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

@test integrate(x^3*exp(arccoth(a*x)), x) == :(1//4*x^4*(1+-1*a^-2*x^-2)^(1/2)+3//8*a^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+1//3*a^-1*x^3*(1+-1*a^-2*x^-2)^(1/2)+2//3*x*a^-3*(1+-1*a^-2*x^-2)^(1/2)+3//8*a^-2*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x^2*exp(arccoth(a*x)), x) == :((1/2)*a^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+1//3*x^3*(1+-1*a^-2*x^-2)^(1/2)+(1/2)*a^-1*x^2*(1+-1*a^-2*x^-2)^(1/2)+2//3*x*a^-2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x*exp(arccoth(a*x)), x) == :((1/2)*a^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+(1/2)*x^2*(1+-1*a^-2*x^-2)^(1/2)+x*a^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(exp(arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)+a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-1*exp(arccoth(a*x)), x) == :(-1*arccsc(a*x)+arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-2*exp(arccoth(a*x)), x) == :(a*(1+-1*a^-2*x^-2)^(1/2)+-1*a*arccsc(a*x))
@test integrate(x^-3*exp(arccoth(a*x)), x) == :(-1//2*a^2*arccsc(a*x)+(1/2)*a*(1+-1*a^-2*x^-2)^(1/2)*(x^-1+2a))
@test integrate(x^-4*exp(arccoth(a*x)), x) == :(a^3*(1+-1*a^-2*x^-2)^(1/2)+-1//2*a^3*arccsc(a*x)+-1//3*a^3*(1+-1*a^-2*x^-2)^3//2+(1/2)*a^2*x^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x^-5*exp(arccoth(a*x)), x) == :(-3//8*a^4*arccsc(a*x)+1//3*a^2*x^-2*(1+-1*a^-2*x^-2)^(1/2)+1//4*a*x^-3*(1+-1*a^-2*x^-2)^(1/2)+1//24*a^3*(1+-1*a^-2*x^-2)^(1/2)*(9*x^-1+16a))
@test integrate(x^3*exp(2*arccoth(a*x)), x) == :(1//4*x^4+a^-2*x^2+2*x*a^-3+2*a^-4*log(1+-1*a*x)+2//3*a^-1*x^3)
@test integrate(x^2*exp(2*arccoth(a*x)), x) == :(1//3*x^3+a^-1*x^2+2*x*a^-2+2*a^-3*log(1+-1*a*x))
@test integrate(x*exp(2*arccoth(a*x)), x) == :((1/2)*x^2+2*x*a^-1+2*a^-2*log(1+-1*a*x))
@test integrate(exp(2*arccoth(a*x)), x) == :(x+2*a^-1*log(1+-1*a*x))
@test integrate(x^-1*exp(2*arccoth(a*x)), x) == :(-1*log(x)+2*log(1+-1*a*x))
@test integrate(x^-2*exp(2*arccoth(a*x)), x) == :(x^-1+-2*a*log(x)+2*a*log(1+-1*a*x))
@test integrate(x^-3*exp(2*arccoth(a*x)), x) == :((1/2)*x^-2+-2*a^2*log(x)+2*a*x^-1+2*a^2*log(1+-1*a*x))
@test integrate(x^-4*exp(2*arccoth(a*x)), x) == :(1//3*x^-3+a*x^-2+-2*a^3*log(x)+2*a^2*x^-1+2*a^3*log(1+-1*a*x))
@test integrate(x^2*exp(3*arccoth(a*x)), x) == :(1//3*x^3*(1+-1*a^-2*x^-2)^(1/2)+11//2*a^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-4*a^-2*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+3//2*a^-1*x^2*(1+-1*a^-2*x^-2)^(1/2)+14//3*x*a^-2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x*exp(3*arccoth(a*x)), x) == :((1/2)*x^2*(1+-1*a^-2*x^-2)^(1/2)+9//2*a^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+-4*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+3*x*a^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(exp(3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)+-4*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+3*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-1*exp(3*arccoth(a*x)), x) == :(-4*a*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+arccsc(a*x)+arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-2*exp(3*arccoth(a*x)), x) == :(-3*a*(1+-1*a^-2*x^-2)^(1/2)+3*a*arccsc(a*x)+-2*a^-1*(1+-1*a^-2*x^-2)^-1//2*(a+x^-1)^2)
@test integrate(x^-3*exp(3*arccoth(a*x)), x) == :(-9//2*a^2*(1+-1*a^-2*x^-2)^(1/2)+9//2*a^2*arccsc(a*x)+-1*a^5*(1+-1*a^-2*x^-2)^5//2*(a+-1*x^-1)^-3+-3*a^3*(1+-1*a^-2*x^-2)^3//2*(-2*x^-1+2a)^-1)
@test integrate(x^-4*exp(3*arccoth(a*x)), x) == :(-1*(1+-1*a^-2*x^-2)^-1//2*(a+x^-1)^3+11//2*a^3*arccsc(a*x)+-1//3*a*(1+-1*a^-2*x^-2)^(1/2)*(x^-1+3a)^2+-1//6*a^2*(1+-1*a^-2*x^-2)^(1/2)*(3*x^-1+28a))
@test integrate(x^3*exp(4*arccoth(a*x)), x) == :(1//4*x^4+4*a^-4*(1+-1*a*x)^-1+4*a^-2*x^2+12*x*a^-3+16*a^-4*log(1+-1*a*x)+4//3*a^-1*x^3)
@test integrate(x^2*exp(4*arccoth(a*x)), x) == :(1//3*x^3+2*a^-1*x^2+4*a^-3*(1+-1*a*x)^-1+8*x*a^-2+12*a^-3*log(1+-1*a*x))
@test integrate(x*exp(4*arccoth(a*x)), x) == :((1/2)*x^2+4*x*a^-1+4*a^-2*(1+-1*a*x)^-1+8*a^-2*log(1+-1*a*x))
@test integrate(exp(4*arccoth(a*x)), x) == :(x+4*a^-1*(1+-1*a*x)^-1+4*a^-1*log(1+-1*a*x))
@test integrate(x^-1*exp(4*arccoth(a*x)), x) == :(4*(1+-1*a*x)^-1+log(x))
@test integrate(x^-2*exp(4*arccoth(a*x)), x) == :(-1*x^-1+-4*a*log(1+-1*a*x)+4*a*(1+-1*a*x)^-1+4*a*log(x))
@test integrate(x^-3*exp(4*arccoth(a*x)), x) == :(-1//2*x^-2+-8*a^2*log(1+-1*a*x)+-4*a*x^-1+4*a^2*(1+-1*a*x)^-1+8*a^2*log(x))
@test integrate(x^-4*exp(4*arccoth(a*x)), x) == :(-1//3*x^-3+-12*a^3*log(1+-1*a*x)+-8*a^2*x^-1+-2*a*x^-2+4*a^3*(1+-1*a*x)^-1+12*a^3*log(x))
@test integrate(x^3*exp(-1*arccoth(a*x)), x) == :(1//4*x^4*(1+-1*a^-2*x^-2)^(1/2)+3//8*a^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-2//3*x*a^-3*(1+-1*a^-2*x^-2)^(1/2)+-1//3*a^-1*x^3*(1+-1*a^-2*x^-2)^(1/2)+3//8*a^-2*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x^2*exp(-1*arccoth(a*x)), x) == :(-1//2*a^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+1//3*x^3*(1+-1*a^-2*x^-2)^(1/2)+-1//2*a^-1*x^2*(1+-1*a^-2*x^-2)^(1/2)+2//3*x*a^-2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x*exp(-1*arccoth(a*x)), x) == :((1/2)*a^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+(1/2)*x^2*(1+-1*a^-2*x^-2)^(1/2)+-1*x*a^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(exp(-1*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)+-1*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-1*exp(-1*arccoth(a*x)), x) == :(arccsc(a*x)+arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-2*exp(-1*arccoth(a*x)), x) == :(-1*a*(1+-1*a^-2*x^-2)^(1/2)+-1*a*arccsc(a*x))
@test integrate(x^-3*exp(-1*arccoth(a*x)), x) == :((1/2)*a^2*arccsc(a*x)+(1/2)*a*(1+-1*a^-2*x^-2)^(1/2)*(-1*x^-1+2a))
@test integrate(x^-4*exp(-1*arccoth(a*x)), x) == :(-1*a^3*(1+-1*a^-2*x^-2)^(1/2)+-1//2*a^3*arccsc(a*x)+1//3*a^3*(1+-1*a^-2*x^-2)^3//2+(1/2)*a^2*x^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x^-5*exp(-1*arccoth(a*x)), x) == :(3//8*a^4*arccsc(a*x)+-1//4*a*x^-3*(1+-1*a^-2*x^-2)^(1/2)+1//3*a^2*x^-2*(1+-1*a^-2*x^-2)^(1/2)+1//24*a^3*(1+-1*a^-2*x^-2)^(1/2)*(-9*x^-1+16a))
@test integrate(x^3*exp(-2*arccoth(a*x)), x) == :(1//4*x^4+a^-2*x^2+-2*x*a^-3+2*a^-4*log(1+a*x)+-2//3*a^-1*x^3)
@test integrate(x^2*exp(-2*arccoth(a*x)), x) == :(1//3*x^3+-1*a^-1*x^2+-2*a^-3*log(1+a*x)+2*x*a^-2)
@test integrate(x*exp(-2*arccoth(a*x)), x) == :((1/2)*x^2+-2*x*a^-1+2*a^-2*log(1+a*x))
@test integrate(exp(-2*arccoth(a*x)), x) == :(x+-2*a^-1*log(1+a*x))
@test integrate(x^-1*exp(-2*arccoth(a*x)), x) == :(-1*log(x)+2*log(1+a*x))
@test integrate(x^-2*exp(-2*arccoth(a*x)), x) == :(x^-1+-2*a*log(1+a*x)+2*a*log(x))
@test integrate(x^-3*exp(-2*arccoth(a*x)), x) == :((1/2)*x^-2+-2*a*x^-1+-2*a^2*log(x)+2*a^2*log(1+a*x))
@test integrate(x^-4*exp(-2*arccoth(a*x)), x) == :(1//3*x^-3+-1*a*x^-2+-2*a^3*log(1+a*x)+2*a^2*x^-1+2*a^3*log(x))
@test integrate(x^3*exp(-3*arccoth(a*x)), x) == :(1//4*x^4*(1+-1*a^-2*x^-2)^(1/2)+51//8*a^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1*a^-1*x^3*(1+-1*a^-2*x^-2)^(1/2)+-6*x*a^-3*(1+-1*a^-2*x^-2)^(1/2)+-4*a^-3*(1+-1*a^-2*x^-2)^(1/2)*(a+x^-1)^-1+19//8*a^-2*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x^2*exp(-3*arccoth(a*x)), x) == :(-11//2*a^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+1//3*x^3*(1+-1*a^-2*x^-2)^(1/2)+4*a^-2*(1+-1*a^-2*x^-2)^(1/2)*(a+x^-1)^-1+-3//2*a^-1*x^2*(1+-1*a^-2*x^-2)^(1/2)+14//3*x*a^-2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x*exp(-3*arccoth(a*x)), x) == :((1/2)*x^2*(1+-1*a^-2*x^-2)^(1/2)+9//2*a^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+-4*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(a+x^-1)^-1+-3*x*a^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(exp(-3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)+-3*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+4*(1+-1*a^-2*x^-2)^(1/2)*(a+x^-1)^-1)
@test integrate(x^-1*exp(-3*arccoth(a*x)), x) == :(-1*arccsc(a*x)+-4*a*(1+-1*a^-2*x^-2)^(1/2)*(a+x^-1)^-1+arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate(x^-2*exp(-3*arccoth(a*x)), x) == :(3*a*(1+-1*a^-2*x^-2)^(1/2)+3*a*arccsc(a*x)+2*a^-1*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)^2)
@test integrate(x^-3*exp(-3*arccoth(a*x)), x) == :(-9//2*a^2*(1+-1*a^-2*x^-2)^(1/2)+-9//2*a^2*arccsc(a*x)+-1*a^5*(1+-1*a^-2*x^-2)^5//2*(a+x^-1)^-3+-3*a^3*(1+-1*a^-2*x^-2)^3//2*(2a+2*x^-1)^-1)
@test integrate(x^-4*exp(-3*arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)^3+11//2*a^3*arccsc(a*x)+1//3*a*(1+-1*a^-2*x^-2)^(1/2)*(-1*x^-1+3a)^2+1//6*a^2*(1+-1*a^-2*x^-2)^(1/2)*(-3*x^-1+28a))
@test integrate(x^-5*exp(-3*arccoth(a*x)), x) == :(-51//8*a^4*arccsc(a*x)+-27//4*a^4*(1+-1*a^-2*x^-2)^(1/2)+-1*a*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)^3+-1*a^2*x^-2*(1+-1*a^-2*x^-2)^(1/2)+-9//8*a^3*(1+-1*a^-2*x^-2)^(1/2)*(-3*x^-1+2a)+1//4*a*x^-3*(1+-1*a^-2*x^-2)^(1/2))
@test integrate(x^4*exp((1/2)*arccoth(a*x)), x) == :(31//128*a^-5*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+31//128*a^-5*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//5*x^5*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+9//40*a^-1*x^4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+11//48*a^-2*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+269//960*a^-3*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+611//1920*x*a^-4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^3*exp((1/2)*arccoth(a*x)), x) == :(11//64*a^-4*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+11//64*a^-4*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//4*x^4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+7//24*a^-1*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+29//96*a^-2*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+83//192*x*a^-3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^2*exp((1/2)*arccoth(a*x)), x) == :(3//8*a^-3*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+3//8*a^-3*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//3*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+5//12*a^-1*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+11//24*x*a^-2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x*exp((1/2)*arccoth(a*x)), x) == :(1//4*a^-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//4*a^-2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+(1/2)*x^2*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^3//4+1//4*x*a^-1*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(exp((1/2)*arccoth(a*x)), x) == :(a^-1*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+a^-1*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+x*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^-1*exp((1/2)*arccoth(a*x)), x) == :(2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-2*exp((1/2)*arccoth(a*x)), x) == :(a*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+(1/2)*a*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//2*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-3*exp((1/2)*arccoth(a*x)), x) == :((1/2)*a^2*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^3//4+-1//8*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//4*a^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+1//8*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-4*exp((1/2)*arccoth(a*x)), x) == :(-3//16*2^(1/2)*a^3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-3//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//12*a^3*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^3//4+3//8*a^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+3//16*2^(1/2)*a^3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//3*a^2*x^-1*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^4*exp(3//2*arccoth(a*x)), x) == :(-237//128*a^-5*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+237//128*a^-5*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//5*x^5*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+5//16*a^-2*x^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+11//40*a^-1*x^4*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+157//320*a^-3*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+557//640*x*a^-4*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^3*exp(3//2*arccoth(a*x)), x) == :(-123//64*a^-4*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+123//64*a^-4*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//4*x^4*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+3//8*a^-1*x^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+15//32*a^-2*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+63//64*x*a^-3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^2*exp(3//2*arccoth(a*x)), x) == :(-17//8*a^-3*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+17//8*a^-3*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//3*x^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+7//12*a^-1*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+23//24*x*a^-2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x*exp(3//2*arccoth(a*x)), x) == :(-9//4*a^-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+9//4*a^-2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+(1/2)*x^2*(1+a^-1*x^-1)^7//4*(1+-1*a^-1*x^-1)^1//4+3//4*x*a^-1*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(exp(3//2*arccoth(a*x)), x) == :(-3*a^-1*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+3*a^-1*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+x*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^-1*exp(3//2*arccoth(a*x)), x) == :(-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-2*exp(3//2*arccoth(a*x)), x) == :(a*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-3//2*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-3//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//2*a*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-3*exp(3//2*arccoth(a*x)), x) == :((1/2)*a^2*(1+a^-1*x^-1)^7//4*(1+-1*a^-1*x^-1)^1//4+-9//8*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-9//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//4*a^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+9//8*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+9//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-4*exp(3//2*arccoth(a*x)), x) == :(-17//16*2^(1/2)*a^3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-17//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//4*a^3*(1+a^-1*x^-1)^7//4*(1+-1*a^-1*x^-1)^1//4+17//16*2^(1/2)*a^3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+17//24*a^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+17//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//3*a^2*x^-1*(1+a^-1*x^-1)^7//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^4*exp(5//2*arccoth(a*x)), x) == :(1003//128*a^-5*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1003//128*a^-5*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-26111//1920*a^-5*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+1//5*x^5*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+21//40*a^-1*x^4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+181//240*a^-2*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+1189//960*a^-3*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+5533//1920*x*a^-4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)
@test integrate(x^3*exp(5//2*arccoth(a*x)), x) == :(475//64*a^-4*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+475//64*a^-4*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-2467//192*a^-4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+1//4*x^4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+17//24*a^-1*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+113//96*a^-2*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+521//192*x*a^-3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)
@test integrate(x^2*exp(5//2*arccoth(a*x)), x) == :(55//8*a^-3*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+55//8*a^-3*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-287//24*a^-3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+1//3*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+13//12*a^-1*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+61//24*x*a^-2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)
@test integrate(x*exp(5//2*arccoth(a*x)), x) == :(25//4*a^-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+25//4*a^-2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+(1/2)*x^2*(1+a^-1*x^-1)^9//4*(1+-1*a^-1*x^-1)^-1//4+-25//2*a^-2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+5//4*x*a^-1*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^-1//4)
@test integrate(exp(5//2*arccoth(a*x)), x) == :(5*a^-1*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+5*a^-1*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+x*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^-1//4+-10*a^-1*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)
@test integrate(x^-1*exp(5//2*arccoth(a*x)), x) == :(2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-8*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-2*exp(5//2*arccoth(a*x)), x) == :(-5*a*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-4*a*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^-1//4+-5//2*a*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-5//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+5//2*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+5//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-3*exp(5//2*arccoth(a*x)), x) == :(-2*a^2*(1+a^-1*x^-1)^9//4*(1+-1*a^-1*x^-1)^-1//4+-25//4*a^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-25//8*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-25//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-5//2*a^2*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^3//4+25//8*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+25//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-4*exp(5//2*arccoth(a*x)), x) == :(-2*a^3*(1+a^-1*x^-1)^9//4*(1+-1*a^-1*x^-1)^-1//4+-55//8*a^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-55//16*2^(1/2)*a^3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-55//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-11//4*a^3*(1+a^-1*x^-1)^5//4*(1+-1*a^-1*x^-1)^3//4+-1//3*a^3*(1+a^-1*x^-1)^9//4*(1+-1*a^-1*x^-1)^3//4+55//16*2^(1/2)*a^3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+55//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^4*exp(-1//2*arccoth(a*x)), x) == :(-31//128*a^-5*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+31//128*a^-5*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//5*x^5*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-269//960*a^-3*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-9//40*a^-1*x^4*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+11//48*a^-2*x^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+611//1920*x*a^-4*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^3*exp(-1//2*arccoth(a*x)), x) == :(-11//64*a^-4*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+11//64*a^-4*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//4*x^4*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-83//192*x*a^-3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-7//24*a^-1*x^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+29//96*a^-2*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^2*exp(-1//2*arccoth(a*x)), x) == :(-3//8*a^-3*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+3//8*a^-3*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//3*x^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-5//12*a^-1*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+11//24*x*a^-2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x*exp(-1//2*arccoth(a*x)), x) == :(-1//4*a^-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//4*a^-2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+(1/2)*x^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^5//4+-1//4*x*a^-1*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(exp(-1//2*arccoth(a*x)), x) == :(a^-1*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-1*a^-1*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+x*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^-1*exp(-1//2*arccoth(a*x)), x) == :(-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-2*exp(-1//2*arccoth(a*x)), x) == :((1/2)*a*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*a*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-1//2*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-3*exp(-1//2*arccoth(a*x)), x) == :((1/2)*a^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^5//4+-1//8*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//4*a^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+1//8*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-4*exp(-1//2*arccoth(a*x)), x) == :(-3//8*a^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-3//16*2^(1/2)*a^3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-3//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//12*a^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^5//4+3//16*2^(1/2)*a^3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//3*a^2*x^-1*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^5//4)
@test integrate(x^4*exp(-3//2*arccoth(a*x)), x) == :(-237//128*a^-5*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-237//128*a^-5*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//5*x^5*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-157//320*a^-3*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-11//40*a^-1*x^4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+5//16*a^-2*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+557//640*x*a^-4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^3*exp(-3//2*arccoth(a*x)), x) == :(123//64*a^-4*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+123//64*a^-4*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//4*x^4*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-63//64*x*a^-3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-3//8*a^-1*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+15//32*a^-2*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^2*exp(-3//2*arccoth(a*x)), x) == :(-17//8*a^-3*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-17//8*a^-3*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//3*x^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-7//12*a^-1*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+23//24*x*a^-2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x*exp(-3//2*arccoth(a*x)), x) == :(9//4*a^-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+9//4*a^-2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+(1/2)*x^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^7//4+-3//4*x*a^-1*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(exp(-3//2*arccoth(a*x)), x) == :(-3*a^-1*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-3*a^-1*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+x*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4)
@test integrate(x^-1*exp(-3//2*arccoth(a*x)), x) == :(2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-2*exp(-3//2*arccoth(a*x)), x) == :(-1*a*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-3//2*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-3//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//2*a*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-3*exp(-3//2*arccoth(a*x)), x) == :((1/2)*a^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^7//4+-9//8*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-9//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+3//4*a^2*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+9//8*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+9//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-4*exp(-3//2*arccoth(a*x)), x) == :(-17//16*2^(1/2)*a^3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-17//24*a^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^3//4+-17//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1//4*a^3*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^7//4+17//16*2^(1/2)*a^3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+17//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//3*a^2*x^-1*(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^7//4)
@test integrate(x^4*exp(-5//2*arccoth(a*x)), x) == :(-1003//128*a^-5*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1003//128*a^-5*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//5*x^5*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+26111//1920*a^-5*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1189//960*a^-3*x^2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-21//40*a^-1*x^4*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+181//240*a^-2*x^3*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+5533//1920*x*a^-4*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^3*exp(-5//2*arccoth(a*x)), x) == :(-475//64*a^-4*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+475//64*a^-4*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+-2467//192*a^-4*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+1//4*x^4*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-521//192*x*a^-3*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-17//24*a^-1*x^3*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+113//96*a^-2*x^2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^2*exp(-5//2*arccoth(a*x)), x) == :(-55//8*a^-3*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+55//8*a^-3*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+1//3*x^3*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+287//24*a^-3*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-13//12*a^-1*x^2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+61//24*x*a^-2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x*exp(-5//2*arccoth(a*x)), x) == :(-25//4*a^-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+25//4*a^-2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+(1/2)*x^2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^9//4+-25//2*a^-2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-5//4*x*a^-1*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^5//4)
@test integrate(exp(-5//2*arccoth(a*x)), x) == :(-5*a^-1*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+5*a^-1*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+x*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^5//4+10*a^-1*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)
@test integrate(x^-1*exp(-5//2*arccoth(a*x)), x) == :(-2*arctan((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2*arctanh((1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4)+2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-8*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-2*exp(-5//2*arccoth(a*x)), x) == :(4*a*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^5//4+5*a*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-5//2*a*2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-5//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+5//2*a*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+5//4*a*2^(1/2)*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-3*exp(-5//2*arccoth(a*x)), x) == :(-2*a^2*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^9//4+-25//4*a^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+-25//8*2^(1/2)*a^2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-25//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-5//2*a^2*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^5//4+25//8*2^(1/2)*a^2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+25//16*2^(1/2)*a^2*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^-4*exp(-5//2*arccoth(a*x)), x) == :(2*a^3*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^9//4+-55//16*2^(1/2)*a^3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+-55//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+1//3*a^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^9//4+11//4*a^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^5//4+55//8*a^3*(1+a^-1*x^-1)^3//4*(1+-1*a^-1*x^-1)^1//4+55//16*2^(1/2)*a^3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4)+55//32*2^(1/2)*a^3*log(1+(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+-1*2^(1/2)*(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4))
@test integrate(x^2*exp(1//3*arccoth(x)), x) == :(-19//324*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+-1*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+19//81*arctanh((x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+19//324*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+-19//162*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+19//162*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+1//3*x^3*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6+7//18*x^2*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6+11//27*x*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6)
@test integrate(x*exp(1//3*arccoth(x)), x) == :(-1//36*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+-1*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+1//9*arctanh((x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+1//36*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+-1//18*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+1//18*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+(1/2)*x^2*(x^-1*(-1+x))^5//6*(1+x^-1)^7//6+1//6*x*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6)
@test integrate(exp(1//3*arccoth(x)), x) == :(-1//6*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+-1*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+1//6*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+2//3*arctanh((x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+-1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+x*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6)
@test integrate(x^-1*exp(1//3*arccoth(x)), x) == :((1/2)*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+-1*arctan(3^(1/2)+-2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+2*arctan((x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+2*arctanh((x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+-1//2*log(1+(x^-1*(-1+x))^-1//3*(1+x^-1)^1//3+-1*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6)+3^(1/2)*arctan(1//3*3^(1/2)*(1+2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+(1/2)*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+-1*3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+-1*3^(1/2)*arctan(1//3*3^(1/2)*(1+-2*(x^-1*(-1+x))^-1//6*(1+x^-1)^1//6))+-1//2*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+arctan(3^(1/2)+2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6))
@test integrate(x^-2*exp(1//3*arccoth(x)), x) == :(-1//3*arctan(3^(1/2)+-2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//3*arctan(3^(1/2)+2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+2//3*arctan((x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+(x^-1*(-1+x))^5//6*(1+x^-1)^1//6+-1//6*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//6*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+-1*3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6))
@test integrate(x^-3*exp(1//3*arccoth(x)), x) == :(-1//18*arctan(3^(1/2)+-2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//9*arctan((x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//18*arctan(3^(1/2)+2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+(1/2)*(x^-1*(-1+x))^5//6*(1+x^-1)^7//6+-1//36*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//6*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6+1//36*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+-1*3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6))
@test integrate(x^-4*exp(1//3*arccoth(x)), x) == :(-19//162*arctan(3^(1/2)+-2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+19//81*arctan((x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+19//162*arctan(3^(1/2)+2*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+-19//324*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//18*(x^-1*(-1+x))^5//6*(1+x^-1)^7//6+19//54*(x^-1*(-1+x))^5//6*(1+x^-1)^1//6+19//324*3^(1/2)*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3+-1*3^(1/2)*(x^-1*(-1+x))^1//6*(1+x^-1)^-1//6)+1//3*x^-1*(x^-1*(-1+x))^5//6*(1+x^-1)^7//6)
@test integrate(x^2*exp(2//3*arccoth(x)), x) == :(-11//27*log((1+x^-1)^1//3+-1*(x^-1*(-1+x))^1//3)+-11//81*log(x)+-22//81*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+1//3*x^3*(x^-1*(-1+x))^2//3*(1+x^-1)^1//3+4//9*x^2*(x^-1*(-1+x))^2//3*(1+x^-1)^1//3+14//27*x*(x^-1*(-1+x))^2//3*(1+x^-1)^1//3)
@test integrate(x*exp(2//3*arccoth(x)), x) == :(-1//3*log((1+x^-1)^1//3+-1*(x^-1*(-1+x))^1//3)+-1//9*log(x)+-2//9*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+(1/2)*x^2*(x^-1*(-1+x))^2//3*(1+x^-1)^4//3+1//3*x*(x^-1*(-1+x))^2//3*(1+x^-1)^1//3)
@test integrate(exp(2//3*arccoth(x)), x) == :(-1*log((1+x^-1)^1//3+-1*(x^-1*(-1+x))^1//3)+-1//3*log(x)+-2//3*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+x*(x^-1*(-1+x))^2//3*(1+x^-1)^1//3)
@test integrate(x^-1*exp(2//3*arccoth(x)), x) == :(-3//2*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+-3//2*log((1+x^-1)^1//3+-1*(x^-1*(-1+x))^1//3)+-1//2*log(x)+-1//2*log(1+x^-1)+-1*3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+-1*3^(1/2)*arctan(1//3*3^(1/2)+2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3))
@test integrate(x^-2*exp(2//3*arccoth(x)), x) == :(-1*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+-1//3*log(1+x^-1)+(x^-1*(-1+x))^2//3*(1+x^-1)^1//3+-2//3*3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3))
@test integrate(x^-3*exp(2//3*arccoth(x)), x) == :(-1//3*log(1+(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+-1//9*log(1+x^-1)+(1/2)*(x^-1*(-1+x))^2//3*(1+x^-1)^4//3+-2//9*3^(1/2)*arctan(1//3*3^(1/2)+-2//3*3^(1/2)*(x^-1*(-1+x))^1//3*(1+x^-1)^-1//3)+1//3*(x^-1*(-1+x))^2//3*(1+x^-1)^1//3)
@test integrate(x^2*exp(1//4*arccoth(a*x)), x) == :(11//64*a^-3*arctan((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+11//64*a^-3*arctanh((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+-11//128*2^(1/2)*a^-3*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+-11//256*2^(1/2)*a^-3*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//3*x^3*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8+11//128*2^(1/2)*a^-3*arctan(1+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+11//256*2^(1/2)*a^-3*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+3//8*a^-1*x^2*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8+37//96*x*a^-2*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8)
@test integrate(x*exp(1//4*arccoth(a*x)), x) == :(1//16*a^-2*arctan((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//16*a^-2*arctanh((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+(1/2)*x^2*(1+a^-1*x^-1)^9//8*(1+-1*a^-1*x^-1)^7//8+-1//32*2^(1/2)*a^-2*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+-1//64*2^(1/2)*a^-2*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//32*2^(1/2)*a^-2*arctan(1+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//64*2^(1/2)*a^-2*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//8*x*a^-1*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8)
@test integrate(exp(1//4*arccoth(a*x)), x) == :((1/2)*a^-1*arctan((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+(1/2)*a^-1*arctanh((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+x*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8+-1//4*2^(1/2)*a^-1*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+-1//8*2^(1/2)*a^-1*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//4*2^(1/2)*a^-1*arctan(1+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+1//8*2^(1/2)*a^-1*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8))
@test integrate(x^-1*exp(1//4*arccoth(a*x)), x) == :(2*arctan((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+2*arctanh((1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+2^(1/2)*arctan(1+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+(1/2)*2^(1/2)*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+(1/2)*(2+2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+2^(1/2))^(1/2))+(1/2)*(2+-1*2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+-1*2^(1/2))^(1/2))+-1*2^(1/2)*arctan(1+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+-1*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+-1*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+-1//2*2^(1/2)*log(1+(1+a^-1*x^-1)^1//4*(1+-1*a^-1*x^-1)^-1//4+-1*2^(1/2)*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^-1//8)+-1//2*(2+2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+2^(1/2))^(1/2))+-1//2*(2+-1*2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^-2*exp(1//4*arccoth(a*x)), x) == :(a*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8+-1//4*a*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+-1//4*a*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+-1//8*a*(2+2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+2^(1/2))^(1/2))+-1//8*a*(2+-1*2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+-1*2^(1/2))^(1/2))+1//4*a*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+1//4*a*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+1//8*a*(2+2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+2^(1/2))^(1/2))+1//8*a*(2+-1*2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+-1*2^(1/2))^(1/2)))
@test integrate(x^-3*exp(1//4*arccoth(a*x)), x) == :((1/2)*a^2*(1+a^-1*x^-1)^9//8*(1+-1*a^-1*x^-1)^7//8+-1//32*a^2*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+-2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+-1//32*a^2*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+-2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+-1//64*a^2*(2+2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+2^(1/2))^(1/2))+-1//64*a^2*(2+-1*2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+-1*2^(1/2))^(1/2))+1//8*a^2*(1+a^-1*x^-1)^1//8*(1+-1*a^-1*x^-1)^7//8+1//32*a^2*(2+2^(1/2))^(1/2)*arctan((2+2^(1/2))^-1//2*((2+-1*2^(1/2))^(1/2)+2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+1//32*a^2*(2+-1*2^(1/2))^(1/2)*arctan((2+-1*2^(1/2))^-1//2*((2+2^(1/2))^(1/2)+2*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8))+1//64*a^2*(2+2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+2^(1/2))^(1/2))+1//64*a^2*(2+-1*2^(1/2))^(1/2)*log(1+(1+a^-1*x^-1)^-1//4*(1+-1*a^-1*x^-1)^1//4+-1*(1+a^-1*x^-1)^-1//8*(1+-1*a^-1*x^-1)^1//8*(2+-1*2^(1/2))^(1/2)))
@test integrate((c+-1*a*c*x)^4*exp(arccoth(a*x)), x) == :(7//8*a^-1*c^4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-7//8*a*c^4*x^2*(1+-1*a^-2*x^-2)^(1/2)+-3//4*a^3*c^4*x^4*(1+-1*a^-2*x^-2)^3//2+1//5*a^4*c^4*x^5*(1+-1*a^-2*x^-2)^3//2+17//15*a^2*c^4*x^3*(1+-1*a^-2*x^-2)^3//2)
@test integrate((c+-1*a*c*x)^3*exp(arccoth(a*x)), x) == :(5//8*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-5//8*a*c^3*x^2*(1+-1*a^-2*x^-2)^(1/2)+-1//4*a^3*c^3*x^4*(1+-1*a^-2*x^-2)^3//2+2//3*a^2*c^3*x^3*(1+-1*a^-2*x^-2)^3//2)
@test integrate((c+-1*a*c*x)^2*exp(arccoth(a*x)), x) == :((1/2)*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//2*a*c^2*x^2*(1+-1*a^-2*x^-2)^(1/2)+1//3*a^2*c^2*x^3*(1+-1*a^-2*x^-2)^3//2)
@test integrate((c+-1*a*c*x)*exp(arccoth(a*x)), x) == :((1/2)*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//2*a*c*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^-1*exp(arccoth(a*x)), x) == :(-1*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+a^-2*c^-1*(1+-1*a^-2*x^-2)^-1//2*(2a+2*x^-1))
@test integrate((c+-1*a*c*x)^-2*exp(arccoth(a*x)), x) == :(-1//3*a^2*c^-2*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-3)
@test integrate((c+-1*a*c*x)^-3*exp(arccoth(a*x)), x) == :(-4//15*a^2*c^-3*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-3+1//5*a^3*c^-3*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-4)
@test integrate((c+-1*a*c*x)^-4*exp(arccoth(a*x)), x) == :(-23//105*a^2*c^-4*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-3+-1//7*a^4*c^-4*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-5+12//35*a^3*c^-4*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-4)
@test integrate((c+-1*a*c*x)^-5*exp(arccoth(a*x)), x) == :(-58//315*a^2*c^-5*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-3+-8//21*a^4*c^-5*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-5+1//9*a^5*c^-5*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-6+47//105*a^3*c^-5*(1+-1*a^-2*x^-2)^3//2*(a+-1*x^-1)^-4)
@test integrate((c+-1*a*c*x)^p*exp(2*arccoth(a*x)), x) == :(2*a^-1*p^-1*(c+-1*a*c*x)^p+-1*a^-1*c^-1*(1+p)^-1*(c+-1*a*c*x)^(1+p))
@test integrate((c+-1*a*c*x)^5*exp(2*arccoth(a*x)), x) == :(-1//6*a^-1*c^5*(1+-1*a*x)^6+2//5*a^-1*c^5*(1+-1*a*x)^5)
@test integrate((c+-1*a*c*x)^4*exp(2*arccoth(a*x)), x) == :((1/2)*a^-1*c^4*(1+-1*a*x)^4+-1//5*a^-1*c^4*(1+-1*a*x)^5)
@test integrate((c+-1*a*c*x)^3*exp(2*arccoth(a*x)), x) == :(-1//4*a^-1*c^3*(1+-1*a*x)^4+2//3*a^-1*c^3*(1+-1*a*x)^3)
@test integrate((c+-1*a*c*x)^2*exp(2*arccoth(a*x)), x) == :(-1*x*c^2+1//3*a^2*c^2*x^3)
@test integrate((c+-1*a*c*x)^-1*exp(2*arccoth(a*x)), x) == :(-1*a^-1*c^-1*log(1+-1*a*x)+-2*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*a*c*x)^-2*exp(2*arccoth(a*x)), x) == :(-1*x*c^-2*(1+-1*a*x)^-2)
@test integrate((c+-1*a*c*x)^-3*exp(2*arccoth(a*x)), x) == :((1/2)*a^-1*c^-3*(1+-1*a*x)^-2+-2//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^-4*exp(2*arccoth(a*x)), x) == :(-1//2*a^-1*c^-4*(1+-1*a*x)^-4+1//3*a^-1*c^-4*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^4*exp(3*arccoth(a*x)), x) == :(-3//8*a^-1*c^4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//4*a^3*c^4*x^4*(1+-1*a^-2*x^-2)^3//2+1//5*a^4*c^4*x^5*(1+-1*a^-2*x^-2)^5//2+3//8*a*c^4*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^3*exp(3*arccoth(a*x)), x) == :(-3//8*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//4*a^3*c^3*x^4*(1+-1*a^-2*x^-2)^3//2+3//8*a*c^3*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^2*exp(3*arccoth(a*x)), x) == :(-1//2*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+(1/2)*a*c^2*x^2*(1+-1*a^-2*x^-2)^(1/2)+1//3*a^2*c^2*x^3*(1+-1*a^-2*x^-2)^3//2)
@test integrate((c+-1*a*c*x)*exp(3*arccoth(a*x)), x) == :(-2*c*x*(1+-1*a^-2*x^-2)^(1/2)+-3//2*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//2*a*c*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^-1*exp(3*arccoth(a*x)), x) == :(-1*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+1//3*a^-2*c^-1*(1+-1*a^-2*x^-2)^-3//2*(8a+8*x^-1)+4//3*a^-2*c^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2)
@test integrate((c+-1*a*c*x)^-2*exp(3*arccoth(a*x)), x) == :(-1//5*a^4*c^-2*(1+-1*a^-2*x^-2)^5//2*(a+-1*x^-1)^-5)
@test integrate((c+-1*a*c*x)^-3*exp(3*arccoth(a*x)), x) == :(-6//35*a^4*c^-3*(1+-1*a^-2*x^-2)^5//2*(a+-1*x^-1)^-5+1//7*a^5*c^-3*(1+-1*a^-2*x^-2)^5//2*(a+-1*x^-1)^-6)
@test integrate((c+-1*a*c*x)^-4*exp(3*arccoth(a*x)), x) == :(-47//315*a^-6*c^-4*(1+-1*a^-2*x^-2)^-5//2*(a+x^-1)^5+-1//9*a^-8*c^-4*(1+-1*a^-2*x^-2)^-9//2*(a+x^-1)^7+16//63*a^-7*c^-4*(1+-1*a^-2*x^-2)^-7//2*(a+x^-1)^6)
@test integrate((c+-1*a*c*x)^-5*exp(3*arccoth(a*x)), x) == :(-152//1155*a^-6*c^-5*(1+-1*a^-2*x^-2)^-5//2*(a+x^-1)^5+-10//33*a^-8*c^-5*(1+-1*a^-2*x^-2)^-9//2*(a+x^-1)^7+1//11*a^-9*c^-5*(1+-1*a^-2*x^-2)^-11//2*(a+x^-1)^8+79//231*a^-7*c^-5*(1+-1*a^-2*x^-2)^-7//2*(a+x^-1)^6)
@test integrate((c+-1*a*c*x)^p*exp(4*arccoth(a*x)), x) == :(4*a^-1*p^-1*(c+-1*a*c*x)^p+-1*a^-1*c^-1*(1+p)^-1*(c+-1*a*c*x)^(1+p)+4*c*a^-1*(1+-1p)^-1*(c+-1*a*c*x)^(-1+p))
@test integrate((c+-1*a*c*x)^5*exp(4*arccoth(a*x)), x) == :(-1*a^-1*c^5*(1+-1*a*x)^4+-1//6*a^-1*c^5*(1+-1*a*x)^6+4//5*a^-1*c^5*(1+-1*a*x)^5)
@test integrate((c+-1*a*c*x)^4*exp(4*arccoth(a*x)), x) == :(x*c^4+-2//3*a^2*c^4*x^3+1//5*a^4*c^4*x^5)
@test integrate((c+-1*a*c*x)^3*exp(4*arccoth(a*x)), x) == :(-1//4*a^-1*c^3*(1+a*x)^4+2//3*a^-1*c^3*(1+a*x)^3)
@test integrate((c+-1*a*c*x)^2*exp(4*arccoth(a*x)), x) == :(1//3*a^-1*c^2*(1+a*x)^3)
@test integrate((c+-1*a*c*x)*exp(4*arccoth(a*x)), x) == :(-3*c*x+-4*c*a^-1*log(1+-1*a*x)+-1//2*a*c*x^2)
@test integrate((c+-1*a*c*x)^-1*exp(4*arccoth(a*x)), x) == :(-1*a^-1*c^-1*log(1+-1*a*x)+-4*a^-1*c^-1*(1+-1*a*x)^-1+2*a^-1*c^-1*(1+-1*a*x)^-2)
@test integrate((c+-1*a*c*x)^-2*exp(4*arccoth(a*x)), x) == :(1//6*a^-1*c^-2*(1+a*x)^3*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^-3*exp(4*arccoth(a*x)), x) == :(a^-1*c^-3*(1+-1*a*x)^-4+(1/2)*a^-1*c^-3*(1+-1*a*x)^-2+-4//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*a*c*x)^-4*exp(4*arccoth(a*x)), x) == :(-1*a^-1*c^-4*(1+-1*a*x)^-4+1//3*a^-1*c^-4*(1+-1*a*x)^-3+4//5*a^-1*c^-4*(1+-1*a*x)^-5)
@test integrate((c+-1*a*c*x)^3*exp(-1*arccoth(a*x)), x) == :(-35//8*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+20//3*x*c^3*(1+-1*a^-2*x^-2)^(1/2)+-27//8*a*c^3*x^2*(1+-1*a^-2*x^-2)^(1/2)+-1//4*a^3*c^3*x^4*(1+-1*a^-2*x^-2)^(1/2)+4//3*a^2*c^3*x^3*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^2*exp(-1*arccoth(a*x)), x) == :(-5//2*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+11//3*x*c^2*(1+-1*a^-2*x^-2)^(1/2)+-3//2*a*c^2*x^2*(1+-1*a^-2*x^-2)^(1/2)+1//3*a^2*c^2*x^3*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)*exp(-1*arccoth(a*x)), x) == :(2*c*x*(1+-1*a^-2*x^-2)^(1/2)+-3//2*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//2*a*c*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^-1*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate((c+-1*a*c*x)^-2*exp(-1*arccoth(a*x)), x) == :(-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1)
@test integrate((c+-1*a*c*x)^-3*exp(-1*arccoth(a*x)), x) == :(-2//3*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+1//3*a*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-2)
@test integrate((c+-1*a*c*x)^-4*exp(-1*arccoth(a*x)), x) == :(-7//15*c^-4*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+-1//5*a^2*c^-4*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-3+8//15*a*c^-4*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-2)
@test integrate((c+-1*a*c*x)^-5*exp(-1*arccoth(a*x)), x) == :(-12//35*c^-5*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1+-18//35*a^2*c^-5*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-3+1//7*a^3*c^-5*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-4+23//35*a*c^-5*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-2)
@test integrate((c+-1*a*c*x)^4*exp(-2*arccoth(a*x)), x) == :(16*x*c^4+-32*a^-1*c^4*log(1+a*x)+-4*a^-1*c^4*(1+-1*a*x)^2+-4//3*a^-1*c^4*(1+-1*a*x)^3+-1//2*a^-1*c^4*(1+-1*a*x)^4+-1//5*a^-1*c^4*(1+-1*a*x)^5)
@test integrate((c+-1*a*c*x)^3*exp(-2*arccoth(a*x)), x) == :(8*x*c^3+-16*a^-1*c^3*log(1+a*x)+-2*a^-1*c^3*(1+-1*a*x)^2+-2//3*a^-1*c^3*(1+-1*a*x)^3+-1//4*a^-1*c^3*(1+-1*a*x)^4)
@test integrate((c+-1*a*c*x)^2*exp(-2*arccoth(a*x)), x) == :(4*x*c^2+-1*a^-1*c^2*(1+-1*a*x)^2+-8*a^-1*c^2*log(1+a*x)+-1//3*a^-1*c^2*(1+-1*a*x)^3)
@test integrate((c+-1*a*c*x)*exp(-2*arccoth(a*x)), x) == :(3*c*x+-4*c*a^-1*log(1+a*x)+-1//2*a*c*x^2)
@test integrate((c+-1*a*c*x)^-1*exp(-2*arccoth(a*x)), x) == :(-1*a^-1*c^-1*log(1+a*x))
@test integrate((c+-1*a*c*x)^-2*exp(-2*arccoth(a*x)), x) == :(-1*a^-1*c^-2*arctanh(a*x))
@test integrate((c+-1*a*c*x)^-3*exp(-2*arccoth(a*x)), x) == :(-1//2*a^-1*c^-3*(1+-1*a*x)^-1+-1//2*a^-1*c^-3*arctanh(a*x))
@test integrate((c+-1*a*c*x)^-4*exp(-2*arccoth(a*x)), x) == :(-1//4*a^-1*c^-4*(1+-1*a*x)^-1+-1//4*a^-1*c^-4*(1+-1*a*x)^-2+-1//4*a^-1*c^-4*arctanh(a*x))
@test integrate((c+-1*a*c*x)^-5*exp(-2*arccoth(a*x)), x) == :(-1//6*a^-1*c^-5*(1+-1*a*x)^-3+-1//8*a^-1*c^-5*(1+-1*a*x)^-1+-1//8*a^-1*c^-5*(1+-1*a*x)^-2+-1//8*a^-1*c^-5*arctanh(a*x))
@test integrate((c+-1*a*c*x)^3*exp(-3*arccoth(a*x)), x) == :(30*x*c^3*(1+-1*a^-2*x^-2)^(1/2)+-315//8*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+2*a^2*c^3*x^3*(1+-1*a^-2*x^-2)^(1/2)+32*a^-2*c^3*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)+-67//8*a*c^3*x^2*(1+-1*a^-2*x^-2)^(1/2)+-1//4*a^3*c^3*x^4*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^2*exp(-3*arccoth(a*x)), x) == :(-35//2*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+35//3*x*c^2*(1+-1*a^-2*x^-2)^(1/2)+16*a^-2*c^2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)+-5//2*a*c^2*x^2*(1+-1*a^-2*x^-2)^(1/2)+1//3*a^2*c^2*x^3*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)*exp(-3*arccoth(a*x)), x) == :(4*c*x*(1+-1*a^-2*x^-2)^(1/2)+-15//2*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+8*c*a^-2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)+-1//2*a*c*x^2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*a*c*x)^-1*exp(-3*arccoth(a*x)), x) == :(-1*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+a^-2*c^-1*(1+-1*a^-2*x^-2)^-1//2*(-2*x^-1+2a))
@test integrate((c+-1*a*c*x)^-2*exp(-3*arccoth(a*x)), x) == :(a^-2*c^-2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1))
@test integrate((c+-1*a*c*x)^-3*exp(-3*arccoth(a*x)), x) == :(a^-1*c^-3*(1+-1*a^-2*x^-2)^-1//2)
@test integrate((c+-1*a*c*x)^-4*exp(-3*arccoth(a*x)), x) == :(2//3*a^-1*c^-4*(1+-1*a^-2*x^-2)^-1//2+-1//3*a^-2*c^-4*x^-2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)^-1)
@test integrate((c+-1*a*c*x)^-5*exp(-3*arccoth(a*x)), x) == :(-1//5*a^-2*c^-5*(1+-1*a^-2*x^-2)^-3//2*(4a+4*x^-1)+1//5*a^-3*c^-5*(1+-1*a^-2*x^-2)^-5//2*(a+x^-1)^2+1//5*a^-2*c^-5*(1+-1*a^-2*x^-2)^-1//2*(2*x^-1+5a))
@test integrate((c+-1*a*c*x)^-6*exp(-3*arccoth(a*x)), x) == :(-1//7*a^-4*c^-6*(1+-1*a^-2*x^-2)^-7//2*(a+x^-1)^3+-1//35*a^-2*c^-6*(1+-1*a^-2*x^-2)^-3//2*(46a+46*x^-1)+1//35*a^-2*c^-6*(1+-1*a^-2*x^-2)^-1//2*(13*x^-1+35a)+24//35*a^-3*c^-6*(1+-1*a^-2*x^-2)^-5//2*(a+x^-1)^2)
@test integrate((c+-1*a*c*x)^9//2*exp(arccoth(a*x)), x) == :(-768//385*a^-3*x^-2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+-32//99*a^-4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^9//2+128//231*a^-2*x^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+9088//3465*a^-4*x^-3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+2//11*x*a^-4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^4*(c+-1*a*c*x)^9//2)
@test integrate((c+-1*a*c*x)^7//2*exp(arccoth(a*x)), x) == :(-8//21*a^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+-568//315*a^-3*x^-2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+48//35*a^-2*x^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+2//9*x*a^-3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^7//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(arccoth(a*x)), x) == :(2//3*a^-1*(c+-1*a*c*x)^(1/2)*(1+a*x)*exp(arccoth(a*x)))
@test integrate((c+-1*a*c*x)^-1//2*exp(arccoth(a*x)), x) == :(2*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*a*c*x)^-1//2+-2*2^(1/2)*a^-1//2*(x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*a*c*x)^-1//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-3//2*exp(arccoth(a*x)), x) == :(-1*a*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(a+-1*x^-1)^-1*(c+-1*a*c*x)^-3//2+-1//2*2^(1/2)*a^(1/2)*(x^-1)^-3//2*(1+-1*a^-1*x^-1)^3//2*(c+-1*a*c*x)^-3//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-5//2*exp(arccoth(a*x)), x) == :(a^2*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*(-8*x^-1+8a)^-1+-1//4*a^3*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-2*(c+-1*a*c*x)^-5//2+1//16*2^(1/2)*a^3//2*(x^-1)^-5//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(arccoth(a*x)), x) == :(-1*a^3*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*(-32*x^-1+32a)^-1+-1//6*a^4*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-3*(c+-1*a*c*x)^-7//2+-1//64*2^(1/2)*a^5//2*(x^-1)^-7//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2)+1//16*a^4*x^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-2*(c+-1*a*c*x)^-7//2)
@test integrate((c+-1*a*c*x)^7//2*exp(2*arccoth(a*x)), x) == :(4//7*a^-1*(c+-1*a*c*x)^7//2+-2//9*a^-1*c^-1*(c+-1*a*c*x)^9//2)
@test integrate((c+-1*a*c*x)^5//2*exp(2*arccoth(a*x)), x) == :(4//5*a^-1*(c+-1*a*c*x)^5//2+-2//7*a^-1*c^-1*(c+-1*a*c*x)^7//2)
@test integrate((c+-1*a*c*x)^3//2*exp(2*arccoth(a*x)), x) == :(4//3*a^-1*(c+-1*a*c*x)^3//2+-2//5*a^-1*c^-1*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^-1*(c+-1*a*c*x)^(1/2)+-2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(2*arccoth(a*x)), x) == :(-4*a^-1*(c+-1*a*c*x)^-1//2+-2*a^-1*c^-1*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^-3//2*exp(2*arccoth(a*x)), x) == :(-4//3*a^-1*(c+-1*a*c*x)^-3//2+2*a^-1*c^-1*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^-5//2*exp(2*arccoth(a*x)), x) == :(-4//5*a^-1*(c+-1*a*c*x)^-5//2+2//3*a^-1*c^-1*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^-7//2*exp(2*arccoth(a*x)), x) == :(-4//7*a^-1*(c+-1*a*c*x)^-7//2+2//5*a^-1*c^-1*(c+-1*a*c*x)^-5//2)
@test integrate((c+-1*a*c*x)^9//2*exp(3*arccoth(a*x)), x) == :(-8//33*a^-1*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+-856//1155*a^-3*x^-2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+16//21*a^-2*x^-1*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+2//11*x*a^-3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^9//2)
@test integrate((c+-1*a*c*x)^7//2*exp(3*arccoth(a*x)), x) == :(-44//63*a^-1*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+2//9*x*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+214//315*a^-2*x^-1*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2)
@test integrate((c+-1*a*c*x)^5//2*exp(3*arccoth(a*x)), x) == :(-18//35*a^-1*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-5//2*(c+-1*a*c*x)^5//2+2//7*x*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-5//2*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^3//2*exp(3*arccoth(a*x)), x) == :(2//5*a^-1*(c+-1*a*c*x)^3//2*(1+a*x)*exp(3*arccoth(a*x)))
@test integrate((c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*x*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-4*2^(1/2)*a^-3//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-1//2*exp(3*arccoth(a*x)), x) == :(-6*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)*(a+-1*x^-1)^-1*(c+-1*a*c*x)^-1//2+-3*2^(1/2)*a^-1//2*(x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*a*c*x)^-1//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2)+2*a*x*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)*(a+-1*x^-1)^-1*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^-3//2*exp(3*arccoth(a*x)), x) == :(-3*a*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(c+-1*a*c*x)^-3//2*(-4*x^-1+4a)^-1+-3//8*2^(1/2)*a^(1/2)*(x^-1)^-3//2*(1+-1*a^-1*x^-1)^3//2*(c+-1*a*c*x)^-3//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2)+-1//2*x*a^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^3//2*(a+-1*x^-1)^-2*(c+-1*a*c*x)^-3//2)
@test integrate((c+-1*a*c*x)^-5//2*exp(3*arccoth(a*x)), x) == :(a^2*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*(-16*x^-1+16a)^-1+-1//6*a^4*x^2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-3*(c+-1*a*c*x)^-5//2+1//24*a^3*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-2*(c+-1*a*c*x)^-5//2+1//32*2^(1/2)*a^3//2*(x^-1)^-5//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(3*arccoth(a*x)), x) == :(-3*a^3*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*(-256*x^-1+256a)^-1+-3//512*2^(1/2)*a^5//2*(x^-1)^-7//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2)+-1//8*a^5*x^2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-4*(c+-1*a*c*x)^-7//2+-1//128*a^4*x^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-2*(c+-1*a*c*x)^-7//2+1//32*a^5*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-3*(c+-1*a*c*x)^-7//2)
@test integrate((c+-1*a*c*x)^-1//2*exp(-1*arccoth(a*x)), x) == :(a^-1*(c+-1*a*c*x)^-1//2*(2+2*a*x)*exp(-1*arccoth(a*x)))
@test integrate((c+-1*a*c*x)^-3//2*exp(-1*arccoth(a*x)), x) == :(-1*2^(1/2)*a^(1/2)*(x^-1)^-3//2*(1+-1*a^-1*x^-1)^3//2*(c+-1*a*c*x)^-3//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-5//2*exp(-1*arccoth(a*x)), x) == :(-1*a^2*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*(-2*x^-1+2a)^-1+1//4*2^(1/2)*a^3//2*(x^-1)^-5//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(-1*arccoth(a*x)), x) == :(3*a^3*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*(-16*x^-1+16a)^-1+-3//32*2^(1/2)*a^5//2*(x^-1)^-7//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2)+-1//4*a^3*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-2*(c+-1*a*c*x)^-7//2)
@test integrate((c+-1*a*c*x)^7//2*exp(-2*arccoth(a*x)), x) == :(-4//7*a^-1*(c+-1*a*c*x)^7//2+-32*a^-1*c^3*(c+-1*a*c*x)^(1/2)+-16//3*a^-1*c^2*(c+-1*a*c*x)^3//2+-8//5*c*a^-1*(c+-1*a*c*x)^5//2+-2//9*a^-1*c^-1*(c+-1*a*c*x)^9//2+32*2^(1/2)*a^-1*c^7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^5//2*exp(-2*arccoth(a*x)), x) == :(-4//5*a^-1*(c+-1*a*c*x)^5//2+-16*a^-1*c^2*(c+-1*a*c*x)^(1/2)+-8//3*c*a^-1*(c+-1*a*c*x)^3//2+-2//7*a^-1*c^-1*(c+-1*a*c*x)^7//2+16*2^(1/2)*a^-1*c^5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^3//2*exp(-2*arccoth(a*x)), x) == :(-4//3*a^-1*(c+-1*a*c*x)^3//2+-8*c*a^-1*(c+-1*a*c*x)^(1/2)+-2//5*a^-1*c^-1*(c+-1*a*c*x)^5//2+8*2^(1/2)*a^-1*c^3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-4*a^-1*(c+-1*a*c*x)^(1/2)+-2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-1//2*exp(-2*arccoth(a*x)), x) == :(-2*a^-1*c^-1*(c+-1*a*c*x)^(1/2)+2*2^(1/2)*a^-1*c^-1//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-3//2*exp(-2*arccoth(a*x)), x) == :(2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-5//2*exp(-2*arccoth(a*x)), x) == :(-1*a^-1*c^-2*(c+-1*a*c*x)^-1//2+(1/2)*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-7//2*exp(-2*arccoth(a*x)), x) == :(-1//2*a^-1*c^-3*(c+-1*a*c*x)^-1//2+-1//3*a^-1*c^-2*(c+-1*a*c*x)^-3//2+1//4*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^-9//2*exp(-2*arccoth(a*x)), x) == :(-1//4*a^-1*c^-4*(c+-1*a*c*x)^-1//2+-1//5*a^-1*c^-2*(c+-1*a*c*x)^-5//2+-1//6*a^-1*c^-3*(c+-1*a*c*x)^-3//2+1//8*2^(1/2)*a^-1*c^-9//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^9//2*exp(-3*arccoth(a*x)), x) == :(-94208//231*a^-6*x^-5*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+-40960//231*a^-5*x^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+-16//33*a^-6*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^5*(c+-1*a*c*x)^9//2+4096//231*a^-4*x^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*a*c*x)^9//2+-1024//231*a^-6*x^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^9//2+2//11*x*a^-6*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^6*(c+-1*a*c*x)^9//2+320//231*a^-6*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^4*(c+-1*a*c*x)^9//2)
@test integrate((c+-1*a*c*x)^7//2*exp(-3*arccoth(a*x)), x) == :(-512//63*a^-3*x^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+-40//63*a^-5*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^4*(c+-1*a*c*x)^7//2+5120//63*a^-4*x^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+11776//63*a^-5*x^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*a*c*x)^7//2+2//9*x*a^-5*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^5*(c+-1*a*c*x)^7//2+128//63*a^-5*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^7//2)
@test integrate((c+-1*a*c*x)^5//2*exp(-3*arccoth(a*x)), x) == :(-2944//35*a^-4*x^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(c+-1*a*c*x)^5//2+-256//7*a^-3*x^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(c+-1*a*c*x)^5//2+-32//35*a^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^5//2+128//35*a^-2*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(c+-1*a*c*x)^5//2+2//7*x*a^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(a+-1*x^-1)^4*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^3//2*exp(-3*arccoth(a*x)), x) == :(-8//5*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2*(c+-1*a*c*x)^3//2+16*a^-2*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2*(c+-1*a*c*x)^3//2+184//5*a^-3*x^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2*(c+-1*a*c*x)^3//2+2//5*x*a^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2*(a+-1*x^-1)^3*(c+-1*a*c*x)^3//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-20//3*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-46//3*a^-2*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^-1//2*exp(-3*arccoth(a*x)), x) == :(2*x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*a*c*x)^-1//2+6*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*a*c*x)^-1//2)
@test integrate((c+-1*a*c*x)^-3//2*exp(-3*arccoth(a*x)), x) == :(-1*a^-1*(c+-1*a*c*x)^-3//2*(2+2*a*x)*exp(-3*arccoth(a*x)))
@test integrate((c+-1*a*c*x)^-5//2*exp(-3*arccoth(a*x)), x) == :(a*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2+-1//2*2^(1/2)*a^3//2*(x^-1)^-5//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*a*c*x)^-5//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^-7//2*exp(-3*arccoth(a*x)), x) == :(-3//4*a^2*x^3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2+-1*a^2*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*(-2*x^-1+2a)^-1+3//8*2^(1/2)*a^5//2*(x^-1)^-7//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*a*c*x)^-7//2*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x*(1+x)*exp(arccoth(x)), x) == :(x*(x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2)+1//3*x^2*(x^-1*(-1+x))^(1/2)*(1+x^-1)^3//2+1//3*x^3*(x^-1*(-1+x))^(1/2)*(1+x^-1)^5//2+arctanh((x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2)))
@test integrate((1+x)*exp(arccoth(x)), x) == :(3//2*arctanh((x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2))+(1/2)*x^2*(x^-1*(-1+x))^(1/2)*(1+x^-1)^3//2+3//2*x*(x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2))
@test integrate(x*(1+-1x)*exp(arccoth(x)), x) == :(-1//3*x^3*(1+-1*x^-2)^3//2)
@test integrate((1+-1x)*exp(arccoth(x)), x) == :((1/2)*arctanh((1+-1*x^-2)^(1/2))+-1//2*x^2*(1+-1*x^-2)^(1/2))
@test integrate(x*(1+x)^2*exp(arccoth(x)), x) == :(15//8*arctanh((x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2))+1//4*x^3*(x^-1*(-1+x))^(1/2)*(1+x^-1)^5//2+1//4*x^4*(x^-1*(-1+x))^(1/2)*(1+x^-1)^7//2+5//8*x^2*(x^-1*(-1+x))^(1/2)*(1+x^-1)^3//2+15//8*x*(x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2))
@test integrate((1+x)^2*exp(arccoth(x)), x) == :(5//2*arctanh((x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2))+1//3*x^3*(x^-1*(-1+x))^(1/2)*(1+x^-1)^5//2+5//2*x*(x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2)+5//6*x^2*(x^-1*(-1+x))^(1/2)*(1+x^-1)^3//2)
@test integrate(x*(1+-1x)^2*exp(arccoth(x)), x) == :(-1//8*arctanh((1+-1*x^-2)^(1/2))+-1//3*x^3*(1+-1*x^-2)^3//2+1//4*x^4*(1+-1*x^-2)^3//2+1//8*x^2*(1+-1*x^-2)^(1/2))
@test integrate((1+-1x)^2*exp(arccoth(x)), x) == :((1/2)*arctanh((1+-1*x^-2)^(1/2))+-1//2*x^2*(1+-1*x^-2)^(1/2)+1//3*x^3*(1+-1*x^-2)^3//2)
@test integrate(x*(1+x)^-1*exp(arccoth(x)), x) == :(x*(x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2))
@test integrate((1+x)^-1*exp(arccoth(x)), x) == :(arctanh((x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2)))
@test integrate(x*(1+-1x)^-1*exp(arccoth(x)), x) == :(-2*arctanh((1+-1*x^-2)^(1/2))+(1+-1*x^-2)^-1//2*(2+2*x^-1)+-1*x*(1+-1*x^-2)^(1/2))
@test integrate((1+-1x)^-1*exp(arccoth(x)), x) == :(-1*arctanh((1+-1*x^-2)^(1/2))+(1+-1*x^-2)^-1//2*(2+2*x^-1))
@test integrate(x*(1+x)^-2*exp(arccoth(x)), x) == :(-1*(x^-1*(-1+x))^(1/2)*(1+x^-1)^-1//2+arctanh((x^-1*(-1+x))^(1/2)*(1+x^-1)^(1/2)))
@test integrate((1+x)^-2*exp(arccoth(x)), x) == :((x^-1*(-1+x))^(1/2)*(1+x^-1)^-1//2)
@test integrate(x*(1+-1x)^-2*exp(arccoth(x)), x) == :(-1//3*(1+-1*x^-2)^-3//2*(4+4*x^-1)+-1//3*(1+-1*x^-2)^-1//2*(3+5*x^-1)+arctanh((1+-1*x^-2)^(1/2)))
@test integrate((1+-1x)^-2*exp(arccoth(x)), x) == :(-1//3*(1+-1*x^-1)^-3*(1+-1*x^-2)^3//2)
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(arccoth(a*x)), x) == :(2//7*x^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-8//35*a^-1*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+16//105*x*a^-2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(arccoth(a*x)), x) == :(2//5*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-4//15*x*a^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^(1/2)*exp(arccoth(a*x)), x) == :(2//3*a^-1*(c+-1*a*c*x)^(1/2)*(1+a*x)*exp(arccoth(a*x)))
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(arccoth(a*x)), x) == :(2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-2*a^-1//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(arccoth(a*x)), x) == :(-1*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-1*a^(1/2)*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2)))
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^-4*(c+-1*a*c*x)^(1/2)+-14//3*a^-4*c^-1*(c+-1*a*c*x)^3//2+-10//7*a^-4*c^-3*(c+-1*a*c*x)^7//2+2//9*a^-4*c^-4*(c+-1*a*c*x)^9//2+18//5*a^-4*c^-2*(c+-1*a*c*x)^5//2)
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^-3*(c+-1*a*c*x)^(1/2)+-10//3*a^-3*c^-1*(c+-1*a*c*x)^3//2+-2//7*a^-3*c^-3*(c+-1*a*c*x)^7//2+8//5*a^-3*c^-2*(c+-1*a*c*x)^5//2)
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^-2*(c+-1*a*c*x)^(1/2)+-2*a^-2*c^-1*(c+-1*a*c*x)^3//2+2//5*a^-2*c^-2*(c+-1*a*c*x)^5//2)
@test integrate((c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^-1*(c+-1*a*c*x)^(1/2)+-2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2)
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(2*(c+-1*a*c*x)^(1/2)+2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(x^-1*(c+-1*a*c*x)^(1/2)+3*a*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :((1/2)*x^-2*(c+-1*a*c*x)^(1/2)+7//4*a*x^-1*(c+-1*a*c*x)^(1/2)+7//4*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//3*x^-3*(c+-1*a*c*x)^(1/2)+11//8*a^2*x^-1*(c+-1*a*c*x)^(1/2)+11//8*a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+11//12*a*x^-2*(c+-1*a*c*x)^(1/2))
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//4*x^-4*(c+-1*a*c*x)^(1/2)+5//8*a*x^-3*(c+-1*a*c*x)^(1/2)+25//32*a^2*x^-2*(c+-1*a*c*x)^(1/2)+75//64*a^3*x^-1*(c+-1*a*c*x)^(1/2)+75//64*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(2//9*x^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+1576//315*a^-4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+38//63*a^-1*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+92//105*a^-2*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+472//315*x*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-4*2^(1/2)*a^-9//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(2//7*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+104//21*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+6//7*a^-1*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+32//21*x*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-4*2^(1/2)*a^-7//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//5*x^2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*x*a^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-4*2^(1/2)*a^-5//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate((c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*x*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-4*2^(1/2)*a^-3//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2*a^-1//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+-4*2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+5*a^(1/2)*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+-4*2^(1/2)*a^(1/2)*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :((1/2)*a*x^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+7//4*a*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+23//4*a^3//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+-4*2^(1/2)*a^3//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(1//3*a*x^-2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+3//4*a^2*x^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+13//8*a^2*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+45//8*a^5//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+-4*2^(1/2)*a^5//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(3*arccoth(a*x)), x) == :(1//4*a*x^-3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+11//24*a^2*x^-2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+21//32*a^3*x^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+107//64*a^3*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+363//64*a^7//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+-4*2^(1/2)*a^7//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arctanh(2^(1/2)*a^-1//2*(x^-1)^(1/2)*(1+a^-1*x^-1)^-1//2))
@test integrate(x*(1+x)^3//2*exp(arccoth(x)), x) == :(46//21*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2+2//7*x^2*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2+8//7*x*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2+92//21*x^-1*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2)
@test integrate((1+x)^3//2*exp(arccoth(x)), x) == :(28//15*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2+2//5*x*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2+86//15*x^-1*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^3//2*(1+x^-1)^-3//2)
@test integrate(x*(1+-1x)^3//2*exp(arccoth(x)), x) == :(44//105*(1+x^-1)^3//2*(1+-1x)^3//2*(1+-1*x^-1)^-3//2+-22//35*x*(1+x^-1)^3//2*(1+-1x)^3//2*(1+-1*x^-1)^-3//2+2//7*x^2*(1+x^-1)^3//2*(1+-1x)^3//2*(1+-1*x^-1)^-3//2)
@test integrate((1+-1x)^3//2*exp(arccoth(x)), x) == :(-14//15*(1+x^-1)^3//2*(1+-1x)^3//2*(1+-1*x^-1)^-3//2+2//5*x*(1+x^-1)^3//2*(1+-1x)^3//2*(1+-1*x^-1)^-3//2)
@test integrate(x*(1+x)^(1/2)*exp(arccoth(x)), x) == :(12//5*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^(1/2)*(1+x^-1)^-1//2+2//5*x^2*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^(1/2)*(1+x^-1)^-1//2+6//5*x*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^(1/2)*(1+x^-1)^-1//2)
@test integrate((1+x)^(1/2)*exp(arccoth(x)), x) == :(10//3*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^(1/2)*(1+x^-1)^-1//2+2//3*x*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^(1/2)*(1+x^-1)^-1//2)
@test integrate(x*(1+-1x)^(1/2)*exp(arccoth(x)), x) == :(-4//15*x*(1+x^-1)^3//2*(1+-1x)^(1/2)*(1+-1*x^-1)^-1//2+2//5*x^2*(1+x^-1)^3//2*(1+-1x)^(1/2)*(1+-1*x^-1)^-1//2)
@test integrate((1+-1x)^(1/2)*exp(arccoth(x)), x) == :(2//3*(1+-1x)^(1/2)*(1+x)*exp(arccoth(x)))
@test integrate(x*(1+x)^-1//2*exp(arccoth(x)), x) == :(2//3*x^2*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^-1//2*(1+x^-1)^(1/2)+4//3*x*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^-1//2*(1+x^-1)^(1/2))
@test integrate((1+x)^-1//2*exp(arccoth(x)), x) == :(2*x*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^-1//2*(1+x^-1)^(1/2))
@test integrate(x*(1+-1x)^-1//2*exp(arccoth(x)), x) == :(2*x*(1+x^-1)^(1/2)*(1+-1x)^-1//2*(1+-1*x^-1)^(1/2)+2//3*x^2*(1+x^-1)^3//2*(1+-1x)^-1//2*(1+-1*x^-1)^(1/2)+-2*2^(1/2)*(x^-1)^-1//2*(1+-1x)^-1//2*(1+-1*x^-1)^(1/2)*arctanh(2^(1/2)*(x^-1)^(1/2)*(1+x^-1)^-1//2))
@test integrate((1+-1x)^-1//2*exp(arccoth(x)), x) == :(2*x*(1+x^-1)^(1/2)*(1+-1x)^-1//2*(1+-1*x^-1)^(1/2)+-2*2^(1/2)*(x^-1)^-1//2*(1+-1x)^-1//2*(1+-1*x^-1)^(1/2)*arctanh(2^(1/2)*(x^-1)^(1/2)*(1+x^-1)^-1//2))
@test integrate(x*(1+x)^-3//2*exp(arccoth(x)), x) == :(2*x^2*(-1*x^-1*(1+-1x))^(1/2)*(1+x)^-3//2*(1+x^-1)^3//2+2^(1/2)*(x^-1)^-3//2*(1+x)^-3//2*(1+x^-1)^3//2*arctan(2^(1/2)*(x^-1)^(1/2)*(-1*x^-1*(1+-1x))^-1//2))
@test integrate((1+x)^-3//2*exp(arccoth(x)), x) == :(-1*2^(1/2)*(x^-1)^-3//2*(1+x)^-3//2*(1+x^-1)^3//2*arctan(2^(1/2)*(x^-1)^(1/2)*(-1*x^-1*(1+-1x))^-1//2))
@test integrate(x*(1+-1x)^-3//2*exp(arccoth(x)), x) == :(-1//2*x^2*(1+x^-1)^3//2*(1+-1x)^-3//2*(1+-1*x^-1)^(1/2)+5//2*x^2*(1+x^-1)^(1/2)*(1+-1x)^-3//2*(1+-1*x^-1)^3//2+-5//2*2^(1/2)*(x^-1)^-3//2*(1+-1x)^-3//2*(1+-1*x^-1)^3//2*arctanh(2^(1/2)*(x^-1)^(1/2)*(1+x^-1)^-1//2))
@test integrate((1+-1x)^-3//2*exp(arccoth(x)), x) == :(-1*x*(1+x^-1)^(1/2)*(1+-1x)^-3//2*(1+-1*x^-1)^(1/2)+-1//2*2^(1/2)*(x^-1)^-3//2*(1+-1x)^-3//2*(1+-1*x^-1)^3//2*arctanh(2^(1/2)*(x^-1)^(1/2)*(1+x^-1)^-1//2))
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(-1*arccoth(a*x)), x) == :(2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2*a^-1//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(-1*arccoth(a*x)), x) == :(x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-3*a^(1/2)*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2)))
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(4*a^-4*(c+-1*a*c*x)^(1/2)+-2//7*a^-4*c^-3*(c+-1*a*c*x)^7//2+2//3*a^-4*c^-1*(c+-1*a*c*x)^3//2+2//5*a^-4*c^-2*(c+-1*a*c*x)^5//2+2//9*a^-4*c^-4*(c+-1*a*c*x)^9//2+-4*2^(1/2)*a^-4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-4*a^-3*(c+-1*a*c*x)^(1/2)+-2//3*a^-3*c^-1*(c+-1*a*c*x)^3//2+-2//7*a^-3*c^-3*(c+-1*a*c*x)^7//2+4*2^(1/2)*a^-3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(4*a^-2*(c+-1*a*c*x)^(1/2)+2//3*a^-2*c^-1*(c+-1*a*c*x)^3//2+2//5*a^-2*c^-2*(c+-1*a*c*x)^5//2+-4*2^(1/2)*a^-2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate((c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-4*a^-1*(c+-1*a*c*x)^(1/2)+-2//3*a^-1*c^-1*(c+-1*a*c*x)^3//2+4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(2*(c+-1*a*c*x)^(1/2)+2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-4*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x^-1*(c+-1*a*c*x)^(1/2)+-5*a*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+4*a*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :((1/2)*x^-2*(c+-1*a*c*x)^(1/2)+-9//4*a*x^-1*(c+-1*a*c*x)^(1/2)+23//4*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-4*2^(1/2)*a^2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//3*x^-3*(c+-1*a*c*x)^(1/2)+-45//8*a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-13//12*a*x^-2*(c+-1*a*c*x)^(1/2)+19//8*a^2*x^-1*(c+-1*a*c*x)^(1/2)+4*2^(1/2)*a^3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//4*x^-4*(c+-1*a*c*x)^(1/2)+-149//64*a^3*x^-1*(c+-1*a*c*x)^(1/2)+-17//24*a*x^-3*(c+-1*a*c*x)^(1/2)+107//96*a^2*x^-2*(c+-1*a*c*x)^(1/2)+363//64*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*a*c*x)^(1/2))+-4*2^(1/2)*a^4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*a*c*x)^(1/2)))
@test integrate(x^3*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(2//9*x^4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+1312//45*a^-4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-656//45*x*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-82//9*a^-2*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-8//9*a^-1*x^3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+164//15*a^-2*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x^2*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-2672//105*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//7*x^3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-334//35*x*a^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-44//35*a^-1*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+1336//105*x*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-158//15*a^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//5*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+316//15*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-32//15*x*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-20//3*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+2//3*x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-46//3*a^-2*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x^-1*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-2*a^-1//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+10*a^-1*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x^-2*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-1*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-8*x^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+7*a^(1/2)*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2)))
@test integrate(x^-3*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-8*x^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-1//2*x^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-47//4*a^3//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+47//4*a*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x^-4*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-8*x^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-1//3*x^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-119//8*a^2*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+119//8*a^5//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+119//12*a*x^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate(x^-5*(c+-1*a*c*x)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-8*x^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-1//4*x^-4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+-1115//64*a^7//2*(x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)*arcsinh(a^-1//2*(x^-1)^(1/2))+-1115//96*a^2*x^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+223//24*a*x^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2)+1115//64*a^3*x^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*a*c*x)^(1/2))
@test integrate((c+-1*a*c*x)^(2+(1/2)*n)*exp(n*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^(1+(1/2)*n)*(1+-1*a^-1*x^-1)^(-2+-1//2*n)*(6+n)^-1*(c+-1*a*c*x)^(2+(1/2)*n)*(8+n)+-1*x*a^-1*(1+a^-1*x^-1)^(1+(1/2)*n)*(1+-1*a^-1*x^-1)^(-2+-1//2*n)*(c+-1*a*c*x)^(2+(1/2)*n)*(a+-1*x^-1)+-1*a^-1*(1+a^-1*x^-1)^(1+(1/2)*n)*(1+-1*a^-1*x^-1)^(-2+-1//2*n)*(4+n)^-1*(6+n)^-1*(c+-1*a*c*x)^(2+(1/2)*n)*(56+n^2+14n)+a^-2*x^-1*(1+a^-1*x^-1)^(1+(1/2)*n)*(1+-1*a^-1*x^-1)^(-2+-1//2*n)*(6+n)^-1*(c+-1*a*c*x)^(2+(1/2)*n)*(8+n^2+6n)^-1*(112+2*n^2+28n))
@test integrate((c+-1*a*c*x)^((1/2)*n)*exp(n*arccoth(a*x)), x) == :(2*a^-1*(2+n)^-1*(c+-1*a*c*x)^((1/2)*n)*(1+a*x)*exp(n*arccoth(a*x)))
@test integrate((c+-1*a*c*x)^-2*exp(n*arccoth(a*x)), x) == :(-1*a^-1*c^-2*(1+a^-1*x^-1)^(1+(1/2)*n)*(1+-1*a^-1*x^-1)^(-1+-1//2*n)*(2+n)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(arccoth(a*x)), x) == :(x*c^4*(1+-1*a^-2*x^-2)^3//2+-3*a^-1*c^4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//2*a^-1*c^4*arccsc(a*x)+-1//3*a^-1*c^4*(1+-1*a^-2*x^-2)^3//2+(1/2)*a^-2*c^4*(1+-1*a^-2*x^-2)^(1/2)*(-1*x^-1+6a))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^3//2+(1/2)*a^-1*c^3*arccsc(a*x)+-2*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+(1/2)*a^-2*c^3*(1+-1*a^-2*x^-2)^(1/2)*(x^-1+4a))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(arccoth(a*x)), x) == :(a^-1*c^2*arccsc(a*x)+-1*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+x*a^-1*c^2*(1+-1*a^-2*x^-2)^(1/2)*(a+x^-1))
@test integrate((c+-1*c*a^-1*x^-1)*exp(arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^(1/2)+c*a^-1*arccsc(a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)+2*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1*a^-2*c^-1*(1+-1*a^-2*x^-2)^-1//2*(2a+2*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(arccoth(a*x)), x) == :(x*c^-2*(1+-1*a^-2*x^-2)^(1/2)+3*a^-1*c^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//3*a^-2*c^-2*(1+-1*a^-2*x^-2)^-3//2*(4a+4*x^-1)+-1//3*a^-2*c^-2*(1+-1*a^-2*x^-2)^-1//2*(9a+11*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)+4*a^-1*c^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//5*a^-2*c^-3*(1+-1*a^-2*x^-2)^-5//2*(8a+8*x^-1)+-1//15*a^-2*c^-3*(1+-1*a^-2*x^-2)^-3//2*(20a+32*x^-1)+-1//15*a^-2*c^-3*(1+-1*a^-2*x^-2)^-1//2*(60a+79*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(arccoth(a*x)), x) == :(x*c^-4*(1+-1*a^-2*x^-2)^(1/2)+5*a^-1*c^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//7*a^-2*c^-4*(1+-1*a^-2*x^-2)^-7//2*(16a+16*x^-1)+-1//35*a^-2*c^-4*(1+-1*a^-2*x^-2)^-5//2*(28a+68*x^-1)+-1//105*a^-2*c^-4*(1+-1*a^-2*x^-2)^-3//2*(175a+307*x^-1)+-1//105*a^-2*c^-4*(1+-1*a^-2*x^-2)^-1//2*(525a+719*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^5*exp(2*arccoth(a*x)), x) == :(x*c^5+a^-4*c^5*x^-3+-1*a^-3*c^5*x^-2+-3*a^-1*c^5*log(x)+-2*a^-2*c^5*x^-1+-1//4*a^-5*c^5*x^-4)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(2*arccoth(a*x)), x) == :(x*c^4+-1*a^-3*c^4*x^-2+-2*a^-1*c^4*log(x)+1//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(2*arccoth(a*x)), x) == :(x*c^3+a^-2*c^3*x^-1+-1*a^-1*c^3*log(x)+-1//2*a^-3*c^3*x^-2)
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(2*arccoth(a*x)), x) == :(x*c^2+a^-2*c^2*x^-1)
@test integrate((c+-1*c*a^-1*x^-1)*exp(2*arccoth(a*x)), x) == :(c*x+c*a^-1*log(x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(2*arccoth(a*x)), x) == :(x*c^-1+2*a^-1*c^-1*(1+-1*a*x)^-1+3*a^-1*c^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(2*arccoth(a*x)), x) == :(x*c^-2+-1*a^-1*c^-2*(1+-1*a*x)^-2+4*a^-1*c^-2*log(1+-1*a*x)+5*a^-1*c^-2*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(2*arccoth(a*x)), x) == :(x*c^-3+5*a^-1*c^-3*log(1+-1*a*x)+9*a^-1*c^-3*(1+-1*a*x)^-1+-7//2*a^-1*c^-3*(1+-1*a*x)^-2+2//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(2*arccoth(a*x)), x) == :(x*c^-4+-8*a^-1*c^-4*(1+-1*a*x)^-2+3*a^-1*c^-4*(1+-1*a*x)^-3+6*a^-1*c^-4*log(1+-1*a*x)+14*a^-1*c^-4*(1+-1*a*x)^-1+-1//2*a^-1*c^-4*(1+-1*a*x)^-4)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(3*arccoth(a*x)), x) == :(-1*a^-1*c^4*arctanh((1+-1*a^-2*x^-2)^(1/2))+3//2*a^-1*c^4*arccsc(a*x)+(1/2)*a^-2*c^4*(1+-1*a^-2*x^-2)^(1/2)*(2a+3*x^-1)+1//3*x*a^-1*c^4*(1+-1*a^-2*x^-2)^3//2*(x^-1+3a))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(3*arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^3//2+3//2*a^-1*c^3*arccsc(a*x)+3//2*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(3*arccoth(a*x)), x) == :(a^-1*c^2*arccsc(a*x)+a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+x*a^-1*c^2*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)*exp(3*arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^(1/2)+-1*c*a^-1*arccsc(a*x)+2*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(3*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)+4*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//3*a^-2*c^-1*(1+-1*a^-2*x^-2)^-3//2*(8a+8*x^-1)+-1//3*a^-2*c^-1*(1+-1*a^-2*x^-2)^-1//2*(12a+16*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(3*arccoth(a*x)), x) == :(x*c^-2*(1+-1*a^-2*x^-2)^(1/2)+5*a^-1*c^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//5*a^-2*c^-2*(1+-1*a^-2*x^-2)^-5//2*(16a+16*x^-1)+-1//15*a^-2*c^-2*(1+-1*a^-2*x^-2)^-3//2*(20a+44*x^-1)+-1//15*a^-2*c^-2*(1+-1*a^-2*x^-2)^-1//2*(75a+103*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(3*arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)+6*a^-1*c^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-16//7*a^-2*c^-3*x^-1*(1+-1*a^-2*x^-2)^-5//2+-1//7*a^-2*c^-3*(1+-1*a^-2*x^-2)^-7//2*(32a+32*x^-1)+-1//7*a^-2*c^-3*(1+-1*a^-2*x^-2)^-3//2*(14a+26*x^-1)+-1//7*a^-2*c^-3*(1+-1*a^-2*x^-2)^-1//2*(42a+59*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(3*arccoth(a*x)), x) == :(x*c^-4*(1+-1*a^-2*x^-2)^(1/2)+7*a^-1*c^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//9*a^-2*c^-4*(1+-1*a^-2*x^-2)^-9//2*(64a+64*x^-1)+-1//105*a^-2*c^-4*(1+-1*a^-2*x^-2)^-5//2*(168a+328*x^-1)+-1//315*a^-2*c^-4*(1+-1*a^-2*x^-2)^-3//2*(735a+1417*x^-1)+-1//315*a^-2*c^-4*(1+-1*a^-2*x^-2)^-1//2*(2205a+3149*x^-1)+1//63*a^-2*c^-4*(1+-1*a^-2*x^-2)^-7//2*(-80*x^-1+144a))
@test integrate((c+-1*c*a^-1*x^-1)^5*exp(4*arccoth(a*x)), x) == :(x*c^5+-1*a^-1*c^5*log(x)+-1*a^-3*c^5*x^-2+2*a^-2*c^5*x^-1+-1//3*a^-4*c^5*x^-3+1//4*a^-5*c^5*x^-4)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(4*arccoth(a*x)), x) == :(x*c^4+2*a^-2*c^4*x^-1+-1//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(4*arccoth(a*x)), x) == :(x*c^3+a^-1*c^3*log(x)+a^-2*c^3*x^-1+(1/2)*a^-3*c^3*x^-2)
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(4*arccoth(a*x)), x) == :(x*c^2+-1*a^-2*c^2*x^-1+2*a^-1*c^2*log(x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(4*arccoth(a*x)), x) == :(c*x+-1*c*a^-1*log(x)+4*c*a^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(4*arccoth(a*x)), x) == :(x*c^-1+-2*a^-1*c^-1*(1+-1*a*x)^-2+5*a^-1*c^-1*log(1+-1*a*x)+8*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(4*arccoth(a*x)), x) == :(x*c^-2+-6*a^-1*c^-2*(1+-1*a*x)^-2+6*a^-1*c^-2*log(1+-1*a*x)+13*a^-1*c^-2*(1+-1*a*x)^-1+4//3*a^-1*c^-2*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(4*arccoth(a*x)), x) == :(x*c^-3+-1*a^-1*c^-3*(1+-1*a*x)^-4+7*a^-1*c^-3*log(1+-1*a*x)+19*a^-1*c^-3*(1+-1*a*x)^-1+-25//2*a^-1*c^-3*(1+-1*a*x)^-2+16//3*a^-1*c^-3*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(4*arccoth(a*x)), x) == :(x*c^-4+-22*a^-1*c^-4*(1+-1*a*x)^-2+-5*a^-1*c^-4*(1+-1*a*x)^-4+8*a^-1*c^-4*log(1+-1*a*x)+26*a^-1*c^-4*(1+-1*a*x)^-1+4//5*a^-1*c^-4*(1+-1*a*x)^-5+41//3*a^-1*c^-4*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(-1*arccoth(a*x)), x) == :(x*c^4*(1+-1*a^-2*x^-2)^(1/2)+-5*a^-1*c^4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-32//3*a^-1*c^4*(1+-1*a^-2*x^-2)^(1/2)+-25//2*a^-1*c^4*arccsc(a*x)+-1//3*a^-3*c^4*x^-2*(1+-1*a^-2*x^-2)^(1/2)+5//2*a^-2*c^4*x^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(-1*arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^(1/2)+-4*a^-1*c^3*(1+-1*a^-2*x^-2)^(1/2)+-4*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-13//2*a^-1*c^3*arccsc(a*x)+(1/2)*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(-1*arccoth(a*x)), x) == :(x*c^2*(1+-1*a^-2*x^-2)^(1/2)+-1*a^-1*c^2*(1+-1*a^-2*x^-2)^(1/2)+-3*a^-1*c^2*arccsc(a*x)+-3*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)*exp(-1*arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^(1/2)+-1*c*a^-1*arccsc(a*x)+-2*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(-1*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(-1*arccoth(a*x)), x) == :(a^-1*c^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+2*x*c^-2*(1+-1*a^-2*x^-2)^(1/2)+-1*a*x*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(a+-1*x^-1)^-1)
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(-1*arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)+2*a^-1*c^-3*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//3*a^-2*c^-3*(1+-1*a^-2*x^-2)^-3//2*(2a+2*x^-1)+-1//3*a^-2*c^-3*(1+-1*a^-2*x^-2)^-1//2*(6a+7*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(-1*arccoth(a*x)), x) == :(x*c^-4*(1+-1*a^-2*x^-2)^(1/2)+3*a^-1*c^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//5*a^-2*c^-4*(1+-1*a^-2*x^-2)^-5//2*(4a+4*x^-1)+-1//5*a^-2*c^-4*(1+-1*a^-2*x^-2)^-3//2*(5a+7*x^-1)+-1//5*a^-2*c^-4*(1+-1*a^-2*x^-2)^-1//2*(15a+19*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(-2*arccoth(a*x)), x) == :(x*c^4+-32*a^-1*c^4*log(1+a*x)+-3*a^-3*c^4*x^-2+16*a^-2*c^4*x^-1+26*a^-1*c^4*log(x)+1//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(-2*arccoth(a*x)), x) == :(x*c^3+-16*a^-1*c^3*log(1+a*x)+5*a^-2*c^3*x^-1+11*a^-1*c^3*log(x)+-1//2*a^-3*c^3*x^-2)
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(-2*arccoth(a*x)), x) == :(x*c^2+a^-2*c^2*x^-1+-8*a^-1*c^2*log(1+a*x)+4*a^-1*c^2*log(x))
@test integrate((c+-1*c*a^-1*x^-1)*exp(-2*arccoth(a*x)), x) == :(c*x+c*a^-1*log(x)+-4*c*a^-1*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(-2*arccoth(a*x)), x) == :(x*c^-1+-1*a^-1*c^-1*log(1+a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(-2*arccoth(a*x)), x) == :(x*c^-2+-1*a^-1*c^-2*arctanh(a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(-2*arccoth(a*x)), x) == :(x*c^-3+(1/2)*a^-1*c^-3*(1+-1*a*x)^-1+-1//4*a^-1*c^-3*log(1+a*x)+5//4*a^-1*c^-3*log(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(-2*arccoth(a*x)), x) == :(x*c^-4+-1//4*a^-1*c^-4*(1+-1*a*x)^-2+-1//8*a^-1*c^-4*log(1+a*x)+7//4*a^-1*c^-4*(1+-1*a*x)^-1+17//8*a^-1*c^-4*log(1+-1*a*x))
@test integrate((c+-1*c*a^-1*x^-1)^4*exp(-3*arccoth(a*x)), x) == :(x*c^4*(1+-1*a^-2*x^-2)^(1/2)+-7*a^-1*c^4*arctanh((1+-1*a^-2*x^-2)^(1/2))+68//3*a^-1*c^4*(1+-1*a^-2*x^-2)^(1/2)+91//2*a^-1*c^4*arccsc(a*x)+64*a^-2*c^4*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)+-7//2*a^-2*c^4*x^-1*(1+-1*a^-2*x^-2)^(1/2)+1//3*a^-3*c^4*x^-2*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^3*exp(-3*arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^(1/2)+-6*a^-1*c^3*arctanh((1+-1*a^-2*x^-2)^(1/2))+6*a^-1*c^3*(1+-1*a^-2*x^-2)^(1/2)+33//2*a^-1*c^3*arccsc(a*x)+32*a^-2*c^3*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)+-1//2*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^2*exp(-3*arccoth(a*x)), x) == :(x*c^2*(1+-1*a^-2*x^-2)^(1/2)+a^-1*c^2*(1+-1*a^-2*x^-2)^(1/2)+-5*a^-1*c^2*arctanh((1+-1*a^-2*x^-2)^(1/2))+5*a^-1*c^2*arccsc(a*x)+16*a^-2*c^2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)*exp(-3*arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^(1/2)+c*a^-1*arccsc(a*x)+-4*c*a^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+8*c*a^-2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-1*exp(-3*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)+-2*a^-1*c^-1*arctanh((1+-1*a^-2*x^-2)^(1/2))+a^-2*c^-1*(1+-1*a^-2*x^-2)^-1//2*(-2*x^-1+2a))
@test integrate((c+-1*c*a^-1*x^-1)^-2*exp(-3*arccoth(a*x)), x) == :(-1*a^-1*c^-2*arctanh((1+-1*a^-2*x^-2)^(1/2))+2*x*c^-2*(1+-1*a^-2*x^-2)^(1/2)+-1*x*a^-1*c^-2*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^-3*exp(-3*arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^-1//2+-2*a^-2*c^-3*x^-1*(1+-1*a^-2*x^-2)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-4*exp(-3*arccoth(a*x)), x) == :(a^-1*c^-4*arctanh((1+-1*a^-2*x^-2)^(1/2))+8//3*x*c^-4*(1+-1*a^-2*x^-2)^(1/2)+-1//3*a*x*c^-4*(1+-1*a^-2*x^-2)^-1//2*(a+-1*x^-1)^-1+-1//3*x*a^-1*c^-4*(1+-1*a^-2*x^-2)^-1//2*(3*x^-1+4a))
@test integrate((c+-1*c*a^-1*x^-1)^-5*exp(-3*arccoth(a*x)), x) == :(x*c^-5*(1+-1*a^-2*x^-2)^(1/2)+2*a^-1*c^-5*arctanh((1+-1*a^-2*x^-2)^(1/2))+-1//5*a^-2*c^-5*(1+-1*a^-2*x^-2)^-5//2*(2a+2*x^-1)+-1//15*a^-2*c^-5*(1+-1*a^-2*x^-2)^-3//2*(10a+13*x^-1)+-1//15*a^-2*c^-5*(1+-1*a^-2*x^-2)^-1//2*(30a+41*x^-1))
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(arccoth(a*x)), x) == :(-1*a^-1*c^3//2*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+x*c^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+a^-1*c^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(a^-1*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+c*x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+3*a^-1*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arctanh((1+a^-1*x^-1)^(1/2))+-2*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(arccoth(a*x)), x) == :(-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(a+-1*x^-1)^-1*(c+-1*c*a^-1*x^-1)^-3//2+5*a^-1*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh((1+a^-1*x^-1)^(1/2))+-7//2*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+a*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(a+-1*x^-1)^-1*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(arccoth(a*x)), x) == :(-23*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*(-8*x^-1+8a)^-1+7*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1+a^-1*x^-1)^(1/2))+-79//16*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+-3//2*a*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-5//2+x*a^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^9//2+a^-1*c^2*(c+-1*c*a^-1*x^-1)^5//2+-5*a^-1*c^9//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+5*a^-1*c^4*(c+-1*c*a^-1*x^-1)^(1/2)+5//3*a^-1*c^3*(c+-1*c*a^-1*x^-1)^3//2+5//7*c*a^-1*(c+-1*c*a^-1*x^-1)^7//2)
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^7//2+a^-1*c^2*(c+-1*c*a^-1*x^-1)^3//2+-3*a^-1*c^7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+3*a^-1*c^3*(c+-1*c*a^-1*x^-1)^(1/2)+3//5*c*a^-1*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^5//2+a^-1*c^2*(c+-1*c*a^-1*x^-1)^(1/2)+-1*a^-1*c^5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+1//3*c*a^-1*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^3//2+a^-1*c^3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-1*c*a^-1*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^(1/2)+3*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^-1//2+-5*a^-1*(c+-1*c*a^-1*x^-1)^-1//2+5*a^-1*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^-3//2+-7//3*a^-1*(c+-1*c*a^-1*x^-1)^-3//2+-7*a^-1*c^-1*(c+-1*c*a^-1*x^-1)^-1//2+7*a^-1*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^-5//2+-9//5*a^-1*(c+-1*c*a^-1*x^-1)^-5//2+-9*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-1//2+-3*a^-1*c^-1*(c+-1*c*a^-1*x^-1)^-3//2+9*a^-1*c^-5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^-7//2+-11//7*a^-1*(c+-1*c*a^-1*x^-1)^-7//2+-11*a^-1*c^-3*(c+-1*c*a^-1*x^-1)^-1//2+11*a^-1*c^-7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-11//3*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-3//2+-11//5*a^-1*c^-1*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(3*arccoth(a*x)), x) == :(-3*a^-1*(1+-1*a^-1*x^-1)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*arctanh((1+a^-1*x^-1)^(1/2))+3*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-9//2*(c+-1*c*a^-1*x^-1)^9//2+1//35*a^-2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*(-51*x^-1+84a)+9//7*a^-3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^9//2+x*a^-3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^3*(c+-1*c*a^-1*x^-1)^9//2)
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(3*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2+a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2+-1*a^-1*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arctanh((1+a^-1*x^-1)^(1/2))+-2//5*a^-1*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2+1//3*a^-1*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2)
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(3*arccoth(a*x)), x) == :(a^-1*c^5//2*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+x*c^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+-1*a^-1*c^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-1//3*a^-1*c^4*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^3//2*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+x*c^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+-3*a^-1*c^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+5*a^-1*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(3*arccoth(a*x)), x) == :(-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)*(a+-1*x^-1)^-1*(c+-1*c*a^-1*x^-1)^-1//2+7*a^-1*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arctanh((1+a^-1*x^-1)^(1/2))+-5*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+a*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)*(a+-1*x^-1)^-1*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(3*arccoth(a*x)), x) == :(-15*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*(-4*x^-1+4a)^-1+9*a^-1*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh((1+a^-1*x^-1)^(1/2))+-2*a*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-3//2+-51//8*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+x*a^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(3*arccoth(a*x)), x) == :(-73*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*(-16*x^-1+16a)^-1+11*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1+a^-1*x^-1)^(1/2))+-249//32*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+-29//12*a*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-5//2+-5//3*a^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-3*(c+-1*c*a^-1*x^-1)^-5//2+x*a^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-3*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(-1*arccoth(a*x)), x) == :(-9*a^-1*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arctanh((1+a^-1*x^-1)^(1/2))+-1//5*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*(-7*x^-1+80a)+3//5*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^7//2+x*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^3*(c+-1*c*a^-1*x^-1)^7//2)
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(-1*arccoth(a*x)), x) == :(-7*a^-1*(1+-1*a^-1*x^-1)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*arctanh((1+a^-1*x^-1)^(1/2))+-1//3*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*(x^-1+16a)+x*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-5//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(-1*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-3//2*(c+-1*c*a^-1*x^-1)^3//2+-5*a^-1*(1+-1*a^-1*x^-1)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*arctanh((1+a^-1*x^-1)^(1/2))+-2*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-3//2*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(-3*a^-1*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+c*x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(-1*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-1*a^-1*c^-1//2*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(-1*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+a^-1*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh((1+a^-1*x^-1)^(1/2))+-1*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^3//2*(c+-1*c*a^-1*x^-1)^-3//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(-1*arccoth(a*x)), x) == :(-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*(-2*x^-1+2a)^-1+3*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1+a^-1*x^-1)^(1/2))+-9//4*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+a*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2*(a+-1*x^-1)^-1*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(-1*arccoth(a*x)), x) == :(-35*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*(-16*x^-1+16a)^-1+5*a^-1*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arctanh((1+a^-1*x^-1)^(1/2))+-115//32*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+-5//4*a*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-7//2+x*a^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-2*(c+-1*c*a^-1*x^-1)^-7//2)
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^7//2+-21*a^-1*c^3*(c+-1*c*a^-1*x^-1)^(1/2)+-11*a^-1*c^7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-5//3*a^-1*c^2*(c+-1*c*a^-1*x^-1)^3//2+3//5*c*a^-1*(c+-1*c*a^-1*x^-1)^5//2+32*2^(1/2)*a^-1*c^7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^5//2+-9*a^-1*c^5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-7*a^-1*c^2*(c+-1*c*a^-1*x^-1)^(1/2)+1//3*c*a^-1*(c+-1*c*a^-1*x^-1)^3//2+16*2^(1/2)*a^-1*c^5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^3//2+-1*c*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+-7*a^-1*c^3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+8*2^(1/2)*a^-1*c^3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^(1/2)+-5*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(-2*arccoth(a*x)), x) == :(x*c^-1*(c+-1*c*a^-1*x^-1)^(1/2)+-3*a^-1*c^-1//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+2*2^(1/2)*a^-1*c^-1//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(-2*arccoth(a*x)), x) == :(x*c^-2*(c+-1*c*a^-1*x^-1)^(1/2)+-1*a^-1*c^-3//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+2^(1/2)*a^-1*c^-3//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(-2*arccoth(a*x)), x) == :(x*c^-2*(c+-1*c*a^-1*x^-1)^-1//2+a^-1*c^-5//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-2*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-1//2+(1/2)*2^(1/2)*a^-1*c^-5//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(-2*arccoth(a*x)), x) == :(x*c^-2*(c+-1*c*a^-1*x^-1)^-3//2+3*a^-1*c^-7//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-7//2*a^-1*c^-3*(c+-1*c*a^-1*x^-1)^-1//2+-4//3*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-3//2+1//4*2^(1/2)*a^-1*c^-7//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-9//2*exp(-2*arccoth(a*x)), x) == :(x*c^-2*(c+-1*c*a^-1*x^-1)^-5//2+5*a^-1*c^-9//2*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-21//4*a^-1*c^-4*(c+-1*c*a^-1*x^-1)^-1//2+-11//6*a^-1*c^-3*(c+-1*c*a^-1*x^-1)^-3//2+-6//5*a^-1*c^-2*(c+-1*c*a^-1*x^-1)^-5//2+1//8*2^(1/2)*a^-1*c^-9//2*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^9//2*exp(-3*arccoth(a*x)), x) == :(-15*a^-1*(1+-1*a^-1*x^-1)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*arctanh((1+a^-1*x^-1)^(1/2))+10*a^-5*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^4*(c+-1*c*a^-1*x^-1)^9//2+1//7*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-9//2*(c+-1*c*a^-1*x^-1)^9//2*(-325*x^-1+1520a)+65//7*a^-4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^3*(c+-1*c*a^-1*x^-1)^9//2+135//7*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^9//2+x*a^-5*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-9//2*(a+-1*x^-1)^5*(c+-1*c*a^-1*x^-1)^9//2)
@test integrate((c+-1*c*a^-1*x^-1)^7//2*exp(-3*arccoth(a*x)), x) == :(-13*a^-1*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*arctanh((1+a^-1*x^-1)^(1/2))+10*a^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^3*(c+-1*c*a^-1*x^-1)^7//2+1//15*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-7//2*(c+-1*c*a^-1*x^-1)^7//2*(-311*x^-1+1360a)+47//5*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^7//2+x*a^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2*(a+-1*x^-1)^4*(c+-1*c*a^-1*x^-1)^7//2)
@test integrate((c+-1*c*a^-1*x^-1)^5//2*exp(-3*arccoth(a*x)), x) == :(-11*a^-1*(1+-1*a^-1*x^-1)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*arctanh((1+a^-1*x^-1)^(1/2))+10*a^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^5//2+1//3*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-5//2*(c+-1*c*a^-1*x^-1)^5//2*(-29*x^-1+112a)+x*a^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2*(a+-1*x^-1)^3*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-1*x^-1)^3//2*exp(-3*arccoth(a*x)), x) == :(-9*a^-1*(1+-1*a^-1*x^-1)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*arctanh((1+a^-1*x^-1)^(1/2))+a^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2*(c+-1*c*a^-1*x^-1)^3//2*(x^-1+21a)+x*a^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2*(a+-1*x^-1)^2*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-7*a^-1*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+9*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^-1//2*exp(-3*arccoth(a*x)), x) == :(-5*a^-1*c^-1//2*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+x*c^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+5*a^-1*c^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^-3//2*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^-3//2*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+-2*x*c^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+3*x*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^-5//2*exp(-3*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+-1*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1+a^-1*x^-1)^(1/2))+2*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2+-1//2*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^5//2*(c+-1*c*a^-1*x^-1)^-5//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^-7//2*exp(-3*arccoth(a*x)), x) == :(a^-1*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arctanh((1+a^-1*x^-1)^(1/2))+-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*(-2*x^-1+2a)^-1+7//4*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2+-11//8*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^7//2*(c+-1*c*a^-1*x^-1)^-7//2*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+a*x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^7//2*(a+-1*x^-1)^-1*(c+-1*c*a^-1*x^-1)^-7//2)
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(1//8*a^-3*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+1//3*c*x^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-1//8*c*x*a^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+1//12*c*a^-1*x^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(-1//4*a^-2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+(1/2)*c*x^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+1//4*c*x*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(a^-1*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+c*x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+-2*c*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(-2//3*a*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(-2//15*a^2*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+2//5*c*a^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(-8//35*c*a^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-1//2+8//105*a^3*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+-2//7*a*c^2*x^-2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(arccoth(a*x)), x) == :(-16//315*a^4*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+16//105*c*a^4*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-1//2+-2//9*a*c^2*x^-3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+4//21*a^2*c^2*x^-2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//4*x^4*(c+-1*c*a^-1*x^-1)^(1/2)+5//8*a^-1*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+25//32*a^-2*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+75//64*x*a^-3*(c+-1*c*a^-1*x^-1)^(1/2)+75//64*a^-4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//3*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+11//8*x*a^-2*(c+-1*c*a^-1*x^-1)^(1/2)+11//8*a^-3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+11//12*a^-1*x^2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :((1/2)*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+7//4*x*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+7//4*a^-2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^(1/2)+3*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(2*(c+-1*c*a^-1*x^-1)^(1/2)+2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*a*c^-1*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^2*(c+-1*c*a^-1*x^-1)^(1/2)+-2*a^2*c^-1*(c+-1*c*a^-1*x^-1)^3//2+2//5*a^2*c^-2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^3*(c+-1*c*a^-1*x^-1)^(1/2)+-10//3*a^3*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-2//7*a^3*c^-3*(c+-1*c*a^-1*x^-1)^7//2+8//5*a^3*c^-2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(2*arccoth(a*x)), x) == :(4*a^4*(c+-1*c*a^-1*x^-1)^(1/2)+-14//3*a^4*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-10//7*a^4*c^-3*(c+-1*c*a^-1*x^-1)^7//2+2//9*a^4*c^-4*(c+-1*c*a^-1*x^-1)^9//2+18//5*a^4*c^-2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(1//4*x^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+363//64*a^-4*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-4*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+17//24*a^-1*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+107//96*a^-2*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+149//64*x*a^-3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(1//3*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+45//8*a^-3*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-3*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+13//12*a^-1*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+19//8*x*a^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :((1/2)*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+23//4*a^-2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2))+9//4*x*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+5*a^-1*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-1*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-4*2^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(-4*a*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+4*a*c*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+2//3*a*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2)
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(-4*2^(1/2)*a^2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+4*c*a^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+2//3*a^2*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+2//5*a^2*c^3*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(-4*2^(1/2)*a^3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+4*c*a^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-2//7*a^3*c^2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^-1*x^-1)^-3//2+2//3*a^3*c^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^-1*x^-1)^-3//2+4//7*a^3*c^3*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^-1*x^-1)^-5//2)
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//7*a^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2//3*a^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2//5*a^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2//9*a^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-4*2^(1/2)*a^4*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1/2)*2^(1/2)*(1+a^-1*x^-1)^(1/2)))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(-11//8*a^-3*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+1//3*c*x^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-11//12*c*a^-1*x^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+11//8*c*x*a^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(7//4*a^-2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+(1/2)*c*x^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-7//4*c*x*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(-3*a^-1*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+c*x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(2*c^(1/2)*arctanh(c^(1/2)*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)+2*c*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(-2//3*a*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+-8//3*a*c*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(2//5*a^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+2//5*a^2*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^3//2+8//5*c*a^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-1*arccoth(a*x)), x) == :(-104//105*a^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+-104//105*c*a^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+2//7*c*x^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-26//35*a*c*x^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//4*x^4*(c+-1*c*a^-1*x^-1)^(1/2)+-149//64*x*a^-3*(c+-1*c*a^-1*x^-1)^(1/2)+-17//24*a^-1*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+107//96*a^-2*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+363//64*a^-4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//3*x^3*(c+-1*c*a^-1*x^-1)^(1/2)+-45//8*a^-3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-13//12*a^-1*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+19//8*x*a^-2*(c+-1*c*a^-1*x^-1)^(1/2)+4*2^(1/2)*a^-3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :((1/2)*x^2*(c+-1*c*a^-1*x^-1)^(1/2)+-9//4*x*a^-1*(c+-1*c*a^-1*x^-1)^(1/2)+23//4*a^-2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-4*2^(1/2)*a^-2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-1*x^-1)^(1/2)+-5*a^-1*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+4*2^(1/2)*a^-1*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(2*(c+-1*c*a^-1*x^-1)^(1/2)+2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))+-4*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-4*a*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*a*c^-1*(c+-1*c*a^-1*x^-1)^3//2+4*a*2^(1/2)*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(4*a^2*(c+-1*c*a^-1*x^-1)^(1/2)+2//3*a^2*c^-1*(c+-1*c*a^-1*x^-1)^3//2+2//5*a^2*c^-2*(c+-1*c*a^-1*x^-1)^5//2+-4*2^(1/2)*a^2*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-4*a^3*(c+-1*c*a^-1*x^-1)^(1/2)+-2//3*a^3*c^-1*(c+-1*c*a^-1*x^-1)^3//2+-2//7*a^3*c^-3*(c+-1*c*a^-1*x^-1)^7//2+4*2^(1/2)*a^3*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-2*arccoth(a*x)), x) == :(4*a^4*(c+-1*c*a^-1*x^-1)^(1/2)+-2//7*a^4*c^-3*(c+-1*c*a^-1*x^-1)^7//2+2//3*a^4*c^-1*(c+-1*c*a^-1*x^-1)^3//2+2//5*a^4*c^-2*(c+-1*c*a^-1*x^-1)^5//2+2//9*a^4*c^-4*(c+-1*c*a^-1*x^-1)^9//2+-4*2^(1/2)*a^4*c^(1/2)*arctanh((1/2)*2^(1/2)*c^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)))
@test integrate(x^3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-1115//64*a^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+1//4*x^4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+1115//64*a^-4*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-1115//192*x*a^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-25//24*a^-1*x^3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+223//96*a^-2*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-119//8*a^-3*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+1//3*x^3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+119//8*a^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-19//12*a^-1*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+119//24*x*a^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :((1/2)*x^2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-47//4*a^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+47//4*a^-2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+-13//4*x*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(x*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-7*a^-1*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2))+9*a^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate(x^-1*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-8*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)*arctanh((1+a^-1*x^-1)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(64//3*a*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-16//3*a*c^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^3//2+-2//3*a*c^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^5//2)
@test integrate(x^-3*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-56//15*a^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+-1*a^2*c^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^7//2+-224//15*c*a^2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2+-7//5*a^2*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^3//2)
@test integrate(x^-4*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(472//105*a^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^(1/2)+a^3*c^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-1*x^-1)^7//2+2//7*a^3*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^5//2+59//35*a^3*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^3//2+1888//105*c*a^3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-1*x^-1)^-1//2)
@test integrate(x^-5*(c+-1*c*a^-1*x^-1)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-32*a^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-8*a^4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+2*a^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-38//5*a^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+-2//9*a^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2)+50//3*a^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^-1//2*(c+-1*c*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^4*exp(arccoth(a*x)), x) == :(35//128*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+35//128*x*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-7//72*a^7*c^4*x^8*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^5//2+-5//144*a^5*c^4*x^6*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^(1/2)+1//9*a^8*c^4*x^9*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^7//2+1//64*a^3*c^4*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+1//144*a^4*c^4*x^5*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2)+5//72*a^6*c^4*x^7*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^3//2+7//192*a^2*c^4*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+35//384*a*c^4*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3*exp(arccoth(a*x)), x) == :(5//16*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+5//16*x*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-1//7*a^6*c^3*x^7*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^5//2+-1//14*a^4*c^3*x^5*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2)+1//24*a^2*c^3*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+1//56*a^3*c^3*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+5//42*a^5*c^3*x^6*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^3//2+5//48*a*c^3*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^2*exp(arccoth(a*x)), x) == :(3//8*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+3//8*x*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-3//20*a^3*c^2*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+1//5*a^4*c^2*x^5*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^3//2+1//8*a*c^2*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+1//20*a^2*c^2*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)*exp(arccoth(a*x)), x) == :((1/2)*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+(1/2)*c*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-1//3*c*a^2*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+1//6*a*c*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(arccoth(a*x)), x) == :(a^-1*c^-1*exp(arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(arccoth(a*x)), x) == :(2//3*a^-1*c^-2*exp(arccoth(a*x))+-1//3*a^-1*c^-2*(1+-1*a^2*x^2)^-1*(1+-2*a*x)*exp(arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(arccoth(a*x)), x) == :(8//15*a^-1*c^-3*exp(arccoth(a*x))+-4//15*a^-1*c^-3*(1+-1*a^2*x^2)^-1*(1+-2*a*x)*exp(arccoth(a*x))+-1//15*a^-1*c^-3*(1+-1*a^2*x^2)^-2*(1+-4*a*x)*exp(arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(arccoth(a*x)), x) == :(16//35*a^-1*c^-4*exp(arccoth(a*x))+-8//35*a^-1*c^-4*(1+-1*a^2*x^2)^-1*(1+-2*a*x)*exp(arccoth(a*x))+-2//35*a^-1*c^-4*(1+-1*a^2*x^2)^-2*(1+-4*a*x)*exp(arccoth(a*x))+-1//35*a^-1*c^-4*(1+-1*a^2*x^2)^-3*(1+-6*a*x)*exp(arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^5*exp(2*arccoth(a*x)), x) == :(4*a^-1*c^5*(1+a*x)^8+-16//7*a^-1*c^5*(1+a*x)^7+-8//3*a^-1*c^5*(1+a*x)^9+-1//11*a^-1*c^5*(1+a*x)^11+4//5*a^-1*c^5*(1+a*x)^10)
@test integrate((c+-1*c*a^2*x^2)^4*exp(2*arccoth(a*x)), x) == :(-4//3*a^-1*c^4*(1+a*x)^6+-3//4*a^-1*c^4*(1+a*x)^8+1//9*a^-1*c^4*(1+a*x)^9+12//7*a^-1*c^4*(1+a*x)^7)
@test integrate((c+-1*c*a^2*x^2)^3*exp(2*arccoth(a*x)), x) == :(-4//5*a^-1*c^3*(1+a*x)^5+-1//7*a^-1*c^3*(1+a*x)^7+2//3*a^-1*c^3*(1+a*x)^6)
@test integrate((c+-1*c*a^2*x^2)^2*exp(2*arccoth(a*x)), x) == :(-1//2*a^-1*c^2*(1+a*x)^4+1//5*a^-1*c^2*(1+a*x)^5)
@test integrate((c+-1*c*a^2*x^2)*exp(2*arccoth(a*x)), x) == :(-1//3*c*a^-1*(1+a*x)^3)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(2*arccoth(a*x)), x) == :(-1*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-2*exp(2*arccoth(a*x)), x) == :(-1//4*a^-1*c^-2*(1+-1*a*x)^-1+-1//4*a^-1*c^-2*(1+-1*a*x)^-2+-1//4*a^-1*c^-2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(2*arccoth(a*x)), x) == :(-3//16*a^-1*c^-3*(1+-1*a*x)^-1+-1//4*a^-1*c^-3*arctanh(a*x)+-1//8*a^-1*c^-3*(1+-1*a*x)^-2+-1//12*a^-1*c^-3*(1+-1*a*x)^-3+1//16*a^-1*c^-3*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-4*exp(2*arccoth(a*x)), x) == :(-15//64*a^-1*c^-4*arctanh(a*x)+-5//32*a^-1*c^-4*(1+-1*a*x)^-1+-3//32*a^-1*c^-4*(1+-1*a*x)^-2+-1//16*a^-1*c^-4*(1+-1*a*x)^-3+-1//32*a^-1*c^-4*(1+-1*a*x)^-4+1//64*a^-1*c^-4*(1+a*x)^-2+5//64*a^-1*c^-4*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^4*exp(3*arccoth(a*x)), x) == :(-55//128*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-55//128*x*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-55//384*a*c^4*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-11//192*a^2*c^4*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-11//448*a^3*c^4*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-11//1008*a^4*c^4*x^5*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2)+-5//72*a^7*c^4*x^8*(1+a^-1*x^-1)^13//2*(1+-1*a^-1*x^-1)^3//2+-5//1008*a^5*c^4*x^6*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^(1/2)+1//9*a^8*c^4*x^9*(1+a^-1*x^-1)^13//2*(1+-1*a^-1*x^-1)^5//2+5//168*a^6*c^4*x^7*(1+a^-1*x^-1)^13//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3*exp(3*arccoth(a*x)), x) == :(-9//16*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-9//16*x*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-9//280*a^3*c^3*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-3//16*a*c^3*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-3//40*a^2*c^3*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-1//7*a^6*c^3*x^7*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^3//2+-1//70*a^4*c^3*x^5*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2)+1//14*a^5*c^3*x^6*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^2*exp(3*arccoth(a*x)), x) == :(-7//8*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-7//8*x*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-7//24*a*c^2*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-7//60*a^2*c^2*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-1//20*a^3*c^2*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+1//5*a^4*c^2*x^5*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)*exp(3*arccoth(a*x)), x) == :(-5//2*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-5//2*c*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-5//6*a*c*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-1//3*c*a^2*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(3*arccoth(a*x)), x) == :(1//3*a^-1*c^-1*exp(3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(3*arccoth(a*x)), x) == :(-2//15*a^-1*c^-2*exp(3*arccoth(a*x))+1//5*a^-1*c^-2*(1+-1*a^2*x^2)^-1*(3+-2*a*x)*exp(3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(3*arccoth(a*x)), x) == :(-8//35*a^-1*c^-3*exp(3*arccoth(a*x))+-1//7*a^-1*c^-3*(1+-1*a^2*x^2)^-2*(3+-4*a*x)*exp(3*arccoth(a*x))+12//35*a^-1*c^-3*(1+-1*a^2*x^2)^-1*(3+-2*a*x)*exp(3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(3*arccoth(a*x)), x) == :(-16//63*a^-1*c^-4*exp(3*arccoth(a*x))+-10//63*a^-1*c^-4*(1+-1*a^2*x^2)^-2*(3+-4*a*x)*exp(3*arccoth(a*x))+-1//9*a^-1*c^-4*(1+-1*a^2*x^2)^-3*(1+-2*a*x)*exp(3*arccoth(a*x))+8//21*a^-1*c^-4*(1+-1*a^2*x^2)^-1*(3+-2*a*x)*exp(3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^5*exp(4*arccoth(a*x)), x) == :(a^-1*c^5*(1+a*x)^8+-4//3*a^-1*c^5*(1+a*x)^9+-1//11*a^-1*c^5*(1+a*x)^11+3//5*a^-1*c^5*(1+a*x)^10)
@test integrate((c+-1*c*a^2*x^2)^4*exp(4*arccoth(a*x)), x) == :(-1//2*a^-1*c^4*(1+a*x)^8+1//9*a^-1*c^4*(1+a*x)^9+4//7*a^-1*c^4*(1+a*x)^7)
@test integrate((c+-1*c*a^2*x^2)^3*exp(4*arccoth(a*x)), x) == :(-1//7*a^-1*c^3*(1+a*x)^7+1//3*a^-1*c^3*(1+a*x)^6)
@test integrate((c+-1*c*a^2*x^2)^2*exp(4*arccoth(a*x)), x) == :(1//5*a^-1*c^2*(1+a*x)^5)
@test integrate((c+-1*c*a^2*x^2)*exp(4*arccoth(a*x)), x) == :(-4*c*x+-1*c*a^-1*(1+a*x)^2+-8*c*a^-1*log(1+-1*a*x)+-1//3*c*a^-1*(1+a*x)^3)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(4*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a*x)^-2)
@test integrate((c+-1*c*a^2*x^2)^-2*exp(4*arccoth(a*x)), x) == :(1//3*a^-1*c^-2*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^2*x^2)^-3*exp(4*arccoth(a*x)), x) == :(1//8*a^-1*c^-3*(1+-1*a*x)^-4+1//12*a^-1*c^-3*(1+-1*a*x)^-3+1//16*a^-1*c^-3*(1+-1*a*x)^-1+1//16*a^-1*c^-3*(1+-1*a*x)^-2+1//16*a^-1*c^-3*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(4*arccoth(a*x)), x) == :(-1//64*a^-1*c^-4*(1+a*x)^-1+1//16*a^-1*c^-4*(1+-1*a*x)^-4+1//16*a^-1*c^-4*(1+-1*a*x)^-3+1//16*a^-1*c^-4*(1+-1*a*x)^-2+1//20*a^-1*c^-4*(1+-1*a*x)^-5+3//32*a^-1*c^-4*arctanh(a*x)+5//64*a^-1*c^-4*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^4*exp(-1*arccoth(a*x)), x) == :(-35//128*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-35//128*x*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-35//384*a*c^4*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-7//192*a^2*c^4*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-5//48*a^5*c^4*x^6*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^3//2+-1//8*a^7*c^4*x^8*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^7//2+-1//64*a^3*c^4*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+1//8*a^6*c^4*x^7*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^5//2+1//9*a^8*c^4*x^9*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^9//2+1//16*a^4*c^4*x^5*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3*exp(-1*arccoth(a*x)), x) == :(-5//16*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-5//16*x*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-5//48*a*c^3*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-1//6*a^4*c^3*x^5*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^3//2+-1//7*a^6*c^3*x^7*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^7//2+-1//24*a^2*c^3*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+1//6*a^5*c^3*x^6*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^5//2+1//8*a^3*c^3*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^2*exp(-1*arccoth(a*x)), x) == :(-3//8*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-3//8*x*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-1//4*a^3*c^2*x^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^3//2+-1//8*a*c^2*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+1//4*a^2*c^2*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+1//5*a^4*c^2*x^5*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^2*x^2)*exp(-1*arccoth(a*x)), x) == :(-1//2*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-1//2*c*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+(1/2)*a*c*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-1//3*c*a^2*x^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^-1*exp(-1*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(-1*arccoth(a*x)), x) == :(-2//3*a^-1*c^-2*exp(-1*arccoth(a*x))+1//3*a^-1*c^-2*(1+-1*a^2*x^2)^-1*(1+2*a*x)*exp(-1*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(-1*arccoth(a*x)), x) == :(-8//15*a^-1*c^-3*exp(-1*arccoth(a*x))+1//15*a^-1*c^-3*(1+-1*a^2*x^2)^-1*(4+8*a*x)*exp(-1*arccoth(a*x))+1//15*a^-1*c^-3*(1+-1*a^2*x^2)^-2*(1+4*a*x)*exp(-1*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(-1*arccoth(a*x)), x) == :(-16//35*a^-1*c^-4*exp(-1*arccoth(a*x))+1//35*a^-1*c^-4*(1+-1*a^2*x^2)^-1*(8+16*a*x)*exp(-1*arccoth(a*x))+1//35*a^-1*c^-4*(1+-1*a^2*x^2)^-3*(1+6*a*x)*exp(-1*arccoth(a*x))+1//35*a^-1*c^-4*(1+-1*a^2*x^2)^-2*(2+8*a*x)*exp(-1*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^4*exp(-2*arccoth(a*x)), x) == :(-12//7*a^-1*c^4*(1+-1*a*x)^7+-1//9*a^-1*c^4*(1+-1*a*x)^9+3//4*a^-1*c^4*(1+-1*a*x)^8+4//3*a^-1*c^4*(1+-1*a*x)^6)
@test integrate((c+-1*c*a^2*x^2)^3*exp(-2*arccoth(a*x)), x) == :(-2//3*a^-1*c^3*(1+-1*a*x)^6+1//7*a^-1*c^3*(1+-1*a*x)^7+4//5*a^-1*c^3*(1+-1*a*x)^5)
@test integrate((c+-1*c*a^2*x^2)^2*exp(-2*arccoth(a*x)), x) == :((1/2)*a^-1*c^2*(1+-1*a*x)^4+-1//5*a^-1*c^2*(1+-1*a*x)^5)
@test integrate((c+-1*c*a^2*x^2)*exp(-2*arccoth(a*x)), x) == :(1//3*c*a^-1*(1+-1*a*x)^3)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(-2*arccoth(a*x)), x) == :(a^-1*c^-1*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-2*exp(-2*arccoth(a*x)), x) == :(-1//4*a^-1*c^-2*arctanh(a*x)+1//4*a^-1*c^-2*(1+a*x)^-1+1//4*a^-1*c^-2*(1+a*x)^-2)
@test integrate((c+-1*c*a^2*x^2)^-3*exp(-2*arccoth(a*x)), x) == :(-1//4*a^-1*c^-3*arctanh(a*x)+-1//16*a^-1*c^-3*(1+-1*a*x)^-1+1//8*a^-1*c^-3*(1+a*x)^-2+1//12*a^-1*c^-3*(1+a*x)^-3+3//16*a^-1*c^-3*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^-4*exp(-2*arccoth(a*x)), x) == :(-15//64*a^-1*c^-4*arctanh(a*x)+-5//64*a^-1*c^-4*(1+-1*a*x)^-1+-1//64*a^-1*c^-4*(1+-1*a*x)^-2+1//16*a^-1*c^-4*(1+a*x)^-3+1//32*a^-1*c^-4*(1+a*x)^-4+3//32*a^-1*c^-4*(1+a*x)^-2+5//32*a^-1*c^-4*(1+a*x)^-1)
@test integrate((c+-1*c*a^2*x^2)^4*exp(-3*arccoth(a*x)), x) == :(55//128*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+55//128*x*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-11//48*a^5*c^4*x^6*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^5//2+-11//64*a^3*c^4*x^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-11//72*a^7*c^4*x^8*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^9//2+1//9*a^8*c^4*x^9*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^11//2+11//48*a^4*c^4*x^5*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^3//2+11//56*a^6*c^4*x^7*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^7//2+11//192*a^2*c^4*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+55//384*a*c^4*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^3*exp(-3*arccoth(a*x)), x) == :(9//16*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+9//16*x*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-3//8*a^2*c^3*x^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-3//10*a^4*c^3*x^5*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^5//2+-1//7*a^6*c^3*x^7*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^9//2+3//8*a^3*c^3*x^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^3//2+3//14*a^5*c^3*x^6*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^7//2+3//16*a*c^3*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^2*exp(-3*arccoth(a*x)), x) == :(7//8*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+7//8*x*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-7//8*a*c^2*x^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-7//20*a^3*c^2*x^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^5//2+1//5*a^4*c^2*x^5*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^7//2+7//12*a^2*c^2*x^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^2*x^2)*exp(-3*arccoth(a*x)), x) == :(5//2*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-5//2*c*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-1//3*c*a^2*x^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2+5//6*a*c*x^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^2*x^2)^-1*exp(-3*arccoth(a*x)), x) == :(-1//3*a^-1*c^-1*exp(-3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(-3*arccoth(a*x)), x) == :(2//15*a^-1*c^-2*exp(-3*arccoth(a*x))+-1//5*a^-1*c^-2*(1+-1*a^2*x^2)^-1*(3+2*a*x)*exp(-3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3*exp(-3*arccoth(a*x)), x) == :(8//35*a^-1*c^-3*exp(-3*arccoth(a*x))+-1//35*a^-1*c^-3*(1+-1*a^2*x^2)^-1*(36+24*a*x)*exp(-3*arccoth(a*x))+1//7*a^-1*c^-3*(1+-1*a^2*x^2)^-2*(3+4*a*x)*exp(-3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-4*exp(-3*arccoth(a*x)), x) == :(16//63*a^-1*c^-4*exp(-3*arccoth(a*x))+-1//21*a^-1*c^-4*(1+-1*a^2*x^2)^-1*(24+16*a*x)*exp(-3*arccoth(a*x))+1//9*a^-1*c^-4*(1+-1*a^2*x^2)^-3*(1+2*a*x)*exp(-3*arccoth(a*x))+1//63*a^-1*c^-4*(1+-1*a^2*x^2)^-2*(30+40*a*x)*exp(-3*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(arccoth(a*x)), x) == :(3*a^-10*x^-9*(1+a*x)^8*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+-32//7*a^-10*x^-9*(1+a*x)^7*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+-8//9*a^-10*x^-9*(1+a*x)^9*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+1//10*a^-10*x^-9*(1+a*x)^10*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+8//3*a^-10*x^-9*(1+a*x)^6*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2)
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(arccoth(a*x)), x) == :(2*a^-8*x^-7*(1+a*x)^6*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+-8//5*a^-8*x^-7*(1+a*x)^5*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+-6//7*a^-8*x^-7*(1+a*x)^7*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+1//8*a^-8*x^-7*(1+a*x)^8*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2)
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(arccoth(a*x)), x) == :(a^-6*x^-5*(1+a*x)^4*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2+-4//5*a^-6*x^-5*(1+a*x)^5*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2+1//6*a^-6*x^-5*(1+a*x)^6*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(arccoth(a*x)), x) == :(-2//3*a^-4*x^-3*(1+a*x)^3*(1+-1*a^-2*x^-2)^-3//2*(c+-1*c*a^2*x^2)^3//2+1//4*a^-4*x^-3*(1+a*x)^4*(1+-1*a^-2*x^-2)^-3//2*(c+-1*c*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :(a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(a^2*x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+(1/2)*a^2*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(4+-4*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-3//8*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x)+-1//8*a^4*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2)
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(arccoth(a*x)), x) == :(-1*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+3*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(16+-16*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+-1//32*a^6*x^7*(1+a*x)^-2*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+1//24*a^6*x^7*(1+-1*a*x)^-3*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+3//32*a^6*x^7*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+5//16*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(2*arccoth(a*x)), x) == :(11//90*a^-1*(c+-1*c*a^2*x^2)^9//2+-77//256*x*c^4*(c+-1*c*a^2*x^2)^(1/2)+-77//256*a^-1*c^9//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-77//384*x*c^3*(c+-1*c*a^2*x^2)^3//2+-77//480*x*c^2*(c+-1*c*a^2*x^2)^5//2+-11//80*c*x*(c+-1*c*a^2*x^2)^7//2+1//10*a^-1*(c+-1*c*a^2*x^2)^9//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(2*arccoth(a*x)), x) == :(9//56*a^-1*(c+-1*c*a^2*x^2)^7//2+-45//128*x*c^3*(c+-1*c*a^2*x^2)^(1/2)+-45//128*a^-1*c^7//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-15//64*x*c^2*(c+-1*c*a^2*x^2)^3//2+-3//16*c*x*(c+-1*c*a^2*x^2)^5//2+1//8*a^-1*(c+-1*c*a^2*x^2)^7//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(2*arccoth(a*x)), x) == :(7//30*a^-1*(c+-1*c*a^2*x^2)^5//2+-7//16*x*c^2*(c+-1*c*a^2*x^2)^(1/2)+-7//16*a^-1*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-7//24*c*x*(c+-1*c*a^2*x^2)^3//2+1//6*a^-1*(c+-1*c*a^2*x^2)^5//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(2*arccoth(a*x)), x) == :(5//12*a^-1*(c+-1*c*a^2*x^2)^3//2+-5//8*c*x*(c+-1*c*a^2*x^2)^(1/2)+-5//8*a^-1*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//4*a^-1*(c+-1*c*a^2*x^2)^3//2*(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(3//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+a*x)+-3//2*a^-1*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(2*arccoth(a*x)), x) == :(a^-1*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1*a^-1*(c+-1*c*a^2*x^2)^-1//2*(2+2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(2*arccoth(a*x)), x) == :(-1//3*x*c^-1*(c+-1*c*a^2*x^2)^-1//2+-1//3*a^-1*(c+-1*c*a^2*x^2)^-3//2*(2+2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(2*arccoth(a*x)), x) == :(-2//5*x*c^-2*(c+-1*c*a^2*x^2)^-1//2+-1//5*x*c^-1*(c+-1*c*a^2*x^2)^-3//2+-1//5*a^-1*(c+-1*c*a^2*x^2)^-5//2*(2+2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(2*arccoth(a*x)), x) == :(-8//21*x*c^-3*(c+-1*c*a^2*x^2)^-1//2+-4//21*x*c^-2*(c+-1*c*a^2*x^2)^-3//2+-1//7*x*c^-1*(c+-1*c*a^2*x^2)^-5//2+-1//7*a^-1*(c+-1*c*a^2*x^2)^-7//2*(2+2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-9//2*exp(2*arccoth(a*x)), x) == :(-16//45*x*c^-4*(c+-1*c*a^2*x^2)^-1//2+-8//45*x*c^-3*(c+-1*c*a^2*x^2)^-3//2+-2//15*x*c^-2*(c+-1*c*a^2*x^2)^-5//2+-1//9*x*c^-1*(c+-1*c*a^2*x^2)^-7//2+-1//9*a^-1*(c+-1*c*a^2*x^2)^-9//2*(2+2*a*x))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(3*arccoth(a*x)), x) == :(-8//7*a^-10*x^-9*(1+a*x)^7*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+-2//3*a^-10*x^-9*(1+a*x)^9*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+1//10*a^-10*x^-9*(1+a*x)^10*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+3//2*a^-10*x^-9*(1+a*x)^8*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2)
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(3*arccoth(a*x)), x) == :(-4//7*a^-8*x^-7*(1+a*x)^7*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+1//8*a^-8*x^-7*(1+a*x)^8*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+2//3*a^-8*x^-7*(1+a*x)^6*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2)
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(3*arccoth(a*x)), x) == :(-2//5*a^-6*x^-5*(1+a*x)^5*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2+1//6*a^-6*x^-5*(1+a*x)^6*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(3*arccoth(a*x)), x) == :(1//4*a^-4*x^-3*(1+a*x)^4*(1+-1*a^-2*x^-2)^-3//2*(c+-1*c*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :((1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+-1*a*x)+2*x*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(3*arccoth(a*x)), x) == :(-1//2*a^2*x^3*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(3*arccoth(a*x)), x) == :(a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(8+-8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+1//6*a^4*x^5*(1+-1*a*x)^-3*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+1//8*a^4*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+1//8*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(3*arccoth(a*x)), x) == :(a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(32+32*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+-1*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(8+-8*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+-5//32*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2*arctanh(a*x)+-3//32*a^6*x^7*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+-1//12*a^6*x^7*(1+-1*a*x)^-3*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+-1//16*a^6*x^7*(1+-1*a*x)^-4*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2)
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(-1*arccoth(a*x)), x) == :(3*a^-10*x^-9*(1+-1*a*x)^8*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+-32//7*a^-10*x^-9*(1+-1*a*x)^7*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+-8//9*a^-10*x^-9*(1+-1*a*x)^9*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+1//10*a^-10*x^-9*(1+-1*a*x)^10*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+8//3*a^-10*x^-9*(1+-1*a*x)^6*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2)
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(-1*arccoth(a*x)), x) == :(2*a^-8*x^-7*(1+-1*a*x)^6*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+-8//5*a^-8*x^-7*(1+-1*a*x)^5*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+-6//7*a^-8*x^-7*(1+-1*a*x)^7*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+1//8*a^-8*x^-7*(1+-1*a*x)^8*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2)
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(-1*arccoth(a*x)), x) == :(a^-6*x^-5*(1+-1*a*x)^4*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2+-4//5*a^-6*x^-5*(1+-1*a*x)^5*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2+1//6*a^-6*x^-5*(1+-1*a*x)^6*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(-1*arccoth(a*x)), x) == :(-2//3*a^-4*x^-3*(1+-1*a*x)^3*(1+-1*a^-2*x^-2)^-3//2*(c+-1*c*a^2*x^2)^3//2+1//4*a^-4*x^-3*(1+-1*a*x)^4*(1+-1*a^-2*x^-2)^-3//2*(c+-1*c*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :((1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(-1*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(-1*arccoth(a*x)), x) == :(a^2*x^3*(1+-1*a^-2*x^-2)^3//2*(2+2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+-1//2*a^2*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(-1*arccoth(a*x)), x) == :(a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(8+-8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(4+4*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1//8*a^4*x^5*(1+a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+3//8*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(-1*arccoth(a*x)), x) == :(-1*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(8+-8*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+3*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(16+16*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+-5//16*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2*arctanh(a*x)+-1//32*a^6*x^7*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+1//24*a^6*x^7*(1+a*x)^-3*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+3//32*a^6*x^7*(1+a*x)^-2*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2)
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(-2*arccoth(a*x)), x) == :(-7//30*a^-1*(c+-1*c*a^2*x^2)^5//2+-7//16*x*c^2*(c+-1*c*a^2*x^2)^(1/2)+-7//16*a^-1*c^5//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-7//24*c*x*(c+-1*c*a^2*x^2)^3//2+-1//6*a^-1*(c+-1*c*a^2*x^2)^5//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(-2*arccoth(a*x)), x) == :(-5//12*a^-1*(c+-1*c*a^2*x^2)^3//2+-5//8*c*x*(c+-1*c*a^2*x^2)^(1/2)+-5//8*a^-1*c^3//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//4*a^-1*(c+-1*c*a^2*x^2)^3//2*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-3//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)+-3//2*a^-1*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(-2*arccoth(a*x)), x) == :(a^-1*c^-1//2*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+a^-1*(c+-1*c*a^2*x^2)^-1//2*(2+-2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(-2*arccoth(a*x)), x) == :(-1//3*x*c^-1*(c+-1*c*a^2*x^2)^-1//2+1//3*a^-1*(c+-1*c*a^2*x^2)^-3//2*(2+-2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(-2*arccoth(a*x)), x) == :(-2//5*x*c^-2*(c+-1*c*a^2*x^2)^-1//2+-1//5*x*c^-1*(c+-1*c*a^2*x^2)^-3//2+1//5*a^-1*(c+-1*c*a^2*x^2)^-5//2*(2+-2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(-2*arccoth(a*x)), x) == :(-8//21*x*c^-3*(c+-1*c*a^2*x^2)^-1//2+-4//21*x*c^-2*(c+-1*c*a^2*x^2)^-3//2+-1//7*x*c^-1*(c+-1*c*a^2*x^2)^-5//2+1//7*a^-1*(c+-1*c*a^2*x^2)^-7//2*(2+-2*a*x))
@test integrate((c+-1*c*a^2*x^2)^-9//2*exp(-2*arccoth(a*x)), x) == :(-16//45*x*c^-4*(c+-1*c*a^2*x^2)^-1//2+-8//45*x*c^-3*(c+-1*c*a^2*x^2)^-3//2+-2//15*x*c^-2*(c+-1*c*a^2*x^2)^-5//2+-1//9*x*c^-1*(c+-1*c*a^2*x^2)^-7//2+1//9*a^-1*(c+-1*c*a^2*x^2)^-9//2*(2+-2*a*x))
@test integrate((c+-1*c*a^2*x^2)^9//2*exp(-3*arccoth(a*x)), x) == :(-8//7*a^-10*x^-9*(1+-1*a*x)^7*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+-2//3*a^-10*x^-9*(1+-1*a*x)^9*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+1//10*a^-10*x^-9*(1+-1*a*x)^10*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2+3//2*a^-10*x^-9*(1+-1*a*x)^8*(1+-1*a^-2*x^-2)^-9//2*(c+-1*c*a^2*x^2)^9//2)
@test integrate((c+-1*c*a^2*x^2)^7//2*exp(-3*arccoth(a*x)), x) == :(-4//7*a^-8*x^-7*(1+-1*a*x)^7*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+1//8*a^-8*x^-7*(1+-1*a*x)^8*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2+2//3*a^-8*x^-7*(1+-1*a*x)^6*(1+-1*a^-2*x^-2)^-7//2*(c+-1*c*a^2*x^2)^7//2)
@test integrate((c+-1*c*a^2*x^2)^5//2*exp(-3*arccoth(a*x)), x) == :(-2//5*a^-6*x^-5*(1+-1*a*x)^5*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2+1//6*a^-6*x^-5*(1+-1*a*x)^6*(1+-1*a^-2*x^-2)^-5//2*(c+-1*c*a^2*x^2)^5//2)
@test integrate((c+-1*c*a^2*x^2)^3//2*exp(-3*arccoth(a*x)), x) == :(1//4*a^-4*x^-3*(1+-1*a*x)^4*(1+-1*a^-2*x^-2)^-3//2*(c+-1*c*a^2*x^2)^3//2)
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :((1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^-1//2*exp(-3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2*log(1+a*x)+2*x*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^2*x^2)^-1//2)
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(-3*arccoth(a*x)), x) == :(-1//2*a^2*x^3*(1+a*x)^-2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2)
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(-3*arccoth(a*x)), x) == :(a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1//8*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x)+1//6*a^4*x^5*(1+a*x)^-3*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+1//8*a^4*x^5*(1+a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2)
@test integrate((c+-1*c*a^2*x^2)^-7//2*exp(-3*arccoth(a*x)), x) == :(a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(32+-32*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+-1*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-7//2+-3//32*a^6*x^7*(1+a*x)^-2*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+-1//12*a^6*x^7*(1+a*x)^-3*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+-1//16*a^6*x^7*(1+a*x)^-4*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2+5//32*a^6*x^7*(1+-1*a^-2*x^-2)^7//2*(c+-1*c*a^2*x^2)^-7//2*arctanh(a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :(1//4*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//3*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :(1//3*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :(a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :(x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+-1*a^-1*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//5*x^4*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a^-1*x^3*(c+-1*c*a^2*x^2)^(1/2)+-3//4*a^-4*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//20*a^-4*(c+-1*c*a^2*x^2)^(1/2)*(24+15*a*x)+3//5*a^-2*x^2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//4*x^3*(c+-1*c*a^2*x^2)^(1/2)+-7//8*a^-3*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//24*a^-3*(c+-1*c*a^2*x^2)^(1/2)*(32+21*a*x)+2//3*a^-1*x^2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//3*x^2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//3*a^-2*(c+-1*c*a^2*x^2)^(1/2)*(5+3*a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(3//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+a*x)+-3//2*a^-1*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :((c+-1*c*a^2*x^2)^(1/2)+c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+-2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(x^-1*(c+-1*c*a^2*x^2)^(1/2)+-1*a*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+2*a*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :((1/2)*x^-2*(c+-1*c*a^2*x^2)^(1/2)+2*a*x^-1*(c+-1*c*a^2*x^2)^(1/2)+3//2*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//3*x^-3*(c+-1*c*a^2*x^2)^(1/2)+a*x^-2*(c+-1*c*a^2*x^2)^(1/2)+a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+5//3*a^2*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//4*x^-4*(c+-1*c*a^2*x^2)^(1/2)+2//3*a*x^-3*(c+-1*c*a^2*x^2)^(1/2)+4//3*a^3*x^-1*(c+-1*c*a^2*x^2)^(1/2)+7//8*a^2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+7//8*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//5*x^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2*x*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//4*a^-1*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4//3*a^-2*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-5*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//4*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2*x*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-4*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(4*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//3*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3//2*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :((1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+3*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(a^-1*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+(1/2)*a^-1*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(3//2*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//3*a^-1*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(3*arccoth(a*x)), x) == :(x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2*a*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//4*a^-1*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+-1*a*x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :((1/2)*x^5*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+a^-1*x^4*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+(1/2)*a^-2*x^3*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+1//4*a^-2*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+a*x)+7//4*a^-2*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+-1*a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(x^4*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+(1/2)*a^-1*x^3*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+-1//4*a^-1*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+a*x)+5//4*a^-1*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+1//4*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+a*x)+3//4*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+-1*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(a*x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+-1//2*a*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(a^2*x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+(1/2)*a^2*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*arctanh(a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(a^3*x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+a^3*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(x)+-3//4*a^3*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+-1*a*x)+-1//4*a^3*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(-1*a^3*x^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+a^4*x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+a^4*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(x)+-5//4*a^4*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+-1*a*x)+1//4*a^4*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^-3//2*exp(arccoth(a*x)), x) == :(-1*a^4*x^2*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+-1//2*x*a^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2+a^5*x^3*(1+-1*a^-2*x^-2)^3//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-3//2+2*a^5*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(x)+-7//4*a^5*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+-1*a*x)+-1//4*a^5*x^3*(1+-1*a^-2*x^-2)^3//2*(c+-1*c*a^2*x^2)^-3//2*log(1+a*x))
@test integrate(x^5*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(x^6*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+a^-1*x^5*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+-7//16*a^-1*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+a*x)+-1//8*a^-1*x^5*(1+a*x)^-1*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+-1//8*a^-1*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+23//16*a^-1*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+-1*a*x))
@test integrate(x^4*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+3*x^5*(1+-1*a^-2*x^-2)^5//2*(4+-4*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1//8*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+5//16*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+a*x)+11//16*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+-1*a*x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(a*x^5*(1+-1*a^-2*x^-2)^5//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-3//8*a*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x)+-1//8*a*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2)
@test integrate(x^2*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(a^2*x^5*(1+-1*a^-2*x^-2)^5//2*(4+-4*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+a^2*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1//8*a^2*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+1//8*a^2*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(-1*a^3*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1//8*a^3*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+1//8*a^3*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x))
@test integrate((c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(4+-4*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-3//8*a^4*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*arctanh(a*x)+-1//8*a^4*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2)
@test integrate(x^-1*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(-1*a^5*x^5*(1+-1*a^-2*x^-2)^5//2*(2+-2*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a^5*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a^5*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(x)+-1//8*a^5*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+5//16*a^5*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+a*x)+11//16*a^5*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+-1*a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^-5//2*exp(arccoth(a*x)), x) == :(a^5*x^4*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+a^6*x^5*(1+-1*a^-2*x^-2)^5//2*(8+8*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-1*a^6*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(x)+-3*a^6*x^5*(1+-1*a^-2*x^-2)^5//2*(4+-4*a*x)^-1*(c+-1*c*a^2*x^2)^-5//2+-7//16*a^6*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+a*x)+-1//8*a^6*x^5*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2+23//16*a^6*x^5*(1+-1*a^-2*x^-2)^5//2*(c+-1*c*a^2*x^2)^-5//2*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(1//4*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//3*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(1//3*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//2*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :((1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(a^-1*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//5*x^4*(c+-1*c*a^2*x^2)^(1/2)+-1//2*a^-1*x^3*(c+-1*c*a^2*x^2)^(1/2)+1//20*a^-4*(c+-1*c*a^2*x^2)^(1/2)*(24+-15*a*x)+3//4*a^-4*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+3//5*a^-2*x^2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//4*x^3*(c+-1*c*a^2*x^2)^(1/2)+-7//8*a^-3*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-2//3*a^-1*x^2*(c+-1*c*a^2*x^2)^(1/2)+-1//24*a^-3*(c+-1*c*a^2*x^2)^(1/2)*(32+-21*a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//3*x^2*(c+-1*c*a^2*x^2)^(1/2)+a^-2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+1//3*a^-2*(c+-1*c*a^2*x^2)^(1/2)*(5+-3*a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-3//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)+-3//2*a^-1*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-1//2*a^-1*(c+-1*c*a^2*x^2)^(1/2)*(1+-1*a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :((c+-1*c*a^2*x^2)^(1/2)+c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+2*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x^-1*(c+-1*c*a^2*x^2)^(1/2)+-1*a*c^(1/2)*arctan(a*x*c^(1/2)*(c+-1*c*a^2*x^2)^-1//2)+-2*a*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :((1/2)*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-2*a*x^-1*(c+-1*c*a^2*x^2)^(1/2)+3//2*a^2*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//3*x^-3*(c+-1*c*a^2*x^2)^(1/2)+-1*a*x^-2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^3*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2))+5//3*a^2*x^-1*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//4*x^-4*(c+-1*c*a^2*x^2)^(1/2)+-4//3*a^3*x^-1*(c+-1*c*a^2*x^2)^(1/2)+-2//3*a*x^-3*(c+-1*c*a^2*x^2)^(1/2)+7//8*a^2*x^-2*(c+-1*c*a^2*x^2)^(1/2)+7//8*a^4*c^(1/2)*arctanh(c^-1//2*(c+-1*c*a^2*x^2)^(1/2)))
@test integrate(x^3*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(4*a^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//5*x^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-2*x*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3//4*a^-1*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4//3*a^-2*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-5*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^2*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-4*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//4*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+2*x*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-4*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(4*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+1//3*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3//2*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^-3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate((c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :((1/2)*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^-1*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+-4*a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^-2*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-1*a^-1*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^-3*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//2*a^-1*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+4*a*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^-4*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(3//2*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//3*a^-1*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x)+4*a^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x))
@test integrate(x^-5*(c+-1*c*a^2*x^2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-2*a*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+4*a^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-1//4*a^-1*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)+-4*a^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(1+a*x)+4*a^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2)*log(x))
@test integrate(x^m*(c+-1*c*a^2*x^2)^(1/2)*exp(arccoth(a*x)), x) == :(x^(1+m)*(1+-1*a^-2*x^-2)^-1//2*(2+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+a^-1*x^m*(1+m)^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate(x^m*(c+-1*c*a^2*x^2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(x^(1+m)*(1+-1*a^-2*x^-2)^-1//2*(2+m)^-1*(c+-1*c*a^2*x^2)^(1/2)+-1*a^-1*x^m*(1+m)^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^2*x^2)^(1/2))
@test integrate((c+-1*c*a^2*x^2)^-1*exp(n*arccoth(a*x)), x) == :(a^-1*c^-1*n^-1*exp(n*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-2*exp(n*arccoth(a*x)), x) == :(2*a^-1*c^-2*n^-1*(4+-1*n^2)^-1*exp(n*arccoth(a*x))+-1*a^-1*c^-2*(1+-1*a^2*x^2)^-1*(4+-1*n^2)^-1*(n+-2*a*x)*exp(n*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(n*arccoth(a*x)), x) == :(-1*a^-1*c^-1*(1+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-1//2*(n+-1*a*x)*exp(n*arccoth(a*x)))
@test integrate(x*(c+-1*c*a^2*x^2)^-3//2*exp(n*arccoth(a*x)), x) == :(a^-2*c^-1*(1+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-1//2*(1+-1*a*n*x)*exp(n*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^-3//2*exp(n*arccoth(a*x)), x) == :(-1*a^-1*c^-1*(1+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-1//2*(n+-1*a*x)*exp(n*arccoth(a*x)))
@test integrate(x^2*(c+-1*c*a^2*x^2)^-5//2*exp(n*arccoth(a*x)), x) == :(-1*a^-3*c^-1*(9+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-3//2*(n+-3*a*x)*exp(n*arccoth(a*x))+a^-3*c^-2*(c+-1*c*a^2*x^2)^-1//2*(9+n^4+-10*n^2)^-1*(3+-1*n^2)*(n+-1*a*x)*exp(n*arccoth(a*x)))
@test integrate(x*(c+-1*c*a^2*x^2)^-5//2*exp(n*arccoth(a*x)), x) == :(a^-2*c^-1*(9+-1*n^2)^-1*(c+-1*c*a^2*x^2)^-3//2*(3+-1*a*n*x)*exp(n*arccoth(a*x))+2*n*a^-2*c^-2*(c+-1*c*a^2*x^2)^-1//2*(9+n^4+-10*n^2)^-1*(n+-1*a*x)*exp(n*arccoth(a*x)))
@test integrate((c+-1*c*a^2*x^2)^p*exp(2*p*arccoth(a*x)), x) == :(x*(1+2p)^-1*(1+a^-1*x^-1)^(1+2p)*(1+-1*a^-2*x^-2)^(-1p)*(c+-1*c*a^2*x^2)^p)
@test integrate((c+-1*c*a^2*x^2)^p*exp(-2*p*arccoth(a*x)), x) == :(x*(1+2p)^-1*(1+-1*a^-1*x^-1)^(1+2p)*(1+-1*a^-2*x^-2)^(-1p)*(c+-1*c*a^2*x^2)^p)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(arccoth(a*x)), x) == :(a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+35//16*a^-1*c^4*arccsc(a*x)+x*c^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^7//2+-131//280*a^-1*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-91//120*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-67//48*a^-1*c^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-51//16*a^-1*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+8//7*a^-1*c^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^5//2+47//42*a^-1*c^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^3//2+61//70*a^-1*c^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(arccoth(a*x)), x) == :(a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+15//8*a^-1*c^3*arccsc(a*x)+x*c^3*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^5//2+-43//60*a^-1*c^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-31//24*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-23//8*a^-1*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+6//5*a^-1*c^3*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^3//2+23//20*a^-1*c^3*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(arccoth(a*x)), x) == :(a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+3//2*a^-1*c^2*arccsc(a*x)+x*c^2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^3//2+-7//6*a^-1*c^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-5//2*a^-1*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+4//3*a^-1*c^2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)*exp(arccoth(a*x)), x) == :(c*a^-1*arccsc(a*x)+c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+c*x*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-2*c*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(arccoth(a*x)), x) == :(a^-1*c^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2+-2*a^-1*c^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2)
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(arccoth(a*x)), x) == :(a^-1*c^-2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2+-11//3*a^-1*c^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2+-4//3*a^-1*c^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2+8//3*a^-1*c^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(arccoth(a*x)), x) == :(a^-1*c^-3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-5//2+-34//5*a^-1*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-1//2+-29//15*a^-1*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-3//2+-6//5*a^-1*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-5//2+16//5*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+21//5*a^-1*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(arccoth(a*x)), x) == :(a^-1*c^-4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-7//2+-269//21*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-1//2+-62//21*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-3//2+-11//7*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-5//2+-8//7*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-7//2+128//35*a^-1*c^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+163//35*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+262//35*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^5*exp(2*arccoth(a*x)), x) == :(x*c^5+-3*a^-5*c^5*x^-4+2*a^-1*c^5*log(x)+3*a^-2*c^5*x^-1+4*a^-3*c^5*x^-2+-2//3*a^-4*c^5*x^-3+-2//5*a^-6*c^5*x^-5+-1//4*a^-9*c^5*x^-8+-1//9*a^-10*c^5*x^-9+3//7*a^-8*c^5*x^-7+4//3*a^-7*c^5*x^-6)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(2*arccoth(a*x)), x) == :(x*c^4+2*a^-1*c^4*log(x)+2*a^-2*c^4*x^-1+3*a^-3*c^4*x^-2+-3//2*a^-5*c^4*x^-4+-2//5*a^-6*c^4*x^-5+1//3*a^-7*c^4*x^-6+1//7*a^-8*c^4*x^-7)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(2*arccoth(a*x)), x) == :(x*c^3+a^-2*c^3*x^-1+2*a^-1*c^3*log(x)+2*a^-3*c^3*x^-2+-1//2*a^-5*c^3*x^-4+-1//5*a^-6*c^3*x^-5+1//3*a^-4*c^3*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(2*arccoth(a*x)), x) == :(x*c^2+a^-3*c^2*x^-2+2*a^-1*c^2*log(x)+1//3*a^-4*c^2*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)*exp(2*arccoth(a*x)), x) == :(c*x+-1*c*a^-2*x^-1+2*c*a^-1*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(2*arccoth(a*x)), x) == :(x*c^-1+a^-1*c^-1*(1+-1*a*x)^-1+2*a^-1*c^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(2*arccoth(a*x)), x) == :(x*c^-2+-1//4*a^-1*c^-2*(1+-1*a*x)^-2+-1//8*a^-1*c^-2*log(1+a*x)+7//4*a^-1*c^-2*(1+-1*a*x)^-1+17//8*a^-1*c^-2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(2*arccoth(a*x)), x) == :(x*c^-3+-5//8*a^-1*c^-3*(1+-1*a*x)^-2+-1//4*a^-1*c^-3*log(1+a*x)+-1//16*a^-1*c^-3*(1+a*x)^-1+1//12*a^-1*c^-3*(1+-1*a*x)^-3+9//4*a^-1*c^-3*log(1+-1*a*x)+39//16*a^-1*c^-3*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(2*arccoth(a*x)), x) == :(x*c^-4+-47//128*a^-1*c^-4*log(1+a*x)+-35//32*a^-1*c^-4*(1+-1*a*x)^-2+-11//64*a^-1*c^-4*(1+a*x)^-1+-1//32*a^-1*c^-4*(1+-1*a*x)^-4+1//64*a^-1*c^-4*(1+a*x)^-2+13//48*a^-1*c^-4*(1+-1*a*x)^-3+99//32*a^-1*c^-4*(1+-1*a*x)^-1+303//128*a^-1*c^-4*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+15//16*a^-1*c^4*arccsc(a*x)+x*c^4*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^5//2+-303//280*a^-1*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-63//16*a^-1*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-61//40*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-57//70*a^-1*c^4*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2)+-37//16*a^-1*c^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+8//7*a^-1*c^4*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^3//2+15//14*a^-1*c^4*(1+a^-1*x^-1)^11//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+3//8*a^-1*c^3*arccsc(a*x)+x*c^3*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^3//2+-29//20*a^-1*c^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+-27//8*a^-1*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-21//20*a^-1*c^3*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-17//8*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+6//5*a^-1*c^3*(1+a^-1*x^-1)^9//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-1//2*a^-1*c^2*arccsc(a*x)+x*c^2*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+-11//6*a^-1*c^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+-5//2*a^-1*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-4//3*a^-1*c^2*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)*exp(3*arccoth(a*x)), x) == :(-3*c*a^-1*arccsc(a*x)+3*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+c*x*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-3//2+-14//3*a^-1*c^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2+-5//3*a^-1*c^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-3//2)
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^-2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-5//2+-24//5*a^-1*c^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-1//2+-9//5*a^-1*c^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-3//2+-6//5*a^-1*c^-2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^-5//2)
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^-3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2+-281//35*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-1//2+-88//35*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-3//2+-53//35*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-5//2+-8//7*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^-7//2+176//35*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(3*arccoth(a*x)), x) == :(3*a^-1*c^-4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-9//2+-1462//105*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-1//2+-1147//315*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-3//2+-208//105*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-5//2+-29//21*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-7//2+-10//9*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-9//2+1664//315*a^-1*c^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2609//315*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^5*exp(4*arccoth(a*x)), x) == :(x*c^5+(1/2)*a^-9*c^5*x^-8+-3*a^-2*c^5*x^-1+4*a^-1*c^5*log(x)+4*a^-3*c^5*x^-2+-14//5*a^-6*c^5*x^-5+-4//3*a^-7*c^5*x^-6+1//9*a^-10*c^5*x^-9+3//7*a^-8*c^5*x^-7+14//3*a^-4*c^5*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(4*arccoth(a*x)), x) == :(x*c^4+a^-5*c^4*x^-4+-4*a^-2*c^4*x^-1+2*a^-3*c^4*x^-2+4*a^-1*c^4*log(x)+-4//5*a^-6*c^4*x^-5+-2//3*a^-7*c^4*x^-6+-1//7*a^-8*c^4*x^-7+10//3*a^-4*c^4*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(4*arccoth(a*x)), x) == :(x*c^3+a^-5*c^3*x^-4+-5*a^-2*c^3*x^-1+4*a^-1*c^3*log(x)+1//5*a^-6*c^3*x^-5+5//3*a^-4*c^3*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(4*arccoth(a*x)), x) == :(x*c^2+-6*a^-2*c^2*x^-1+-2*a^-3*c^2*x^-2+4*a^-1*c^2*log(x)+-1//3*a^-4*c^2*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)*exp(4*arccoth(a*x)), x) == :(c*x+c*a^-2*x^-1+-4*c*a^-1*log(x)+8*c*a^-1*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(4*arccoth(a*x)), x) == :(x*c^-1+-1*a^-1*c^-1*(1+-1*a*x)^-2+4*a^-1*c^-1*log(1+-1*a*x)+5*a^-1*c^-1*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(4*arccoth(a*x)), x) == :(x*c^-2+-2*a^-1*c^-2*(1+-1*a*x)^-2+4*a^-1*c^-2*log(1+-1*a*x)+6*a^-1*c^-2*(1+-1*a*x)^-1+1//3*a^-1*c^-2*(1+-1*a*x)^-3)
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(4*arccoth(a*x)), x) == :(x*c^-3+-49//16*a^-1*c^-3*(1+-1*a*x)^-2+-1//8*a^-1*c^-3*(1+-1*a*x)^-4+-1//32*a^-1*c^-3*log(1+a*x)+11//12*a^-1*c^-3*(1+-1*a*x)^-3+111//16*a^-1*c^-3*(1+-1*a*x)^-1+129//32*a^-1*c^-3*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(4*arccoth(a*x)), x) == :(x*c^-4+-67//16*a^-1*c^-4*(1+-1*a*x)^-2+-7//16*a^-1*c^-4*(1+-1*a*x)^-4+-5//64*a^-1*c^-4*log(1+a*x)+-1//64*a^-1*c^-4*(1+a*x)^-1+1//20*a^-1*c^-4*(1+-1*a*x)^-5+83//48*a^-1*c^-4*(1+-1*a*x)^-3+261//64*a^-1*c^-4*log(1+-1*a*x)+501//64*a^-1*c^-4*(1+-1*a*x)^-1)
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+35//16*a^-1*c^4*arccsc(a*x)+x*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^9//2+-19//16*a^-1*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+-1//16*a^-1*c^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+7//6*a^-1*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^5//2+7//40*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+8//7*a^-1*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^7//2+19//40*a^-1*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^(1/2)+29//30*a^-1*c^4*(1+a^-1*x^-1)^7//2*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+15//8*a^-1*c^3*arccsc(a*x)+x*c^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^7//2+-7//8*a^-1*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+1//24*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+5//4*a^-1*c^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^3//2+6//5*a^-1*c^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^5//2+11//12*a^-1*c^3*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+3//2*a^-1*c^2*arccsc(a*x)+x*c^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^5//2+-1//2*a^-1*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+3//2*a^-1*c^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+4//3*a^-1*c^2*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-2*x^-2)*exp(-1*arccoth(a*x)), x) == :(c*a^-1*arccsc(a*x)+-1*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+c*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2+2*c*a^-1*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2)+2*a^-1*c^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^-2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-2*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-1//2+-2*a^-1*c^-2*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^-1//2+5//3*a^-1*c^-2*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+8//3*a^-1*c^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^-3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-3*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-3//2+-13//3*a^-1*c^-3*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-1//2+-4//3*a^-1*c^-3*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^-3//2+11//5*a^-1*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+14//5*a^-1*c^-3*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2)+16//5*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(-1*arccoth(a*x)), x) == :(-1*a^-1*c^-4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-4*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^-5//2+-31//15*a^-1*c^-4*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^-3//2+-28//3*a^-1*c^-4*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^-1//2+-6//5*a^-1*c^-4*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^-5//2+93//35*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+115//21*a^-1*c^-4*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^(1/2)+122//35*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2)+128//35*a^-1*c^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(-2*arccoth(a*x)), x) == :(x*c^4+-3*a^-3*c^4*x^-2+-2*a^-1*c^4*log(x)+2*a^-2*c^4*x^-1+-2//5*a^-6*c^4*x^-5+-1//3*a^-7*c^4*x^-6+1//7*a^-8*c^4*x^-7+3//2*a^-5*c^4*x^-4)
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(-2*arccoth(a*x)), x) == :(x*c^3+a^-2*c^3*x^-1+(1/2)*a^-5*c^3*x^-4+-2*a^-1*c^3*log(x)+-2*a^-3*c^3*x^-2+-1//5*a^-6*c^3*x^-5+1//3*a^-4*c^3*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(-2*arccoth(a*x)), x) == :(x*c^2+-1*a^-3*c^2*x^-2+-2*a^-1*c^2*log(x)+1//3*a^-4*c^2*x^-3)
@test integrate((c+-1*c*a^-2*x^-2)*exp(-2*arccoth(a*x)), x) == :(c*x+-1*c*a^-2*x^-1+-2*c*a^-1*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(-2*arccoth(a*x)), x) == :(x*c^-1+-1*a^-1*c^-1*(1+a*x)^-1+-2*a^-1*c^-1*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(-2*arccoth(a*x)), x) == :(x*c^-2+-17//8*a^-1*c^-2*log(1+a*x)+-7//4*a^-1*c^-2*(1+a*x)^-1+1//4*a^-1*c^-2*(1+a*x)^-2+1//8*a^-1*c^-2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(-2*arccoth(a*x)), x) == :(x*c^-3+-39//16*a^-1*c^-3*(1+a*x)^-1+-9//4*a^-1*c^-3*log(1+a*x)+-1//12*a^-1*c^-3*(1+a*x)^-3+1//4*a^-1*c^-3*log(1+-1*a*x)+1//16*a^-1*c^-3*(1+-1*a*x)^-1+5//8*a^-1*c^-3*(1+a*x)^-2)
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(-2*arccoth(a*x)), x) == :(x*c^-4+-303//128*a^-1*c^-4*log(1+a*x)+-99//32*a^-1*c^-4*(1+a*x)^-1+-13//48*a^-1*c^-4*(1+a*x)^-3+-1//64*a^-1*c^-4*(1+-1*a*x)^-2+1//32*a^-1*c^-4*(1+a*x)^-4+11//64*a^-1*c^-4*(1+-1*a*x)^-1+35//32*a^-1*c^-4*(1+a*x)^-2+47//128*a^-1*c^-4*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^4*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+15//16*a^-1*c^4*arccsc(a*x)+x*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^11//2+-3//8*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^(1/2)+5//8*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^3//2+8//7*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^9//2+11//10*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^5//2+17//14*a^-1*c^4*(1+a^-1*x^-1)^5//2*(1+-1*a^-1*x^-1)^7//2+27//16*a^-1*c^4*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+33//16*a^-1*c^4*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+3//8*a^-1*c^3*arccsc(a*x)+x*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^9//2+3//8*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^(1/2)+5//4*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^3//2+6//5*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^7//2+21//8*a^-1*c^3*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+27//20*a^-1*c^3*(1+a^-1*x^-1)^3//2*(1+-1*a^-1*x^-1)^5//2)
@test integrate((c+-1*c*a^-2*x^-2)^2*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+-1//2*a^-1*c^2*arccsc(a*x)+x*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^7//2+4//3*a^-1*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^5//2+5//2*a^-1*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2)+11//6*a^-1*c^2*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-2*x^-2)*exp(-3*arccoth(a*x)), x) == :(-3*c*a^-1*arccsc(a*x)+-3*c*a^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+c*x*(1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^3//2)
@test integrate((c+-1*c*a^-2*x^-2)^-1*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^-1*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-1*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+5//3*a^-1*c^-1*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+14//3*a^-1*c^-1*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-2*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^-2*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-2*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2)+6//5*a^-1*c^-2*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2)+9//5*a^-1*c^-2*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+24//5*a^-1*c^-2*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-3*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^-3*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-3*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^-1//2+-2*a^-1*c^-3*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^-1//2+11//7*a^-1*c^-3*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^(1/2)+54//35*a^-1*c^-3*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2)+71//35*a^-1*c^-3*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+176//35*a^-1*c^-3*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^-4*exp(-3*arccoth(a*x)), x) == :(-3*a^-1*c^-4*arctanh((1+a^-1*x^-1)^(1/2)*(1+-1*a^-1*x^-1)^(1/2))+x*c^-4*(1+a^-1*x^-1)^-9//2*(1+-1*a^-1*x^-1)^-3//2+-5*a^-1*c^-4*(1+a^-1*x^-1)^-9//2*(1+-1*a^-1*x^-1)^-1//2+-4//3*a^-1*c^-4*(1+a^-1*x^-1)^-9//2*(1+-1*a^-1*x^-1)^-3//2+28//9*a^-1*c^-4*(1+a^-1*x^-1)^-9//2*(1+-1*a^-1*x^-1)^(1/2)+139//63*a^-1*c^-4*(1+a^-1*x^-1)^-7//2*(1+-1*a^-1*x^-1)^(1/2)+202//105*a^-1*c^-4*(1+a^-1*x^-1)^-5//2*(1+-1*a^-1*x^-1)^(1/2)+719//315*a^-1*c^-4*(1+a^-1*x^-1)^-3//2*(1+-1*a^-1*x^-1)^(1/2)+1664//315*a^-1*c^-4*(1+a^-1*x^-1)^-1//2*(1+-1*a^-1*x^-1)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a^-4*c^3*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//4*a^-5*c^3*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//5*a^-6*c^3*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//6*a^-7*c^3*x^-6*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//2*a^-3*c^3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(arccoth(a*x)), x) == :(x*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+a^-3*c^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^-2*c^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*a^-4*c^2*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*a^-5*c^2*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+c*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+c*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*c*a^-3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+a^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+(1/2)*a^-1*c^-1*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//4*a^-1*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+5//4*a^-1*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(arccoth(a*x)), x) == :(x*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-7//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-1//8*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//8*a^-1*c^-2*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+23//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-19//32*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-11//32*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-5//16*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//24*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//32*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+3//2*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+51//32*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(2*arccoth(a*x)), x) == :(x*(6+-6*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2*(1+a*x)+11//30*a^3*x^4*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-57//16*a^6*x^7*(1+a*x)^-3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-13//40*a^2*x^3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2*(1+a*x)+1//15*a*x^2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^7//2*(1+a*x)+41//24*a^5*x^6*(1+a*x)^-2*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+57//80*a^4*x^5*(1+a*x)^-1*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+2*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arcsin(a*x)+25//16*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(2*arccoth(a*x)), x) == :(x*(4+-4*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2*(1+a*x)+-5//8*a^2*x^3*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+-17//12*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+1//6*a*x^2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2*(1+a*x)+25//8*a^4*x^5*(1+a*x)^-2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+-2*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arcsin(a*x)+-9//8*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(2*arccoth(a*x)), x) == :(a*x^2*(1+-1*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+x*(2+-2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2*(1+a*x)+-5*a^2*x^3*(1+a*x)^-1*(2+-2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+(1/2)*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+2*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+-2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(2*arccoth(a*x)), x) == :(-1*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-1//2+-1*a^-2*x^-1*(c+-1*c*a^-2*x^-2)^-1//2*(1+a*x)*(2+-2*a*x)+2*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(2*arccoth(a*x)), x) == :(-1//3*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2+-2*a^-4*x^-3*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*arcsin(a*x)+1//3*a^-4*x^-3*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2*(1+-1*a*x)*(10+-4*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(2*arccoth(a*x)), x) == :(-1//5*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2+-58//15*a^-4*x^-3*(1+a*x)^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2+1//3*a^-3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2*(2+-2*a*x)+2*a^-6*x^-5*(1+a*x)^5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*arcsin(a*x)+-2//15*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2*(28+43*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(2*arccoth(a*x)), x) == :(-1//7*a^-2*x^-1*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2+-124//105*a^-4*x^-3*(1+a*x)^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2+1//5*a^-3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2*(2+-2*a*x)+142//35*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2+782//105*a^-5*x^-4*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-7//2+-2*a^-8*x^-7*(1+a*x)^7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*arcsin(a*x)+2//35*a^-8*x^-7*(1+a*x)^3*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2*(72+107*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(3*arccoth(a*x)), x) == :(x*c^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^-4*c^4*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*a^-1*c^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a^-3*c^4*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-8//5*a^-6*c^4*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//2*a^-5*c^4*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//8*a^-9*c^4*x^-8*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//7*a^-8*c^4*x^-7*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(3*arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*a^-1*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-3//5*a^-6*c^3*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*a^-5*c^3*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//6*a^-7*c^3*x^-6*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+5//2*a^-3*c^3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+5//3*a^-4*c^3*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(3*arccoth(a*x)), x) == :(x*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-4*c^2*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-3*c^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-2*a^-2*c^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*a^-1*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+1//4*a^-5*c^2*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(3*arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*c*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*c*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1//2*c*a^-3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+2*a^-1*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+3*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(3*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+3*a^-1*c^-1*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+3*a^-1*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x)+-1//2*a^-1*c^-1*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2)
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(3*arccoth(a*x)), x) == :(x*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-9//8*a^-1*c^-2*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+1//6*a^-1*c^-2*(1+-1*a*x)^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+31//8*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+49//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(3*arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+(1/2)*a^-1*c^-3*(1+-1*a*x)^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-59//32*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-9//64*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-1//16*a^-1*c^-3*(1+-1*a*x)^-4*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//32*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+75//16*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+201//64*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(-1*arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a^-4*c^3*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//2*a^-3*c^3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//6*a^-7*c^3*x^-6*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//5*a^-6*c^3*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//4*a^-5*c^3*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(-1*arccoth(a*x)), x) == :(x*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a^-3*c^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^-2*c^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*a^-4*c^2*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//4*a^-5*c^2*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(-1*arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+c*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*c*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1//2*c*a^-3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(-1*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(-1*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-5//4*a^-1*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-1//2*a^-1*c^-1*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//4*a^-1*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(-1*arccoth(a*x)), x) == :(x*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-23//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+1//8*a^-1*c^-2*(1+a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//8*a^-1*c^-2*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+7//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(-1*arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-51//32*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-3//2*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//24*a^-1*c^-3*(1+a*x)^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//32*a^-1*c^-3*(1+-1*a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+5//16*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+11//32*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+19//32*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(-2*arccoth(a*x)), x) == :(x*(6+6*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2*(1+-1*a*x)+-1*a*x^2*(15+15*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2+-23*a^2*x^3*(1+a*x)^-1*(120+-120*a*x)^-1*(c+-1*c*a^-2*x^-2)^7//2+-19//16*a^4*x^5*(1+a*x)^-1*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+2//3*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^7//2+3//8*a^5*x^6*(1+a*x)^-2*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+7//16*a^6*x^7*(1+a*x)^-3*(1+-1*a*x)^-3*(c+-1*c*a^-2*x^-2)^7//2+-2*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arcsin(a*x)+25//16*a^6*x^7*(1+a*x)^-7//2*(1+-1*a*x)^-7//2*(c+-1*c*a^-2*x^-2)^7//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(-2*arccoth(a*x)), x) == :(x*(4+4*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2*(1+-1*a*x)+-1*a*x^2*(6+6*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2+-7*a^2*x^3*(1+a*x)^-1*(24+-24*a*x)^-1*(c+-1*c*a^-2*x^-2)^5//2+2*a^3*x^4*(1+a*x)^-1*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+-7//8*a^4*x^5*(1+a*x)^-2*(1+-1*a*x)^-2*(c+-1*c*a^-2*x^-2)^5//2+2*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arcsin(a*x)+-9//8*a^4*x^5*(1+a*x)^-5//2*(1+-1*a*x)^-5//2*(c+-1*c*a^-2*x^-2)^5//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(-2*arccoth(a*x)), x) == :(x*(2+2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2*(1+-1*a*x)+-1*a*x^2*(1+a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+-5*a^2*x^3*(1+a*x)^-1*(2+-2*a*x)^-1*(c+-1*c*a^-2*x^-2)^3//2+(1/2)*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+-2*a^2*x^3*(1+a*x)^-3//2*(1+-1*a*x)^-3//2*(c+-1*c*a^-2*x^-2)^3//2*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(-2*arccoth(a*x)), x) == :(-1*a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-1//2+-1*a^-2*x^-1*(c+-1*c*a^-2*x^-2)^-1//2*(1+a*x)*(2+-2*a*x)+-2*a^-2*x^-1*(1+a*x)^(1/2)*(1+-1*a*x)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(-2*arccoth(a*x)), x) == :(-1//3*a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2+2*a^-4*x^-3*(1+a*x)^3//2*(1+-1*a*x)^3//2*(c+-1*c*a^-2*x^-2)^-3//2*arcsin(a*x)+2//3*a^-4*x^-3*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-3//2*(1+a*x)*(5+2*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(-2*arccoth(a*x)), x) == :(-1*a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-5//2+-2//5*a^-3*x^-2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2+2//15*a^-4*x^-3*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2*(1+a*x)+-2*a^-6*x^-5*(1+a*x)^5//2*(1+-1*a*x)^5//2*(c+-1*c*a^-2*x^-2)^-5//2*arcsin(a*x)+-2//15*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-5//2*(28+13*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(-2*arccoth(a*x)), x) == :(-1//3*a^-2*x^-1*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^-7//2+10//3*a^-3*x^-2*(1+-1*a*x)^3*(c+-1*c*a^-2*x^-2)^-7//2+12//7*a^-4*x^-3*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2+2//35*a^-6*x^-5*(1+a*x)^2*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2+82//105*a^-5*x^-4*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2*(1+a*x)+2*a^-8*x^-7*(1+a*x)^7//2*(1+-1*a*x)^7//2*(c+-1*c*a^-2*x^-2)^-7//2*arcsin(a*x)+2//35*a^-8*x^-7*(1+a*x)^3*(1+-1*a*x)^4*(c+-1*c*a^-2*x^-2)^-7//2*(72+37*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^9//2*exp(-3*arccoth(a*x)), x) == :(x*c^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^-3*c^4*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*a^-1*c^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+2*a^-4*c^4*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-8//5*a^-6*c^4*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//8*a^-9*c^4*x^-8*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//2*a^-5*c^4*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3//7*a^-8*c^4*x^-7*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^7//2*exp(-3*arccoth(a*x)), x) == :(x*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-2*c^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*a^-1*c^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-5//2*a^-3*c^3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//5*a^-6*c^3*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//4*a^-5*c^3*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+1//6*a^-7*c^3*x^-6*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+5//3*a^-4*c^3*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^5//2*exp(-3*arccoth(a*x)), x) == :(x*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-4*c^2*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-3*c^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*a^-1*c^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-2*a^-2*c^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//4*a^-5*c^2*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^3//2*exp(-3*arccoth(a*x)), x) == :(c*x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*c*a^-3*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*c*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-3*c*a^-2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-4*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-1//2*exp(-3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-3*a^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-2*a^-1*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2)
@test integrate((c+-1*c*a^-2*x^-2)^-3//2*exp(-3*arccoth(a*x)), x) == :(x*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+(1/2)*a^-1*c^-1*(1+a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-3*a^-1*c^-1*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-3*a^-1*c^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^-5//2*exp(-3*arccoth(a*x)), x) == :(x*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-49//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-31//8*a^-1*c^-2*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//6*a^-1*c^-2*(1+a*x)^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//16*a^-1*c^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x)+9//8*a^-1*c^-2*(1+a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2)
@test integrate((c+-1*c*a^-2*x^-2)^-7//2*exp(-3*arccoth(a*x)), x) == :(x*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-201//64*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+a*x)+-75//16*a^-1*c^-3*(1+a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+-1//2*a^-1*c^-3*(1+a*x)^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//16*a^-1*c^-3*(1+a*x)^-4*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+1//32*a^-1*c^-3*(1+-1*a*x)^-1*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2+9//64*a^-1*c^-3*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2*log(1+-1*a*x)+59//32*a^-1*c^-3*(1+a*x)^-2*(1+-1*a^-2*x^-2)^(1/2)*(c+-1*c*a^-2*x^-2)^-1//2)
@test integrate(x^m*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :(x^(1+m)*(1+m)^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*m^-1*x^m*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :(1//3*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :((1/2)*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1*a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(arccoth(a*x)), x) == :(-1//2*a^-1*x^-2*(1+a*x)^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(7//8*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)+1//4*a^-2*x^2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//6*x*a^-3*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+7//24*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+-7//8*x*a^-3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*x*a^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+-1*x*a^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(3//2*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+-3//2*x*a^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+-2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :((c+-1*c*a^-2*x^-2)^(1/2)+-1*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x)+2*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(3//2*a*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+3//2*x*a^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(a^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*x^-2*(1+a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*a*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+a*x)+x*a^3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//4*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+4//3*a^3*(c+-1*c*a^-2*x^-2)^(1/2)+2//3*a*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+7//8*a^2*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+7//8*x*a^4*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(2*arccoth(a*x)), x) == :(1//5*x^-4*(c+-1*c*a^-2*x^-2)^(1/2)+6//5*a^4*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*a*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+3//4*a^3*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+3//5*a^2*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+3//4*x*a^5*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(1//4*x^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^-2*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*x*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(1//3*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*x*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+3//2*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :((1/2)*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+3*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*a^-1*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(3//2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+1//3*a^-1*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+2*a*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+1//4*a^-1*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(3*arccoth(a*x)), x) == :(3//4*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+2*a^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+-1*a*x)+1//5*a^-1*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4//3*a*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^m*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(x^(1+m)*(1+m)^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*m^-1*x^m*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(1//3*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :((1/2)*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :((1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-1*arccoth(a*x)), x) == :((1/2)*a^-1*x^-2*(1+-1*a*x)^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-7//8*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-7//24*x*a^-3*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+-1//6*x*a^-3*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//4*a^-2*x^2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+-7//8*x*a^-3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*x*a^-2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*x*a^-2*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+x*a^-2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-3//2*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*x*a^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+-3//2*x*a^-1*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(x*(c+-1*c*a^-2*x^-2)^(1/2)+x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2))+2*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :((c+-1*c*a^-2*x^-2)^(1/2)+-1*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arcsin(a*x)+-2*a*x*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-3//2*a*(c+-1*c*a^-2*x^-2)^(1/2)+(1/2)*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+3//2*x*a^2*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(a^2*(c+-1*c*a^-2*x^-2)^(1/2)+1//3*x^-2*(1+-1*a*x)^2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//3*a*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*(1+-1*a*x)+-1*x*a^3*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(-4//3*a^3*(c+-1*c*a^-2*x^-2)^(1/2)+1//4*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+-2//3*a*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+7//8*a^2*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+7//8*x*a^4*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-2*arccoth(a*x)), x) == :(1//5*x^-4*(c+-1*c*a^-2*x^-2)^(1/2)+6//5*a^4*(c+-1*c*a^-2*x^-2)^(1/2)+-3//4*a^3*x^-1*(c+-1*c*a^-2*x^-2)^(1/2)+-1//2*a*x^-3*(c+-1*c*a^-2*x^-2)^(1/2)+3//5*a^2*x^-2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//4*x*a^5*(1+a*x)^-1//2*(1+-1*a*x)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*arctanh((1+a*x)^(1/2)*(1+-1*a*x)^(1/2)))
@test integrate(x^3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(1//4*x^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1*a^-1*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*x*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+2*a^-2*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x^2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(1//3*x^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+4*x*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3//2*a^-1*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :((1/2)*x^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-3*x*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate((c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(x*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-4*a^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x))
@test integrate(x^-1*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+-1*a^-1*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-2*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+4*a*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1//2*a^-1*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-3*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(3//2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+4*a^2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+-1//3*a^-1*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-4*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+-2*a*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^2*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+-1//4*a^-1*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))
@test integrate(x^-5*(c+-1*c*a^-2*x^-2)^(1/2)*exp(-3*arccoth(a*x)), x) == :(3//4*x^-4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^3*x^-1*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-4*a^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(x)+2*a^2*x^-2*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+4*a^4*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)*log(1+a*x)+-4//3*a*x^-3*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2)+-1//5*a^-1*x^-5*(1+-1*a^-2*x^-2)^-1//2*(c+-1*c*a^-2*x^-2)^(1/2))

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.4 Inverse hyperbolic cotangent/7.4.2 Exponentials of inverse hyperbolic cotangent functions.jl