^2*x^2)^5//2+8//15*x*c^2*arcsinh(a*x)^3+298//75*x*c^2*arcsinh(a*x)+-8//5*a^-1*c^2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+-4//15*a^-1*c^2*(1+a^2*x^2)^3//2*arcsinh(a*x)^2+-3//25*a^-1*c^2*(1+a^2*x^2)^5//2*arcsinh(a*x)^2+1//5*x*c^2*(1+a^2*x^2)^2*arcsinh(a*x)^3+4//15*x*c^2*arcsinh(a*x)^3*(1+a^2*x^2)+6//125*a^4*c^2*x^5*arcsinh(a*x)+76//225*a^2*c^2*x^3*arcsinh(a*x))
@test integrate(arcsinh(a*x)^3*(c+c*a^2*x^2), x) == :(-40//9*c*a^-1*(1+a^2*x^2)^(1/2)+-2//27*c*a^-1*(1+a^2*x^2)^3//2+2//3*c*x*arcsinh(a*x)^3+14//3*c*x*arcsinh(a*x)+-2*c*a^-1*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^2+-1//3*c*a^-1*(1+a^2*x^2)^3//2*arcsinh(a*x)^2+1//3*c*x*arcsinh(a*x)^3*(1+a^2*x^2)+2//9*c*a^2*x^3*arcsinh(a*x))
@test integrate((c+c*a^2*x^2)^-1*arcsinh(a*x)^3, x) == :(-6*im*a^-1*c^-1*Polylogarithms.polylog(4,-1*im*exp(arcsinh(a*x)))+2*a^-1*c^-1*arcsinh(a*x)^3*arctan(exp(arcsinh(a*x)))+6*im*a^-1*c^-1*Polylogarithms.polylog(4,im*exp(arcsinh(a*x)))+-6*im*a^-1*c^-1*Polylogarithms.polylog(3,im*exp(arcsinh(a*x)))*arcsinh(a*x)+-3*im*a^-1*c^-1*arcsinh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(a*x)))+3*im*a^-1*c^-1*arcsinh(a*x)^2*Polylogarithms.polylog(2,im*exp(arcsinh(a*x)))+6*im*a^-1*c^-1*Polylogarithms.polylog(3,-1*im*exp(arcsinh(a*x)))*arcsinh(a*x))
@test integrate((c+c*a^2*x^2)^-2*arcsinh(a*x)^3, x) == :(a^-1*c^-2*arcsinh(a*x)^3*arctan(exp(arcsinh(a*x)))+(1/2)*x*c^-2*(1+a^2*x^2)^-1*arcsinh(a*x)^3+-6*a^-1*c^-2*arcsinh(a*x)*arctan(exp(arcsinh(a*x)))+-3*im*a^-1*c^-2*Polylogarithms.polylog(2,im*exp(arcsinh(a*x)))+-3*im*a^-1*c^-2*Polylogarithms.polylog(4,-1*im*exp(arcsinh(a*x)))+3*im*a^-1*c^-2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(a*x)))+3*im*a^-1*c^-2*Polylogarithms.polylog(4,im*exp(arcsinh(a*x)))+3//2*a^-1*c^-2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2+-3*im*a^-1*c^-2*Polylogarithms.polylog(3,im*exp(arcsinh(a*x)))*arcsinh(a*x)+3*im*a^-1*c^-2*Polylogarithms.polylog(3,-1*im*exp(arcsinh(a*x)))*arcsinh(a*x)+-3//2*im*a^-1*c^-2*arcsinh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(a*x)))+3//2*im*a^-1*c^-2*arcsinh(a*x)^2*Polylogarithms.polylog(2,im*exp(arcsinh(a*x))))
@test integrate((c+c*a^2*x^2)^-3*arcsinh(a*x)^3, x) == :(-1//4*a^-1*c^-3*(1+a^2*x^2)^-1//2+-5*a^-1*c^-3*arcsinh(a*x)*arctan(exp(arcsinh(a*x)))+-9//4*im*a^-1*c^-3*Polylogarithms.polylog(4,-1*im*exp(arcsinh(a*x)))+-5//2*im*a^-1*c^-3*Polylogarithms.polylog(2,im*exp(arcsinh(a*x)))+-1//4*x*c^-3*(1+a^2*x^2)^-1*arcsinh(a*x)+1//4*x*c^-3*(1+a^2*x^2)^-2*arcsinh(a*x)^3+1//4*a^-1*c^-3*(1+a^2*x^2)^-3//2*arcsinh(a*x)^2+3//4*a^-1*c^-3*arcsinh(a*x)^3*arctan(exp(arcsinh(a*x)))+3//8*x*c^-3*(1+a^2*x^2)^-1*arcsinh(a*x)^3+5//2*im*a^-1*c^-3*Polylogarithms.polylog(2,-1*im*exp(arcsinh(a*x)))+9//4*im*a^-1*c^-3*Polylogarithms.polylog(4,im*exp(arcsinh(a*x)))+9//8*a^-1*c^-3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^2+-9//4*im*a^-1*c^-3*Polylogarithms.polylog(3,im*exp(arcsinh(a*x)))*arcsinh(a*x)+-9//8*im*a^-1*c^-3*arcsinh(a*x)^2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(a*x)))+9//4*im*a^-1*c^-3*Polylogarithms.polylog(3,-1*im*exp(arcsinh(a*x)))*arcsinh(a*x)+9//8*im*a^-1*c^-3*arcsinh(a*x)^2*Polylogarithms.polylog(2,im*exp(arcsinh(a*x))))
@test integrate((c+c*a^2*x^2)^5//2*arcsinh(a*x)^3, x) == :(1//6*x*(c+c*a^2*x^2)^5//2*arcsinh(a*x)^3+-1//216*a^-1*c^2*(1+a^2*x^2)^5//2*(c+c*a^2*x^2)^(1/2)+5//16*x*c^2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3+5//24*c*x*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^3+245//384*x*c^2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)+-865//2304*a*c^2*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)+-115//768*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2+-65//2304*a^3*c^2*x^4*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)+-5//32*a^-1*c^2*(1+a^2*x^2)^3//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2+-1//12*a^-1*c^2*(1+a^2*x^2)^5//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2+1//36*x*c^2*(1+a^2*x^2)^2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)+5//64*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^4+65//576*x*c^2*(c+c*a^2*x^2)^(1/2)*(1+a^2*x^2)*arcsinh(a*x)+-15//32*a*c^2*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^3, x) == :(1//4*x*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^3+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3+45//64*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)+-51//128*a*c*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)+-27//128*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2+-3//16*c*a^-1*(1+a^2*x^2)^3//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2+-3//128*c*a^3*x^4*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)+3//32*c*x*(c+c*a^2*x^2)^(1/2)*(1+a^2*x^2)*arcsinh(a*x)+3//32*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^4+-9//16*a*c*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3, x) == :((1/2)*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3+3//4*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)+-3//8*a*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)+-3//8*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2+1//8*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^4+-3//4*a*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^2)
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(1//4*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^4)
@test integrate((c+c*a^2*x^2)^-3//2*arcsinh(a*x)^3, x) == :(x*c^-1*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3+a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3+3//2*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(2*arcsinh(a*x)))+-3*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2*log(1+exp(2*arcsinh(a*x)))+-3*a^-1*c^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(a*x)))*arcsinh(a*x))
@test integrate((c+c*a^2*x^2)^-5//2*arcsinh(a*x)^3, x) == :(-1*x*c^-2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)+1//3*x*c^-1*(c+c*a^2*x^2)^-3//2*arcsinh(a*x)^3+2//3*x*c^-2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3+a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(2*arcsinh(a*x)))+(1/2)*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*log(1+a^2*x^2)+(1/2)*a^-1*c^-2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2+2//3*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3+-2*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2*log(1+exp(2*arcsinh(a*x)))+-2*a^-1*c^-2*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(a*x)))*arcsinh(a*x))
@test integrate((c+c*a^2*x^2)^-7//2*arcsinh(a*x)^3, x) == :(-1*x*c^-3*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)+-1//20*a^-1*c^-3*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^-1//2+1//5*x*c^-1*(c+c*a^2*x^2)^-5//2*arcsinh(a*x)^3+4//15*x*c^-2*(c+c*a^2*x^2)^-3//2*arcsinh(a*x)^3+8//15*x*c^-3*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3+(1/2)*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*log(1+a^2*x^2)+-1//10*x*c^-3*(1+a^2*x^2)^-1*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)+2//5*a^-1*c^-3*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2+3//20*a^-1*c^-3*(1+a^2*x^2)^-3//2*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2+4//5*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(3,-1*exp(2*arcsinh(a*x)))+8//15*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3+-8//5*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^2*log(1+exp(2*arcsinh(a*x)))+-8//5*a^-1*c^-3*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(a*x)))*arcsinh(a*x))
@test integrate(x^4*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-3//128*a^-1*x^4+3//32*a^-5*arcsinh(a*x)^4+45//128*a^-5*arcsinh(a*x)^2+45//128*a^-3*x^2+-3//16*a^-1*x^4*arcsinh(a*x)^2+9//16*a^-3*x^2*arcsinh(a*x)^2+-45//64*x*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)+-3//8*x*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+1//4*a^-2*x^3*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+3//32*a^-2*x^3*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x^3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-2//27*a^-1*x^3+40//9*x*a^-3+2*x*a^-3*arcsinh(a*x)^2+-40//9*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)+-2//3*a^-4*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+-1//3*a^-1*x^3*arcsinh(a*x)^2+1//3*a^-2*x^2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+2//9*a^-2*x^2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x^2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-3//8*a^-1*x^2+-3//8*a^-3*arcsinh(a*x)^2+-1//8*a^-3*arcsinh(a*x)^4+-3//4*a^-1*x^2*arcsinh(a*x)^2+(1/2)*x*a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+3//4*x*a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate(x*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-6*x*a^-1+a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+-3*x*a^-1*arcsinh(a*x)^2+6*a^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x))
@test integrate((1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(1//4*a^-1*arcsinh(a*x)^4)
@test integrate(x^-1*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-6*Polylogarithms.polylog(4,-1*exp(arcsinh(a*x)))+6*Polylogarithms.polylog(4,exp(arcsinh(a*x)))+-6*Polylogarithms.polylog(3,exp(arcsinh(a*x)))*arcsinh(a*x)+-3*arcsinh(a*x)^2*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x)))+-2*arcsinh(a*x)^3*arctanh(exp(arcsinh(a*x)))+3*arcsinh(a*x)^2*Polylogarithms.polylog(2,exp(arcsinh(a*x)))+6*Polylogarithms.polylog(3,-1*exp(arcsinh(a*x)))*arcsinh(a*x))
@test integrate(x^-2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-1*a*arcsinh(a*x)^3+-3//2*a*Polylogarithms.polylog(3,exp(2*arcsinh(a*x)))+-1*x^-1*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+3*a*arcsinh(a*x)^2*log(1+-1*exp(2*arcsinh(a*x)))+3*a*Polylogarithms.polylog(2,exp(2*arcsinh(a*x)))*arcsinh(a*x))
@test integrate(x^-3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^3, x) == :(-3*a^2*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x)))+-3*a^2*Polylogarithms.polylog(4,exp(arcsinh(a*x)))+3*a^2*Polylogarithms.polylog(2,exp(arcsinh(a*x)))+3*a^2*Polylogarithms.polylog(4,-1*exp(arcsinh(a*x)))+a^2*arcsinh(a*x)^3*arctanh(exp(arcsinh(a*x)))+-6*a^2*arcsinh(a*x)*arctanh(exp(arcsinh(a*x)))+-3*a^2*Polylogarithms.polylog(3,-1*exp(arcsinh(a*x)))*arcsinh(a*x)+3*a^2*Polylogarithms.polylog(3,exp(arcsinh(a*x)))*arcsinh(a*x)+-3//2*a*x^-1*arcsinh(a*x)^2+-3//2*a^2*arcsinh(a*x)^2*Polylogarithms.polylog(2,exp(arcsinh(a*x)))+-1//2*x^-2*(1+a^2*x^2)^(1/2)*arcsinh(a*x)^3+3//2*a^2*arcsinh(a*x)^2*Polylogarithms.polylog(2,-1*exp(arcsinh(a*x))))
@test integrate((c+c*a^2*x^2)^3*arcsinh(a*x)^-1, x) == :(1//64*a^-1*c^3*coshintegral(7*arcsinh(a*x))+7//64*a^-1*c^3*coshintegral(5*arcsinh(a*x))+21//64*a^-1*c^3*coshintegral(3*arcsinh(a*x))+35//64*a^-1*c^3*coshintegral(arcsinh(a*x)))
@test integrate((c+c*a^2*x^2)^2*arcsinh(a*x)^-1, x) == :(1//16*a^-1*c^2*coshintegral(5*arcsinh(a*x))+5//8*a^-1*c^2*coshintegral(arcsinh(a*x))+5//16*a^-1*c^2*coshintegral(3*arcsinh(a*x)))
@test integrate(arcsinh(a*x)^-1*(c+c*a^2*x^2), x) == :(1//4*c*a^-1*coshintegral(3*arcsinh(a*x))+3//4*c*a^-1*coshintegral(arcsinh(a*x)))
@test integrate(x^4*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-1, x) == :(1//16*b^-1*c^-5*log(a+b*arcsinh(c*x))+-1//16*b^-1*c^-5*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1)+-1//32*b^-1*c^-5*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//32*b^-1*c^-5*sinh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+1//16*b^-1*c^-5*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+1//32*b^-1*c^-5*cosh(6*a*b^-1)*coshintegral(6*arcsinh(c*x)+6*a*b^-1)+1//32*b^-1*c^-5*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-1, x) == :(-1//8*b^-1*c^-4*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-1//16*b^-1*c^-4*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-1//16*b^-1*c^-4*coshintegral(5*arcsinh(c*x)+5*a*b^-1)*sinh(5*a*b^-1)+1//8*b^-1*c^-4*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1)+1//16*b^-1*c^-4*cosh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+1//16*b^-1*c^-4*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1))
@test integrate(x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-1, x) == :(-1//8*b^-1*c^-3*log(a+b*arcsinh(c*x))+-1//8*b^-1*c^-3*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+1//8*b^-1*c^-3*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1))
@test integrate(x*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-1, x) == :(-1//4*b^-1*c^-2*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1)+-1//4*b^-1*c^-2*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1)+1//4*b^-1*c^-2*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+1//4*b^-1*c^-2*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1))
@test integrate((1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-1, x) == :((1/2)*b^-1*c^-1*log(a+b*arcsinh(c*x))+(1/2)*b^-1*c^-1*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//2*b^-1*c^-1*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1, x) == :(-3//64*b^-1*c^-4*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-3//64*b^-1*c^-4*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-1//64*b^-1*c^-4*coshintegral(5*arcsinh(c*x)+5*a*b^-1)*sinh(5*a*b^-1)+-1//64*b^-1*c^-4*coshintegral(7*arcsinh(c*x)+7*a*b^-1)*sinh(7*a*b^-1)+1//64*b^-1*c^-4*cosh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+1//64*b^-1*c^-4*cosh(7*a*b^-1)*sinhintegral(7*arcsinh(c*x)+7*a*b^-1)+3//64*b^-1*c^-4*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1)+3//64*b^-1*c^-4*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1))
@test integrate(x^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1, x) == :(-1//16*b^-1*c^-3*log(a+b*arcsinh(c*x))+-1//16*b^-1*c^-3*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+-1//32*b^-1*c^-3*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//32*b^-1*c^-3*sinh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+1//16*b^-1*c^-3*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1)+1//32*b^-1*c^-3*cosh(6*a*b^-1)*coshintegral(6*arcsinh(c*x)+6*a*b^-1)+1//32*b^-1*c^-3*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1))
@test integrate(x*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1, x) == :(-3//16*b^-1*c^-2*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1)+-1//8*b^-1*c^-2*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1)+-1//16*b^-1*c^-2*coshintegral(5*arcsinh(c*x)+5*a*b^-1)*sinh(5*a*b^-1)+1//8*b^-1*c^-2*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+1//16*b^-1*c^-2*cosh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+3//16*b^-1*c^-2*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1))
@test integrate((1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1, x) == :(3//8*b^-1*c^-1*log(a+b*arcsinh(c*x))+(1/2)*b^-1*c^-1*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//2*b^-1*c^-1*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//8*b^-1*c^-1*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+1//8*b^-1*c^-1*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1, x) == :(-3//128*b^-1*c^-4*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-3//256*b^-1*c^-4*coshintegral(7*arcsinh(c*x)+7*a*b^-1)*sinh(7*a*b^-1)+-1//32*b^-1*c^-4*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-1//256*b^-1*c^-4*coshintegral(9*arcsinh(c*x)+9*a*b^-1)*sinh(9*a*b^-1)+1//32*b^-1*c^-4*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1)+1//256*b^-1*c^-4*cosh(9*a*b^-1)*sinhintegral(9*arcsinh(c*x)+9*a*b^-1)+3//128*b^-1*c^-4*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1)+3//256*b^-1*c^-4*cosh(7*a*b^-1)*sinhintegral(7*arcsinh(c*x)+7*a*b^-1))
@test integrate(x^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1, x) == :(-5//128*b^-1*c^-3*log(a+b*arcsinh(c*x))+-1//32*b^-1*c^-3*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//32*b^-1*c^-3*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+-1//32*b^-1*c^-3*sinh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+-1//128*b^-1*c^-3*sinh(8*a*b^-1)*sinhintegral(8*arcsinh(c*x)+8*a*b^-1)+1//32*b^-1*c^-3*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1)+1//32*b^-1*c^-3*cosh(6*a*b^-1)*coshintegral(6*arcsinh(c*x)+6*a*b^-1)+1//32*b^-1*c^-3*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+1//128*b^-1*c^-3*cosh(8*a*b^-1)*coshintegral(8*arcsinh(c*x)+8*a*b^-1))
@test integrate(x*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1, x) == :(-9//64*b^-1*c^-2*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1)+-5//64*b^-1*c^-2*coshintegral(5*arcsinh(c*x)+5*a*b^-1)*sinh(5*a*b^-1)+-5//64*b^-1*c^-2*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1)+-1//64*b^-1*c^-2*coshintegral(7*arcsinh(c*x)+7*a*b^-1)*sinh(7*a*b^-1)+1//64*b^-1*c^-2*cosh(7*a*b^-1)*sinhintegral(7*arcsinh(c*x)+7*a*b^-1)+5//64*b^-1*c^-2*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+5//64*b^-1*c^-2*cosh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+9//64*b^-1*c^-2*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1))
@test integrate((1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1, x) == :(5//16*b^-1*c^-1*log(a+b*arcsinh(c*x))+-15//32*b^-1*c^-1*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-3//16*b^-1*c^-1*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+-1//32*b^-1*c^-1*sinh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+1//32*b^-1*c^-1*cosh(6*a*b^-1)*coshintegral(6*arcsinh(c*x)+6*a*b^-1)+3//16*b^-1*c^-1*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1)+15//32*b^-1*c^-1*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1))
@test integrate(x^4*(1+a^2*x^2)^-1//2*arcsinh(a*x)^-1, x) == :(-1//2*a^-5*coshintegral(2*arcsinh(a*x))+1//8*a^-5*coshintegral(4*arcsinh(a*x))+3//8*a^-5*log(arcsinh(a*x)))
@test integrate(x^3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^-1, x) == :(-3//4*a^-4*sinhintegral(arcsinh(a*x))+1//4*a^-4*sinhintegral(3*arcsinh(a*x)))
@test integrate(x^2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^-1, x) == :((1/2)*a^-3*coshintegral(2*arcsinh(a*x))+-1//2*a^-3*log(arcsinh(a*x)))
@test integrate(x^2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^-1, x) == :((1/2)*a^-3*coshintegral(2*arcsinh(a*x))+-1//2*a^-3*log(arcsinh(a*x)))
@test integrate(x*(1+a^2*x^2)^-1//2*arcsinh(a*x)^-1, x) == :(a^-2*sinhintegral(arcsinh(a*x)))
@test integrate((1+a^2*x^2)^-1//2*arcsinh(a*x)^-1, x) == :(a^-1*log(arcsinh(a*x)))
@test integrate(x^5*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-1, x) == :(-5//8*b^-1*c^-6*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1)+-5//16*b^-1*c^-6*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-1//16*b^-1*c^-6*coshintegral(5*arcsinh(c*x)+5*a*b^-1)*sinh(5*a*b^-1)+1//16*b^-1*c^-6*cosh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+5//8*b^-1*c^-6*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+5//16*b^-1*c^-6*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1))
@test integrate(x^4*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-1, x) == :(3//8*b^-1*c^-5*log(a+b*arcsinh(c*x))+(1/2)*b^-1*c^-5*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//2*b^-1*c^-5*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//8*b^-1*c^-5*sinh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+1//8*b^-1*c^-5*cosh(4*a*b^-1)*coshintegral(4*arcsinh(c*x)+4*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-1, x) == :(-3//4*b^-1*c^-4*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-1//4*b^-1*c^-4*coshintegral(3*arcsinh(c*x)+3*a*b^-1)*sinh(3*a*b^-1)+1//4*b^-1*c^-4*cosh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+3//4*b^-1*c^-4*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1))
@test integrate(x^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-1, x) == :(-1//2*b^-1*c^-3*log(a+b*arcsinh(c*x))+(1/2)*b^-1*c^-3*cosh(2*a*b^-1)*coshintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//2*b^-1*c^-3*sinh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1))
@test integrate(x*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-1, x) == :(b^-1*c^-2*cosh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-1*b^-1*c^-2*coshintegral(a*b^-1+arcsinh(c*x))*sinh(a*b^-1))
@test integrate((1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-1, x) == :(b^-1*c^-1*log(a+b*arcsinh(c*x)))
@test integrate((c+c*a^2*x^2)^3*arcsinh(a*x)^-2, x) == :(7//64*a^-1*c^3*sinhintegral(7*arcsinh(a*x))+35//64*a^-1*c^3*sinhintegral(5*arcsinh(a*x))+35//64*a^-1*c^3*sinhintegral(arcsinh(a*x))+63//64*a^-1*c^3*sinhintegral(3*arcsinh(a*x))+-1*a^-1*c^3*(1+a^2*x^2)^7//2*arcsinh(a*x)^-1)
@test integrate((c+c*a^2*x^2)^2*arcsinh(a*x)^-2, x) == :(5//8*a^-1*c^2*sinhintegral(arcsinh(a*x))+5//16*a^-1*c^2*sinhintegral(5*arcsinh(a*x))+15//16*a^-1*c^2*sinhintegral(3*arcsinh(a*x))+-1*a^-1*c^2*(1+a^2*x^2)^5//2*arcsinh(a*x)^-1)
@test integrate(arcsinh(a*x)^-2*(c+c*a^2*x^2), x) == :(3//4*c*a^-1*sinhintegral(3*arcsinh(a*x))+3//4*c*a^-1*sinhintegral(arcsinh(a*x))+-1*c*a^-1*(1+a^2*x^2)^3//2*arcsinh(a*x)^-1)
@test integrate(x^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-2, x) == :(-5//16*b^-2*c^-4*sinh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+-3//16*b^-2*c^-4*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+-1//8*b^-2*c^-4*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+1//8*b^-2*c^-4*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+3//16*b^-2*c^-4*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+5//16*b^-2*c^-4*cosh(5*a*b^-1)*coshintegral(5*arcsinh(c*x)+5*a*b^-1)+-1*b^-1*c^-1*x^3*(a+b*arcsinh(c*x))^-1*(1+c^2*x^2))
@test integrate(x^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-2, x) == :((1/2)*b^-2*c^-3*cosh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+-1//2*b^-2*c^-3*coshintegral(4*arcsinh(c*x)+4*a*b^-1)*sinh(4*a*b^-1)+-1*b^-1*c^-1*x^2*(a+b*arcsinh(c*x))^-1*(1+c^2*x^2))
@test integrate(x*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-2, x) == :(b^-2*c^-2*cosh(a*b^-1)*coshintegral(b^-1*(a+b*arcsinh(c*x)))+-1*b^-2*c^-2*sinh(a*b^-1)*sinhintegral(b^-1*(a+b*arcsinh(c*x)))+-3//4*b^-2*c^-2*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+-3//4*b^-2*c^-2*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+3//4*b^-2*c^-2*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+3//4*b^-2*c^-2*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-1*x*b^-1*c^-1*(a+b*arcsinh(c*x))^-1*(1+c^2*x^2))
@test integrate((1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^-2, x) == :(b^-2*c^-1*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-1*b^-1*c^-1*(a+b*arcsinh(c*x))^-1*(1+c^2*x^2)+-1*b^-2*c^-1*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-2, x) == :(-9//64*b^-2*c^-4*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+-7//64*b^-2*c^-4*sinh(7*a*b^-1)*sinhintegral(7*arcsinh(c*x)+7*a*b^-1)+-5//64*b^-2*c^-4*sinh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+-3//64*b^-2*c^-4*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+3//64*b^-2*c^-4*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+5//64*b^-2*c^-4*cosh(5*a*b^-1)*coshintegral(5*arcsinh(c*x)+5*a*b^-1)+7//64*b^-2*c^-4*cosh(7*a*b^-1)*coshintegral(7*arcsinh(c*x)+7*a*b^-1)+9//64*b^-2*c^-4*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-1*b^-1*c^-1*x^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^-1)
@test integrate(x^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-2, x) == :(-3//16*b^-2*c^-3*coshintegral(6*arcsinh(c*x)+6*a*b^-1)*sinh(6*a*b^-1)+-1//4*b^-2*c^-3*coshintegral(4*arcsinh(c*x)+4*a*b^-1)*sinh(4*a*b^-1)+-1//16*b^-2*c^-3*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+1//4*b^-2*c^-3*cosh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+1//16*b^-2*c^-3*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1)+3//16*b^-2*c^-3*cosh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+-1*b^-1*c^-1*x^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^-1)
@test integrate(x*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-2, x) == :(-9//16*b^-2*c^-2*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-5//16*b^-2*c^-2*sinh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+-1//8*b^-2*c^-2*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+1//8*b^-2*c^-2*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+5//16*b^-2*c^-2*cosh(5*a*b^-1)*coshintegral(5*arcsinh(c*x)+5*a*b^-1)+9//16*b^-2*c^-2*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+-1*x*b^-1*c^-1*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^-1)
@test integrate((1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-2, x) == :(b^-2*c^-1*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+(1/2)*b^-2*c^-1*cosh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+-1*b^-1*c^-1*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^-1+-1*b^-2*c^-1*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1)+-1//2*b^-2*c^-1*coshintegral(4*arcsinh(c*x)+4*a*b^-1)*sinh(4*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-2, x) == :(-21//256*b^-2*c^-4*sinh(7*a*b^-1)*sinhintegral(7*arcsinh(c*x)+7*a*b^-1)+-9//256*b^-2*c^-4*sinh(9*a*b^-1)*sinhintegral(9*arcsinh(c*x)+9*a*b^-1)+-3//32*b^-2*c^-4*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+-3//128*b^-2*c^-4*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+3//32*b^-2*c^-4*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+3//128*b^-2*c^-4*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+9//256*b^-2*c^-4*cosh(9*a*b^-1)*coshintegral(9*arcsinh(c*x)+9*a*b^-1)+21//256*b^-2*c^-4*cosh(7*a*b^-1)*coshintegral(7*arcsinh(c*x)+7*a*b^-1)+-1*b^-1*c^-1*x^3*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^-1)
@test integrate(x^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-2, x) == :(-3//16*b^-2*c^-3*coshintegral(6*arcsinh(c*x)+6*a*b^-1)*sinh(6*a*b^-1)+-1//8*b^-2*c^-3*coshintegral(4*arcsinh(c*x)+4*a*b^-1)*sinh(4*a*b^-1)+-1//16*b^-2*c^-3*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//16*b^-2*c^-3*coshintegral(8*arcsinh(c*x)+8*a*b^-1)*sinh(8*a*b^-1)+1//8*b^-2*c^-3*cosh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+1//16*b^-2*c^-3*cosh(8*a*b^-1)*sinhintegral(8*arcsinh(c*x)+8*a*b^-1)+1//16*b^-2*c^-3*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1)+3//16*b^-2*c^-3*cosh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+-1*b^-1*c^-1*x^2*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^-1)
@test integrate(x*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-2, x) == :(-27//64*b^-2*c^-2*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+-25//64*b^-2*c^-2*sinh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+-7//64*b^-2*c^-2*sinh(7*a*b^-1)*sinhintegral(7*arcsinh(c*x)+7*a*b^-1)+-5//64*b^-2*c^-2*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+5//64*b^-2*c^-2*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+7//64*b^-2*c^-2*cosh(7*a*b^-1)*coshintegral(7*arcsinh(c*x)+7*a*b^-1)+25//64*b^-2*c^-2*cosh(5*a*b^-1)*coshintegral(5*arcsinh(c*x)+5*a*b^-1)+27//64*b^-2*c^-2*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+-1*x*b^-1*c^-1*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^-1)
@test integrate((1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-2, x) == :(-1*b^-1*c^-1*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^-1+-15//16*b^-2*c^-1*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1)+-3//4*b^-2*c^-1*coshintegral(4*arcsinh(c*x)+4*a*b^-1)*sinh(4*a*b^-1)+-3//16*b^-2*c^-1*coshintegral(6*arcsinh(c*x)+6*a*b^-1)*sinh(6*a*b^-1)+3//4*b^-2*c^-1*cosh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+3//16*b^-2*c^-1*cosh(6*a*b^-1)*sinhintegral(6*arcsinh(c*x)+6*a*b^-1)+15//16*b^-2*c^-1*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1))
@test integrate(x^5*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-2, x) == :(-1*b^-1*c^-1*x^5*(a+b*arcsinh(c*x))^-1+-15//16*b^-2*c^-6*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+-5//8*b^-2*c^-6*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x))+-5//16*b^-2*c^-6*sinh(5*a*b^-1)*sinhintegral(5*arcsinh(c*x)+5*a*b^-1)+5//8*b^-2*c^-6*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+5//16*b^-2*c^-6*cosh(5*a*b^-1)*coshintegral(5*arcsinh(c*x)+5*a*b^-1)+15//16*b^-2*c^-6*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1))
@test integrate(x^4*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-2, x) == :(b^-2*c^-5*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1)+(1/2)*b^-2*c^-5*cosh(4*a*b^-1)*sinhintegral(4*arcsinh(c*x)+4*a*b^-1)+-1*b^-1*c^-1*x^4*(a+b*arcsinh(c*x))^-1+-1*b^-2*c^-5*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-1//2*b^-2*c^-5*coshintegral(4*arcsinh(c*x)+4*a*b^-1)*sinh(4*a*b^-1))
@test integrate(x^3*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-2, x) == :(-1*b^-1*c^-1*x^3*(a+b*arcsinh(c*x))^-1+-3//4*b^-2*c^-4*cosh(a*b^-1)*coshintegral(a*b^-1+arcsinh(c*x))+-3//4*b^-2*c^-4*sinh(3*a*b^-1)*sinhintegral(3*arcsinh(c*x)+3*a*b^-1)+3//4*b^-2*c^-4*cosh(3*a*b^-1)*coshintegral(3*arcsinh(c*x)+3*a*b^-1)+3//4*b^-2*c^-4*sinh(a*b^-1)*sinhintegral(a*b^-1+arcsinh(c*x)))
@test integrate(x^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-2, x) == :(b^-2*c^-3*cosh(2*a*b^-1)*sinhintegral(2*arcsinh(c*x)+2*a*b^-1)+-1*b^-1*c^-1*x^2*(a+b*arcsinh(c*x))^-1+-1*b^-2*c^-3*coshintegral(2*arcsinh(c*x)+2*a*b^-1)*sinh(2*a*b^-1))
@test integrate(x*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-2, x) == :(b^-2*c^-2*cosh(a*b^-1)*coshintegral(b^-1*(a+b*arcsinh(c*x)))+-1*x*b^-1*c^-1*(a+b*arcsinh(c*x))^-1+-1*b^-2*c^-2*sinh(a*b^-1)*sinhintegral(b^-1*(a+b*arcsinh(c*x))))
@test integrate((1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^-2, x) == :(-1*b^-1*c^-1*(a+b*arcsinh(c*x))^-1)
@test integrate((1+a^2*x^2)^-1//2*arcsinh(a*x)^-3, x) == :(-1//2*a^-1*arcsinh(a*x)^-2)
@test integrate(x^3*(a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2), x) == :(-2*d*b^-1*c^-1*x^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1//2+-3//32*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*erf(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(2*a*b^-1)+-3//32*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*erfi(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-2*a*b^-1)+1//32*d*6^(1/2)*pi^(1/2)*b^-3//2*c^-4*erf(6^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(6*a*b^-1)+1//32*d*6^(1/2)*pi^(1/2)*b^-3//2*c^-4*erfi(6^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-6*a*b^-1))
@test integrate(x^2*(a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2), x) == :(-2*d*b^-1*c^-1*x^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1//2+-1//8*d*pi^(1/2)*b^-3//2*c^-3*erfi(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-1*a*b^-1)+1//8*d*pi^(1/2)*b^-3//2*c^-3*erf(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(a*b^-1)+-1//16*d*3^(1/2)*pi^(1/2)*b^-3//2*c^-3*erf(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(3*a*b^-1)+-1//16*d*5^(1/2)*pi^(1/2)*b^-3//2*c^-3*erf(5^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(5*a*b^-1)+1//16*d*3^(1/2)*pi^(1/2)*b^-3//2*c^-3*erfi(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-3*a*b^-1)+1//16*d*5^(1/2)*pi^(1/2)*b^-3//2*c^-3*erfi(5^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-5*a*b^-1))
@test integrate(x*(a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2), x) == :(-2*d*x*b^-1*c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1//2+1//4*d*pi^(1/2)*b^-3//2*c^-2*erf(2*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(4*a*b^-1)+1//4*d*pi^(1/2)*b^-3//2*c^-2*erfi(2*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-4*a*b^-1)+1//4*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*erf(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(2*a*b^-1)+1//4*d*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*erfi(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-2*a*b^-1))
@test integrate((a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2), x) == :(-2*d*b^-1*c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^-1//2+-3//4*d*pi^(1/2)*b^-3//2*c^-1*erf(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(a*b^-1)+3//4*d*pi^(1/2)*b^-3//2*c^-1*erfi(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-1*a*b^-1)+-1//4*d*3^(1/2)*pi^(1/2)*b^-3//2*c^-1*erf(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(3*a*b^-1)+1//4*d*3^(1/2)*pi^(1/2)*b^-3//2*c^-1*erfi(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-3*a*b^-1))
@test integrate(x^3*(a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2)^2, x) == :(-2*b^-1*c^-1*d^2*x^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1//2+-1//32*pi^(1/2)*b^-3//2*c^-4*d^2*erf(2*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(4*a*b^-1)+-1//32*pi^(1/2)*b^-3//2*c^-4*d^2*erfi(2*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-4*a*b^-1)+-3//64*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*erf(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(2*a*b^-1)+-3//64*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*erfi(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-2*a*b^-1)+1//64*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*erf(2*2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(8*a*b^-1)+1//64*2^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*erfi(2*2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-8*a*b^-1)+1//64*6^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*erf(6^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(6*a*b^-1)+1//64*6^(1/2)*pi^(1/2)*b^-3//2*c^-4*d^2*erfi(6^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-6*a*b^-1))
@test integrate(x^2*(a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2)^2, x) == :(-2*b^-1*c^-1*d^2*x^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1//2+-5//64*pi^(1/2)*b^-3//2*c^-3*d^2*erfi(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-1*a*b^-1)+5//64*pi^(1/2)*b^-3//2*c^-3*d^2*erf(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(a*b^-1)+-3//64*5^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*erf(5^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(5*a*b^-1)+-1//64*3^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*erf(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(3*a*b^-1)+-1//64*7^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*erf(7^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(7*a*b^-1)+1//64*3^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*erfi(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-3*a*b^-1)+1//64*7^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*erfi(7^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-7*a*b^-1)+3//64*5^(1/2)*pi^(1/2)*b^-3//2*c^-3*d^2*erfi(5^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-5*a*b^-1))
@test integrate(x*(a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2)^2, x) == :(-2*x*b^-1*c^-1*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1//2+1//4*pi^(1/2)*b^-3//2*c^-2*d^2*erf(2*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(4*a*b^-1)+1//4*pi^(1/2)*b^-3//2*c^-2*d^2*erfi(2*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-4*a*b^-1)+1//32*6^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*erf(6^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(6*a*b^-1)+1//32*6^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*erfi(6^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-6*a*b^-1)+5//32*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*erf(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(2*a*b^-1)+5//32*2^(1/2)*pi^(1/2)*b^-3//2*c^-2*d^2*erfi(2^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-2*a*b^-1))
@test integrate((a+b*arcsinh(c*x))^-3//2*(d+d*c^2*x^2)^2, x) == :(-2*b^-1*c^-1*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^-1//2+-5//8*pi^(1/2)*b^-3//2*c^-1*d^2*erf(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(a*b^-1)+5//8*pi^(1/2)*b^-3//2*c^-1*d^2*erfi(b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-1*a*b^-1)+-5//16*3^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*erf(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(3*a*b^-1)+-1//16*5^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*erf(5^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(5*a*b^-1)+1//16*5^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*erfi(5^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-5*a*b^-1)+5//16*3^(1/2)*pi^(1/2)*b^-3//2*c^-1*d^2*erfi(3^(1/2)*b^-1//2*(a+b*arcsinh(c*x))^(1/2))*exp(-3*a*b^-1))
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^(1/2), x) == :(1//4*x*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^(1/2)+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+1//4*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-1//256*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+1//256*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+-1//32*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2))+1//32*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2), x) == :((1/2)*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+1//3*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-1//32*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2))+1//32*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^(1/2), x) == :(2//3*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3//2)
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^3//2, x) == :(1//4*x*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^3//2+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-27//256*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+-3//32*c*a^-1*(1+a^2*x^2)^3//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+3//20*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^5//2+-9//32*a*c*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+3//2048*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+3//2048*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+3//128*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+3//128*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2, x) == :((1/2)*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-3//16*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+1//5*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^5//2+-3//8*a*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+3//128*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+3//128*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^3//2, x) == :(2//5*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^5//2)
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^5//2, x) == :(1//4*x*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^5//2+3//8*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^5//2+225//512*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+-45//256*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-5//32*c*a^-1*(1+a^2*x^2)^3//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+3//28*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^7//2+15//256*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)*(1+a^2*x^2)+-15//32*a*c*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-15//16384*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+15//16384*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+-15//512*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2))+15//512*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^5//2, x) == :((1/2)*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^5//2+15//32*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+-5//16*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+1//7*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^7//2+-5//8*a*x^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^3//2+-15//512*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2))+15//512*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^5//2, x) == :(2//7*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^7//2)
@test integrate((a^2+x^2)^3//2*arcsinh(x*a^-1)^(1/2), x) == :(1//4*x*(a^2+x^2)^3//2*arcsinh(x*a^-1)^(1/2)+1//4*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^3//2+3//8*x*a^2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2)+-1//256*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erfi(2*arcsinh(x*a^-1)^(1/2))+1//256*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erf(2*arcsinh(x*a^-1)^(1/2))+-1//32*2^(1/2)*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erfi(2^(1/2)*arcsinh(x*a^-1)^(1/2))+1//32*2^(1/2)*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erf(2^(1/2)*arcsinh(x*a^-1)^(1/2)))
@test integrate((a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2), x) == :((1/2)*x*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2)+1//3*a*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^3//2+-1//32*a*2^(1/2)*pi^(1/2)*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erfi(2^(1/2)*arcsinh(x*a^-1)^(1/2))+1//32*a*2^(1/2)*pi^(1/2)*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erf(2^(1/2)*arcsinh(x*a^-1)^(1/2)))
@test integrate((a^2+x^2)^-1//2*arcsinh(x*a^-1)^(1/2), x) == :(2//3*a*(1+a^-2*x^2)^(1/2)*(a^2+x^2)^-1//2*arcsinh(x*a^-1)^3//2)
@test integrate((a^2+x^2)^3//2*arcsinh(x*a^-1)^3//2, x) == :(1//4*x*(a^2+x^2)^3//2*arcsinh(x*a^-1)^3//2+-27//256*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2)+-3//32*a^-1*(1+a^-2*x^2)^-1//2*(a^2+x^2)^5//2*arcsinh(x*a^-1)^(1/2)+3//8*x*a^2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^3//2+3//20*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^5//2+-9//32*a*x^2*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2)+3//2048*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erf(2*arcsinh(x*a^-1)^(1/2))+3//2048*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erfi(2*arcsinh(x*a^-1)^(1/2))+3//128*2^(1/2)*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erf(2^(1/2)*arcsinh(x*a^-1)^(1/2))+3//128*2^(1/2)*pi^(1/2)*a^3*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erfi(2^(1/2)*arcsinh(x*a^-1)^(1/2)))
@test integrate((a^2+x^2)^(1/2)*arcsinh(x*a^-1)^3//2, x) == :((1/2)*x*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^3//2+-3//16*a*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2)+1//5*a*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^5//2+-3//8*a^-1*x^2*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*arcsinh(x*a^-1)^(1/2)+3//128*a*2^(1/2)*pi^(1/2)*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erf(2^(1/2)*arcsinh(x*a^-1)^(1/2))+3//128*a*2^(1/2)*pi^(1/2)*(1+a^-2*x^2)^-1//2*(a^2+x^2)^(1/2)*erfi(2^(1/2)*arcsinh(x*a^-1)^(1/2)))
@test integrate((a^2+x^2)^-1//2*arcsinh(x*a^-1)^3//2, x) == :(2//5*a*(1+a^-2*x^2)^(1/2)*(a^2+x^2)^-1//2*arcsinh(x*a^-1)^5//2)
@test integrate(x*(1+x^2)^-1//2*arcsinh(x)^-1//2, x) == :((1/2)*pi^(1/2)*erfi(arcsinh(x)^(1/2))+-1//2*pi^(1/2)*erf(arcsinh(x)^(1/2)))
@test integrate((c+c*a^2*x^2)^5//2*arcsinh(a*x)^-1//2, x) == :(5//8*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+3//64*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+3//64*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+1//384*6^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(6^(1/2)*arcsinh(a*x)^(1/2))+1//384*6^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(6^(1/2)*arcsinh(a*x)^(1/2))+15//128*2^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+15//128*2^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^-1//2, x) == :(3//4*c*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+1//32*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+1//32*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+1//8*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+1//8*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-1//2, x) == :(a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^(1/2)+1//8*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+1//8*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^-1//2, x) == :(2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^(1/2))
@test integrate((c+c*a^2*x^2)^5//2*arcsinh(a*x)^-3//2, x) == :(-2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^5//2*arcsinh(a*x)^-1//2+-3//8*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+3//8*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+-15//32*2^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+-1//32*6^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(6^(1/2)*arcsinh(a*x)^(1/2))+1//32*6^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(6^(1/2)*arcsinh(a*x)^(1/2))+15//32*2^(1/2)*pi^(1/2)*a^-1*c^2*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^-3//2, x) == :(-2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^-1//2+-1//4*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+1//4*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+(1/2)*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2))+-1//2*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-3//2, x) == :(-2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-1//2+(1/2)*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2))+-1//2*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^-3//2, x) == :(-2*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^-1//2)
@test integrate((c+c*a^2*x^2)^3//2*arcsinh(a*x)^-5//2, x) == :(-2//3*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^3//2*arcsinh(a*x)^-3//2+-16//3*c*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-1//2*(1+a^2*x^2)+2//3*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2*arcsinh(a*x)^(1/2))+2//3*c*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2*arcsinh(a*x)^(1/2))+2//3*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+2//3*c*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-5//2, x) == :(-8//3*x*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-1//2+-2//3*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^(1/2)*arcsinh(a*x)^-3//2+2//3*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erf(2^(1/2)*arcsinh(a*x)^(1/2))+2//3*2^(1/2)*pi^(1/2)*a^-1*(1+a^2*x^2)^-1//2*(c+c*a^2*x^2)^(1/2)*erfi(2^(1/2)*arcsinh(a*x)^(1/2)))
@test integrate((c+c*a^2*x^2)^-1//2*arcsinh(a*x)^-5//2, x) == :(-2//3*a^-1*(1+a^2*x^2)^(1/2)*(c+c*a^2*x^2)^-1//2*arcsinh(a*x)^-3//2)
@test integrate(x^2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2), x) == :(-1//8*b^-1*c^-3*(1+n)^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^(1+n)*(d+d*c^2*x^2)^(1/2)+2^(-6+-2n)*c^-3*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-4a+-4*b*arcsinh(c*x)))*exp(-4*a*b^-1)+-1*2^(-6+-2n)*c^-3*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(4a+4*b*arcsinh(c*x)))*exp(4*a*b^-1))
@test integrate(x*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2), x) == :(1//8*c^-2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(a+b*arcsinh(c*x)))*exp(a*b^-1)+1//8*c^-2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-1*b^-1*(a+b*arcsinh(c*x)))*exp(-1*a*b^-1)+1//8*3^(-1+-1n)*c^-2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(3a+3*b*arcsinh(c*x)))*exp(3*a*b^-1)+1//8*3^(-1+-1n)*c^-2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-3a+-3*b*arcsinh(c*x)))*exp(-3*a*b^-1))
@test integrate((a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2), x) == :((1/2)*b^-1*c^-1*(1+n)^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^(1+n)*(d+d*c^2*x^2)^(1/2)+2^(-3+-1n)*c^-1*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-2a+-2*b*arcsinh(c*x)))*exp(-2*a*b^-1)+-1*2^(-3+-1n)*c^-1*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(2a+2*b*arcsinh(c*x)))*exp(2*a*b^-1))
@test integrate(x^2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^3//2, x) == :(-1//16*d*b^-1*c^-3*(1+n)^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^(1+n)*(d+d*c^2*x^2)^(1/2)+d*2^(-7+-1n)*c^-3*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(2a+2*b*arcsinh(c*x)))*exp(2*a*b^-1)+d*2^(-7+-2n)*c^-3*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-4a+-4*b*arcsinh(c*x)))*exp(-4*a*b^-1)+-1*d*2^(-7+-1n)*c^-3*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-2a+-2*b*arcsinh(c*x)))*exp(-2*a*b^-1)+-1*d*2^(-7+-2n)*c^-3*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(4a+4*b*arcsinh(c*x)))*exp(4*a*b^-1)+d*2^(-7+-1n)*3^(-1+-1n)*c^-3*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-6a+-6*b*arcsinh(c*x)))*exp(-6*a*b^-1)+-1*d*2^(-7+-1n)*3^(-1+-1n)*c^-3*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(6a+6*b*arcsinh(c*x)))*exp(6*a*b^-1))
@test integrate(x*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^3//2, x) == :(1//16*d*c^-2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(a+b*arcsinh(c*x)))*exp(a*b^-1)+1//16*d*c^-2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-1*b^-1*(a+b*arcsinh(c*x)))*exp(-1*a*b^-1)+1//32*d*3^(-1n)*c^-2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(3a+3*b*arcsinh(c*x)))*exp(3*a*b^-1)+1//32*d*3^(-1n)*c^-2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-3a+-3*b*arcsinh(c*x)))*exp(-3*a*b^-1)+1//32*d*5^(-1+-1n)*c^-2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(5a+5*b*arcsinh(c*x)))*exp(5*a*b^-1)+1//32*d*5^(-1+-1n)*c^-2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-5a+-5*b*arcsinh(c*x)))*exp(-5*a*b^-1))
@test integrate((a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^3//2, x) == :(3//8*d*b^-1*c^-1*(1+n)^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^(1+n)*(d+d*c^2*x^2)^(1/2)+d*2^(-6+-2n)*c^-1*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-4a+-4*b*arcsinh(c*x)))*exp(-4*a*b^-1)+d*2^(-3+-1n)*c^-1*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-2a+-2*b*arcsinh(c*x)))*exp(-2*a*b^-1)+-1*d*2^(-6+-2n)*c^-1*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(4a+4*b*arcsinh(c*x)))*exp(4*a*b^-1)+-1*d*2^(-3+-1n)*c^-1*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(2a+2*b*arcsinh(c*x)))*exp(2*a*b^-1))
@test integrate(x^2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^5//2, x) == :(-5//128*b^-1*c^-3*d^2*(1+n)^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^(1+n)*(d+d*c^2*x^2)^(1/2)+2^(-11+-3n)*c^-3*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-8a+-8*b*arcsinh(c*x)))*exp(-8*a*b^-1)+2^(-8+-2n)*c^-3*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-4a+-4*b*arcsinh(c*x)))*exp(-4*a*b^-1)+2^(-7+-1n)*c^-3*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(2a+2*b*arcsinh(c*x)))*exp(2*a*b^-1)+-1*2^(-11+-3n)*c^-3*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(8a+8*b*arcsinh(c*x)))*exp(8*a*b^-1)+-1*2^(-8+-2n)*c^-3*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(4a+4*b*arcsinh(c*x)))*exp(4*a*b^-1)+-1*2^(-7+-1n)*c^-3*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-2a+-2*b*arcsinh(c*x)))*exp(-2*a*b^-1)+2^(-7+-1n)*3^(-1+-1n)*c^-3*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-6a+-6*b*arcsinh(c*x)))*exp(-6*a*b^-1)+-1*2^(-7+-1n)*3^(-1+-1n)*c^-3*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(6a+6*b*arcsinh(c*x)))*exp(6*a*b^-1))
@test integrate(x*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^5//2, x) == :(5//128*c^-2*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(a+b*arcsinh(c*x)))*exp(a*b^-1)+5//128*c^-2*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,-1*b^-1*(a+b*arcsinh(c*x)))*exp(-1*a*b^-1)+1//128*3^(1+-1n)*c^-2*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(3a+3*b*arcsinh(c*x)))*exp(3*a*b^-1)+1//128*3^(1+-1n)*c^-2*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-3a+-3*b*arcsinh(c*x)))*exp(-3*a*b^-1)+1//128*5^(-1n)*c^-2*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(5a+5*b*arcsinh(c*x)))*exp(5*a*b^-1)+1//128*5^(-1n)*c^-2*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-5a+-5*b*arcsinh(c*x)))*exp(-5*a*b^-1)+1//128*7^(-1+-1n)*c^-2*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(7a+7*b*arcsinh(c*x)))*exp(7*a*b^-1)+1//128*7^(-1+-1n)*c^-2*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-7a+-7*b*arcsinh(c*x)))*exp(-7*a*b^-1))
@test integrate((a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^5//2, x) == :(5//16*b^-1*c^-1*d^2*(1+n)^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^(1+n)*(d+d*c^2*x^2)^(1/2)+-15*2^(-7+-1n)*c^-1*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(2a+2*b*arcsinh(c*x)))*exp(2*a*b^-1)+-3*2^(-7+-2n)*c^-1*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(4a+4*b*arcsinh(c*x)))*exp(4*a*b^-1)+3*2^(-7+-2n)*c^-1*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-4a+-4*b*arcsinh(c*x)))*exp(-4*a*b^-1)+15*2^(-7+-1n)*c^-1*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-2a+-2*b*arcsinh(c*x)))*exp(-2*a*b^-1)+2^(-7+-1n)*3^(-1+-1n)*c^-1*d^2*(-1*b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(-6a+-6*b*arcsinh(c*x)))*exp(-6*a*b^-1)+-1*2^(-7+-1n)*3^(-1+-1n)*c^-1*d^2*(b^-1*(a+b*arcsinh(c*x)))^(-1n)*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^n*(d+d*c^2*x^2)^(1/2)*SpecialFunctions.gamma(1+n,b^-1*(6a+6*b*arcsinh(c*x)))*exp(6*a*b^-1))
@test integrate(x^3*(1+a^2*x^2)^-1//2*arcsinh(a*x)^n, x) == :(-3//8*a^-4*SpecialFunctions.gamma(1+n,arcsinh(a*x))+1//8*3^(-1+-1n)*a^-4*SpecialFunctions.gamma(1+n,3*arcsinh(a*x))+-3//8*a^-4*(-1*arcsinh(a*x))^(-1n)*arcsinh(a*x)^n*SpecialFunctions.gamma(1+n,-1*arcsinh(a*x))+1//8*3^(-1+-1n)*a^-4*(-1*arcsinh(a*x))^(-1n)*arcsinh(a*x)^n*SpecialFunctions.gamma(1+n,-3*arcsinh(a*x)))
@test integrate(x^2*(1+a^2*x^2)^-1//2*arcsinh(a*x)^n, x) == :(-1*2^(-3+-1n)*a^-3*SpecialFunctions.gamma(1+n,2*arcsinh(a*x))+-1//2*a^-3*(1+n)^-1*arcsinh(a*x)^(1+n)+2^(-3+-1n)*a^-3*(-1*arcsinh(a*x))^(-1n)*arcsinh(a*x)^n*SpecialFunctions.gamma(1+n,-2*arcsinh(a*x)))
@test integrate(x*(1+a^2*x^2)^-1//2*arcsinh(a*x)^n, x) == :((1/2)*a^-2*SpecialFunctions.gamma(1+n,arcsinh(a*x))+(1/2)*a^-2*(-1*arcsinh(a*x))^(-1n)*arcsinh(a*x)^n*SpecialFunctions.gamma(1+n,-1*arcsinh(a*x)))
@test integrate((1+a^2*x^2)^-1//2*arcsinh(a*x)^n, x) == :(a^-1*(1+n)^-1*arcsinh(a*x)^(1+n))
@test integrate((d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)), x) == :(3//8*x*d^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-1//4*c^2*d^2*x^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-3//16*b*c*d^2*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-2//3*im*b*x*d^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//16*b*c^3*d^2*x^4*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+2//3*im*c^-1*d^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))+5//16*b^-1*c^-1*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-2//9*im*b*c^2*d^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2))
@test integrate((d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)), x) == :((1/2)*d*x*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-1//3*im*b*d*x*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//4*b*c*d*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//3*im*d*c^-1*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))+1//4*d*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//9*im*b*d*c^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2))
@test integrate((d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)), x) == :((1/2)*x*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-1//4*b*c*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//4*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2))
@test integrate((d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)), x) == :(im*b*f*x*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+(1/2)*f*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+-1*im*f*c^-1*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)), x) == :(-2*b*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+-1*c*x)+-1//2*b^-1*c^-1*f^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+2*im*c^-1*f^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(1+-1*im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)), x) == :(1//3*b*c^-1*f^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(im+-1*c*x)+1//3*im*c^-1*f^3*(1+-1*im*c*x)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+2//3*im*b*c^-1*f^3*(1+c^2*x^2)^5//2*(im+-1*c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2)
@test integrate((d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)), x) == :(1//4*d*x*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+3*d*x*(8+8*c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+-5//16*b*c*d*x^2*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-1//5*im*b*d*x*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-1//16*b*d*c^3*x^4*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+1//5*im*d*c^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+3//16*d*b^-1*c^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-2//15*im*b*d*c^2*x^3*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-1//25*im*b*d*c^4*x^5*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2)
@test integrate((d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)), x) == :(1//4*x*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+3*x*(8+8*c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+-5//16*b*c*x^2*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-1//16*b*c^3*x^4*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+3//16*b^-1*c^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2)
@test integrate((d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)), x) == :((1/2)*f*x*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-1//3*im*f*c^-1*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1//4*b*c*f*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//3*im*b*f*x*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//4*f*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//9*im*b*f*c^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2))
@test integrate((d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)), x) == :(-1//2*x*f^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-2*im*c^-1*f^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+2*im*b*x*f^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+1//4*b*c*f^2*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+3//4*b^-1*c^-1*f^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2)
@test integrate((d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)), x) == :(im*c^-1*f^3*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))+-1*im*b*x*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-4*b*c^-1*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+-1*c*x)+-3//2*b^-1*c^-1*f^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+4*im*c^-1*f^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(1+-1*im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)), x) == :(c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arcsinh(c*x)+-1//2*b*c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)^2+8//3*b*c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(im+-1*c*x)+-2*im*c^-1*f^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+-1*im*c*x)*(a+b*arcsinh(c*x))+2//3*im*c^-1*f^4*(1+-1*im*c*x)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+4//3*im*b*c^-1*f^4*(1+c^2*x^2)^5//2*(im+-1*c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2)
@test integrate((d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)), x) == :(1//6*x*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x))+5*x*(24+24*c^2*x^2)^-1*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x))+-1//36*b*c^-1*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+5//16*x*(1+c^2*x^2)^-2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x))+-25//96*b*c*x^2*(1+c^2*x^2)^-5//2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+-5//96*b*c^3*x^4*(1+c^2*x^2)^-5//2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+5//32*b^-1*c^-1*(1+c^2*x^2)^-5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2)
@test integrate((d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)), x) == :(1//4*f*x*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+3*f*x*(8+8*c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+-5//16*b*c*f*x^2*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-1//5*im*f*c^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1//16*b*f*c^3*x^4*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+1//5*im*b*f*x*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+3//16*f*b^-1*c^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+1//25*im*b*f*c^4*x^5*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+2//15*im*b*f*c^2*x^3*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2)
@test integrate((d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)), x) == :(3//8*x*f^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-1//4*c^2*f^2*x^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-3//16*b*c*f^2*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-2//3*im*c^-1*f^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)*(a+b*arcsinh(c*x))+1//16*b*c^3*f^2*x^4*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+2//3*im*b*x*f^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+5//16*b^-1*c^-1*f^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+2//9*im*b*c^2*f^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2))
@test integrate((d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)), x) == :(-3//2*x*f^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-11//3*im*c^-1*f^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+3//4*b*c*f^3*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+5//4*b^-1*c^-1*f^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+11//3*im*b*x*f^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+-1//9*im*b*c^2*f^3*x^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+1//3*im*c*f^3*x^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)), x) == :(b*c*f^4*x^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-8*b*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+-1*c*x)+-15//2*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arcsinh(c*x)+-3//2*im*b*x*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+5//4*b*c^-1*f^4*(1+c^2*x^2)^3//2*(1+-1*im*c*x)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+15//2*im*c^-1*f^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))+15//4*b*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)^2+2*im*c^-1*f^4*(1+-1*im*c*x)^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+5//2*im*c^-1*f^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+-1*im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)), x) == :(im*b*x*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-5*im*c^-1*f^5*(1+c^2*x^2)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+5*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arcsinh(c*x)+-5//2*b*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)^2+28//3*b*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(im+-1*c*x)+-10//3*im*c^-1*f^5*(1+c^2*x^2)^2*(1+-1*im*c*x)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+2//3*im*c^-1*f^5*(1+-1*im*c*x)^4*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+8//3*im*b*c^-1*f^5*(1+c^2*x^2)^5//2*(im+-1*c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2)
@test integrate((d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)), x) == :(-3//2*x*d^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-11//3*im*b*x*d^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+3//4*b*c*d^3*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+5//4*b^-1*c^-1*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+11//3*im*c^-1*d^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1//3*im*c*d^3*x^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+1//9*im*b*c^2*d^3*x^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2)
@test integrate((d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)), x) == :(-1//2*x*d^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-2*im*b*x*d^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+2*im*c^-1*d^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+1//4*b*c*d^2*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+3//4*b^-1*c^-1*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2)
@test integrate((d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)), x) == :(im*d*c^-1*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+(1/2)*d*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+-1*im*b*d*x*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2)
@test integrate((d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)), x) == :((1/2)*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2)
@test integrate((d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)), x) == :(f*c^-1*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(im+c*x)*(a+b*arcsinh(c*x))+-1*b*f*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+-1*c*x))
@test integrate((d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)), x) == :(1//3*x*f^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-1//6*b*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(1+c^2*x^2)+-1//3*im*b*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arctan(c*x)+1//3*im*b*c^-1*f^2*(1+c^2*x^2)^5//2*(im+-1*c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*im*c^-1*f^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(1+-1*im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x)), x) == :(b*c*d^4*x^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-8*b*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+c*x)+-15//2*im*c^-1*d^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))+-15//2*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arcsinh(c*x)+3//2*im*b*x*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+5//4*b*c^-1*d^4*(1+c^2*x^2)^3//2*(1+im*c*x)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+15//4*b*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)^2+-2*im*c^-1*d^4*(1+im*c*x)^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-5//2*im*c^-1*d^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x)), x) == :(im*b*x*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1*im*c^-1*d^3*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))+-4*b*c^-1*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+c*x)+-3//2*b^-1*c^-1*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-4*im*c^-1*d^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(1+im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x)), x) == :(-2*b*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+c*x)+-1//2*b^-1*c^-1*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-2*im*c^-1*d^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(1+im*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x)), x) == :(-1*b*d*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(im+c*x)+-1*d*c^-1*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(im+-1*c*x)*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x)), x) == :(x*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+-1//2*b*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*log(1+c^2*x^2))
@test integrate((d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x)), x) == :(2//3*f*x*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-1//3*b*f*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(1+c^2*x^2)+1//3*f*c^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(im+c*x)*(a+b*arcsinh(c*x))+-1//6*im*b*f*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arctan(c*x)+1//6*im*b*f*c^-1*(1+c^2*x^2)^5//2*(im+-1*c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2)
@test integrate((d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)), x) == :(-1*im*b*x*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+5*im*c^-1*d^5*(1+c^2*x^2)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+5*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arcsinh(c*x)+-5//2*b*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)^2+28//3*b*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(im+c*x)+-2//3*im*c^-1*d^5*(1+im*c*x)^4*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+8//3*im*b*c^-1*d^5*(1+c^2*x^2)^5//2*(im+c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+10//3*im*c^-1*d^5*(1+c^2*x^2)^2*(1+im*c*x)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)))
@test integrate((d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)), x) == :(c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arcsinh(c*x)+-1//2*b*c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)^2+8//3*b*c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(im+c*x)+2*im*c^-1*d^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+im*c*x)*(a+b*arcsinh(c*x))+-2//3*im*c^-1*d^4*(1+im*c*x)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+4//3*im*b*c^-1*d^4*(1+c^2*x^2)^5//2*(im+c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2)
@test integrate((d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)), x) == :(1//3*b*c^-1*d^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(im+c*x)+-1//3*im*c^-1*d^3*(1+im*c*x)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+2//3*im*b*c^-1*d^3*(1+c^2*x^2)^5//2*(im+c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2)
@test integrate((d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)), x) == :(1//3*x*d^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-1//6*b*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(1+c^2*x^2)+-2//3*im*c^-1*d^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(1+im*c*x)*(a+b*arcsinh(c*x))+1//3*im*b*c^-1*d^2*(1+c^2*x^2)^5//2*(im+c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*im*b*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arctan(c*x))
@test integrate((d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)), x) == :(2//3*d*x*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-1//3*b*d*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(1+c^2*x^2)+-1//3*d*c^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(im+-1*c*x)*(a+b*arcsinh(c*x))+1//6*im*b*d*c^-1*(1+c^2*x^2)^5//2*(im+c*x)^-1*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//6*im*b*d*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arctan(c*x))
@test integrate((d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x)), x) == :(1//3*x*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)*(a+b*arcsinh(c*x))+1//6*b*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*x*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-1//3*b*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*log(1+c^2*x^2))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^(1/2), x) == :(3//8*x*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+15//64*x*b^2*d^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//4*c^2*d^2*x^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//32*b^2*c^2*d^2*x^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+8//9*im*b^2*c^-1*d^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-15//64*b^2*c^-1*d^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*arcsinh(c*x)+2//3*im*c^-1*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+4//27*im*b^2*c^-1*d^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+5//24*b^-1*c^-1*d^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-4//3*im*b*x*d^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-3//8*b*c*d^2*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+1//8*b*c^3*d^2*x^4*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-4//9*im*b*c^2*d^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^(1/2), x) == :((1/2)*d*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//4*d*x*b^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+4//9*im*d*b^2*c^-1*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//4*d*b^2*c^-1*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*arcsinh(c*x)+1//3*im*d*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+1//6*d*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+2//27*im*d*b^2*c^-1*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+-2//3*im*b*d*x*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-1//2*b*c*d*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+-2//9*im*b*d*c^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2), x) == :((1/2)*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//4*x*b^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//4*b^2*c^-1*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*arcsinh(c*x)+1//6*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//2*b*c*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^(1/2), x) == :(-1*im*f*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-2*im*f*b^2*c^-1*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+1//3*f*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+2*im*a*b*f*x*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+2*im*f*x*b^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*arcsinh(c*x))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^(1/2), x) == :(2*x*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+2*c^-1*f^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-4*b^2*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-2*b^2*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+2*im*c^-1*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+4*b^2*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//3*b^-1*c^-1*f^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-4*b*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-8*im*b*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^(1/2), x) == :(-1//3*c^-1*f^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+4//3*b^2*c^-1*f^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-4//3*im*b^2*c^-1*f^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*cot(1//4*pi+(1/2)*im*arcsinh(c*x))+-1//3*im*c^-1*f^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*cot(1//4*pi+(1/2)*im*arcsinh(c*x))+2//3*b*c^-1*f^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*csc(1//4*pi+(1/2)*im*arcsinh(c*x))^2*(a+b*arcsinh(c*x))+4//3*b*c^-1*f^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+im*exp(arcsinh(c*x)))+1//3*im*c^-1*f^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*csc(1//4*pi+(1/2)*im*arcsinh(c*x))^2*cot(1//4*pi+(1/2)*im*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^3//2, x) == :(1//4*d*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+1//32*d*x*b^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+3*d*x*(8+8*c^2*x^2)^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+15*d*x*b^2*(64+64*c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+8//225*im*d*b^2*c^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-9//64*d*b^2*c^-1*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*arcsinh(c*x)+-1//8*b*d*c^-1*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+1//5*im*d*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(1+c^2*x^2)+1//8*d*b^-1*c^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+2//125*im*d*b^2*c^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(1+c^2*x^2)+16//75*im*d*b^2*c^-1*(1+c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-3//8*b*c*d*x^2*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+-2//5*im*b*d*x*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+-4//15*im*b*d*c^2*x^3*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+-2//25*im*b*d*c^4*x^5*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2, x) == :(1//4*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+1//32*x*b^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+3*x*(8+8*c^2*x^2)^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+15*x*b^2*(64+64*c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-9//64*b^2*c^-1*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*arcsinh(c*x)+-1//8*b*c^-1*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+1//8*b^-1*c^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-3//8*b*c*x^2*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^3//2, x) == :((1/2)*f*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+1//4*f*x*b^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-4//9*im*f*b^2*c^-1*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-2//27*im*f*b^2*c^-1*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+-1//3*im*f*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+-1//4*f*b^2*c^-1*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*arcsinh(c*x)+1//6*f*b^-1*c^-1*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//2*b*c*f*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+2//3*im*b*f*x*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+2//9*im*b*f*c^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^3//2, x) == :(-1//2*x*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-1//4*x*b^2*f^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+(1/2)*b^-1*c^-1*f^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+-4*im*b^2*c^-1*f^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-2*im*c^-1*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+1//4*b^2*c^-1*f^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*arcsinh(c*x)+(1/2)*b*c*f^2*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x))+4*im*b*x*f^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^3//2, x) == :(4*x*f^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+4*c^-1*f^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+im*c^-1*f^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1*b^-1*c^-1*f^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-8*b^2*c^-1*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-4*b^2*c^-1*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+2*im*b^2*c^-1*f^3*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+4*im*c^-1*f^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+8*b^2*c^-1*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-8*b*c^-1*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-2*im*a*b*x*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-2*im*x*b^2*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)+-16*im*b*c^-1*f^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^3//2, x) == :(-8//3*c^-1*f^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*b^-1*c^-1*f^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+32//3*b^2*c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-8//3*im*b^2*c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*cot(1//4*pi+(1/2)*im*arcsinh(c*x))+-8//3*im*c^-1*f^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*cot(1//4*pi+(1/2)*im*arcsinh(c*x))+4//3*b*c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*csc(1//4*pi+(1/2)*im*arcsinh(c*x))^2*(a+b*arcsinh(c*x))+32//3*b*c^-1*f^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+im*exp(arcsinh(c*x)))+2//3*im*c^-1*f^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*csc(1//4*pi+(1/2)*im*arcsinh(c*x))^2*cot(1//4*pi+(1/2)*im*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2, x) == :(1//6*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+1//108*x*b^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+5*x*(24+24*c^2*x^2)^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+65*x*b^2*(1728+1728*c^2*x^2)^-1*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+5//16*x*(1+c^2*x^2)^-2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+245//1152*x*b^2*(1+c^2*x^2)^-2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+-115//1152*b^2*c^-1*(1+c^2*x^2)^-5//2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*arcsinh(c*x)+-5//48*b*c^-1*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x))+-1//18*b*c^-1*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x))+5//48*b^-1*c^-1*(1+c^2*x^2)^-5//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2+-5//16*b*c*x^2*(1+c^2*x^2)^-5//2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^5//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^5//2, x) == :(1//4*f*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+1//32*f*x*b^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+3*f*x*(8+8*c^2*x^2)^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+15*f*x*b^2*(64+64*c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-8//225*im*f*b^2*c^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-16//75*im*f*b^2*c^-1*(1+c^2*x^2)^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-9//64*f*b^2*c^-1*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*arcsinh(c*x)+-2//125*im*f*b^2*c^-1*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(1+c^2*x^2)+-1//5*im*f*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(1+c^2*x^2)+-1//8*b*f*c^-1*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+1//8*f*b^-1*c^-1*(1+c^2*x^2)^-3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2+-3//8*b*c*f*x^2*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+2//5*im*b*f*x*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+2//25*im*b*f*c^4*x^5*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x))+4//15*im*b*f*c^2*x^3*(1+c^2*x^2)^-3//2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^3//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^5//2, x) == :(3//8*x*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+15//64*x*b^2*f^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-8//9*im*b^2*c^-1*f^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//4*c^2*f^2*x^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-1//32*b^2*c^2*f^2*x^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-15//64*b^2*c^-1*f^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*arcsinh(c*x)+-4//27*im*b^2*c^-1*f^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+-2//3*im*c^-1*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(1+c^2*x^2)+5//24*b^-1*c^-1*f^2*(1+c^2*x^2)^-1//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)+-3//8*b*c*f^2*x^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+1//8*b*c^3*f^2*x^4*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+4//3*im*b*x*f^2*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x))+4//9*im*b*c^2*f^2*x^3*(1+c^2*x^2)^-1//2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^(1/2)*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^5//2, x) == :(-3//2*x*f^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-3//4*x*b^2*f^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-68//9*im*b^2*c^-1*f^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-11//3*im*c^-1*f^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+2//27*im*b^2*c^-1*f^3*(1+c^2*x^2)^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+3//4*b^2*c^-1*f^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*arcsinh(c*x)+5//6*b^-1*c^-1*f^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+1//3*im*c*f^3*x^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+3//2*b*c*f^3*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x))+22//3*im*b*x*f^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x))+-2//9*im*b*c^2*f^3*x^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^5//2, x) == :((1/2)*x*f^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+8*x*f^4*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+8*c^-1*f^4*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+1//4*x*b^2*f^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-16*b^2*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-8*b^2*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+4*im*c^-1*f^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+8*im*b^2*c^-1*f^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+8*im*c^-1*f^4*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+16*b^2*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-5//2*b^-1*c^-1*f^4*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1//4*b^2*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)+-16*b*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-8*im*a*b*x*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-8*im*x*b^2*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)+-1//2*b*c*f^4*x^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))+-32*im*b*c^-1*f^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^5//2, x) == :(-28//3*c^-1*f^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-1*im*c^-1*f^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2*im*b^2*c^-1*f^5*(1+c^2*x^2)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+5//3*b^-1*c^-1*f^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+112//3*b^2*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*im*a*b*x*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2*im*x*b^2*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)+-28//3*im*c^-1*f^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*cot(1//4*pi+(1/2)*im*arcsinh(c*x))+-16//3*im*b^2*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*cot(1//4*pi+(1/2)*im*arcsinh(c*x))+8//3*b*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*csc(1//4*pi+(1/2)*im*arcsinh(c*x))^2*(a+b*arcsinh(c*x))+112//3*b*c^-1*f^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+im*exp(arcsinh(c*x)))+4//3*im*c^-1*f^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*csc(1//4*pi+(1/2)*im*arcsinh(c*x))^2*cot(1//4*pi+(1/2)*im*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^-1//2, x) == :(-3//2*x*d^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-3//4*x*b^2*d^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-2//27*im*b^2*c^-1*d^3*(1+c^2*x^2)^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+3//4*b^2*c^-1*d^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*arcsinh(c*x)+5//6*b^-1*c^-1*d^3*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+11//3*im*c^-1*d^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+68//9*im*b^2*c^-1*d^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-22//3*im*b*x*d^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x))+-1//3*im*c*d^3*x^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+3//2*b*c*d^3*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x))+2//9*im*b*c^2*d^3*x^3*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^-1//2, x) == :(-1//2*x*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+-1//4*x*b^2*d^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+(1/2)*b^-1*c^-1*d^2*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+2*im*c^-1*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+4*im*b^2*c^-1*d^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+1//4*b^2*c^-1*d^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*arcsinh(c*x)+(1/2)*b*c*d^2*x^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x))+-4*im*b*x*d^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(a+b*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^-1//2, x) == :(im*d*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+2*im*d*b^2*c^-1*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*(1+c^2*x^2)+1//3*d*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+-2*im*a*b*d*x*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2+-2*im*d*x*b^2*(1+c^2*x^2)^(1/2)*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2*arcsinh(c*x))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2, x) == :(1//3*b^-1*c^-1*(1+c^2*x^2)^(1/2)*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-1//2)
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-1//2, x) == :(f*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+f*c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+im*f*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+-1*f*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-2*f*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+2*f*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-2*b*f*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-4*im*b*f*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-1//2, x) == :(-2//3*x*b^2*f^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*x*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+1//3*c^-1*f^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*x*f^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2//3*im*b^2*c^-1*f^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2//3*b^2*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//3*b^2*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//3*c^2*f^2*x^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+1//3*b*c^-1*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+1//3*b^2*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)+2//3*im*c^-1*f^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+2//3*b^2*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-2//3*im*b*x*f^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-2//3*b*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//3*b*c*f^2*x^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-4//3*im*b*c^-1*f^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^-3//2, x) == :((1/2)*x*d^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+8*x*d^4*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+8*c^-1*d^4*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+1//4*x*b^2*d^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-16*b^2*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-8*im*b^2*c^-1*d^4*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-8*im*c^-1*d^4*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+-8*b^2*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-4*im*c^-1*d^4*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+16*b^2*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-5//2*b^-1*c^-1*d^4*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1//4*b^2*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)+-16*b*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+8*im*a*b*x*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+8*im*x*b^2*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)+-1//2*b*c*d^4*x^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))+32*im*b*c^-1*d^4*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^-3//2, x) == :(4*x*d^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+4*c^-1*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1*im*c^-1*d^3*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1*b^-1*c^-1*d^3*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-8*b^2*c^-1*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-4*im*c^-1*d^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+-4*b^2*c^-1*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-2*im*b^2*c^-1*d^3*(1+c^2*x^2)^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+8*b^2*c^-1*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-8*b*c^-1*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+2*im*a*b*x*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+2*im*x*b^2*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*arcsinh(c*x)+16*im*b*c^-1*d^3*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^-3//2, x) == :(2*x*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+2*c^-1*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-4*b^2*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-2*im*c^-1*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+-2*b^2*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+4*b^2*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-1//3*b^-1*c^-1*d^2*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-4*b*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+8*im*b*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-3//2, x) == :(d*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+d*c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1*im*d*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+-1*d*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-2*d*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+2*d*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-2*b*d*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+4*im*b*d*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2, x) == :(x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(1+c^2*x^2)+c^-1*(1+c^2*x^2)^3//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2+-1*b^2*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-2*b*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-3//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-3//2, x) == :(-1//3*f*x*b^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*f*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+2//3*f*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*f*c^-1*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2//3*f*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//3*im*f*b^2*c^-1*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-1//3*f*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+1//3*im*f*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+1//3*b*f*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+1//3*f*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-4//3*b*f*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//3*im*b*f*x*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-2//3*im*b*f*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^5//2*(f+-1*im*c*f*x)^-5//2, x) == :(28//3*c^-1*d^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+im*c^-1*d^5*(1+c^2*x^2)^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2*im*b^2*c^-1*d^5*(1+c^2*x^2)^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-112//3*b^2*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(-1*arcsinh(c*x)))+5//3*b^-1*c^-1*d^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2*im*a*b*x*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2*im*x*b^2*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)+8//3*b*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*sec(1//4*pi+(1/2)*im*arcsinh(c*x))^2*(a+b*arcsinh(c*x))+16//3*im*b^2*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*tan(1//4*pi+(1/2)*im*arcsinh(c*x))+28//3*im*c^-1*d^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*tan(1//4*pi+(1/2)*im*arcsinh(c*x))+112//3*b*c^-1*d^5*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+im*exp(-1*arcsinh(c*x)))+-4//3*im*c^-1*d^5*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*sec(1//4*pi+(1/2)*im*arcsinh(c*x))^2*tan(1//4*pi+(1/2)*im*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^3//2*(f+-1*im*c*f*x)^-5//2, x) == :(8//3*c^-1*d^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-32//3*b^2*c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(-1*arcsinh(c*x)))+1//3*b^-1*c^-1*d^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^3*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+4//3*b*c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*sec(1//4*pi+(1/2)*im*arcsinh(c*x))^2*(a+b*arcsinh(c*x))+8//3*im*b^2*c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*tan(1//4*pi+(1/2)*im*arcsinh(c*x))+8//3*im*c^-1*d^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*tan(1//4*pi+(1/2)*im*arcsinh(c*x))+32//3*b*c^-1*d^4*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+im*exp(-1*arcsinh(c*x)))+-2//3*im*c^-1*d^4*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*sec(1//4*pi+(1/2)*im*arcsinh(c*x))^2*tan(1//4*pi+(1/2)*im*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^(1/2)*(f+-1*im*c*f*x)^-5//2, x) == :(1//3*c^-1*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-4//3*b^2*c^-1*d^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(-1*arcsinh(c*x)))+1//3*im*c^-1*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*tan(1//4*pi+(1/2)*im*arcsinh(c*x))+2//3*b*c^-1*d^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*sec(1//4*pi+(1/2)*im*arcsinh(c*x))^2*(a+b*arcsinh(c*x))+4//3*im*b^2*c^-1*d^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*tan(1//4*pi+(1/2)*im*arcsinh(c*x))+4//3*b*c^-1*d^3*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+im*exp(-1*arcsinh(c*x)))+-1//3*im*c^-1*d^3*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*sec(1//4*pi+(1/2)*im*arcsinh(c*x))^2*tan(1//4*pi+(1/2)*im*arcsinh(c*x)))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-1//2*(f+-1*im*c*f*x)^-5//2, x) == :(-2//3*x*b^2*d^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*x*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+1//3*c^-1*d^2*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*x*d^2*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2//3*im*c^-1*d^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+-2//3*b^2*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+-1//3*b^2*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//3*c^2*d^2*x^3*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+1//3*b*c^-1*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+1//3*b^2*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*arcsinh(c*x)+2//3*im*b^2*c^-1*d^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*b^2*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-2//3*b*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+-1//3*b*c*d^2*x^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+2//3*im*b*x*d^2*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+4//3*im*b*c^-1*d^2*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-3//2*(f+-1*im*c*f*x)^-5//2, x) == :(-1//3*d*x*b^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*d*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+2//3*d*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*d*c^-1*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2//3*d*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+-1//3*im*d*c^-1*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+-1//3*d*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,im*exp(arcsinh(c*x)))+1//3*im*d*b^2*c^-1*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*b*d*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+1//3*d*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*im*exp(arcsinh(c*x)))+-4//3*b*d*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x)))+1//3*im*b*d*x*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+2//3*im*b*d*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*arctan(exp(arcsinh(c*x))))
@test integrate((a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2, x) == :(-1//3*x*b^2*(1+c^2*x^2)^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+1//3*x*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(1+c^2*x^2)+2//3*x*(1+c^2*x^2)^2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+2//3*c^-1*(1+c^2*x^2)^5//2*(a+b*arcsinh(c*x))^2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2+-2//3*b^2*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*Polylogarithms.polylog(2,-1*exp(2*arcsinh(c*x)))+1//3*b*c^-1*(1+c^2*x^2)^3//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))+-4//3*b*c^-1*(1+c^2*x^2)^5//2*(d+im*c*d*x)^-5//2*(f+-1*im*c*f*x)^-5//2*(a+b*arcsinh(c*x))*log(1+exp(2*arcsinh(c*x))))

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.1 Inverse hyperbolic sine/7.1.4a (f x)^m (d+c^2 d x^2)^p (a+b arcsinh(c x))^n.jl