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

@test integrate((a^2+b^2*x^4+2*a*b*x^2)^3//4, x) == :(1//4*x*(a^2+b^2*x^4+2*a*b*x^2)^3//4+3*a*x*(8a+8*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^3//4+3//8*a^(1/2)*b^-1//2*(1+b*a^-1*x^2)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^3//4*arcsinh(x*a^-1//2*b^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^1//4, x) == :((1/2)*x*(a^2+b^2*x^4+2*a*b*x^2)^1//4+(1/2)*a^(1/2)*b^-1//2*(1+b*a^-1*x^2)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^1//4*arcsinh(x*a^-1//2*b^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-1//4, x) == :(a^(1/2)*b^-1//2*(1+b*a^-1*x^2)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//4*arcsinh(x*a^-1//2*b^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-3//4, x) == :(x*a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//4*(a+b*x^2))
@test integrate((b+a^2+x^4+2*a*x^2)^-1, x) == :(-1//4*2^(1/2)*(a+(b+a^2)^(1/2))^-1//2*(b+a^2)^-1//2*arctan((a+(b+a^2)^(1/2))^-1//2*(((b+a^2)^(1/2)+-1a)^(1/2)+-1*x*2^(1/2)))+-1//8*2^(1/2)*(b+a^2)^-1//2*((b+a^2)^(1/2)+-1a)^-1//2*log(x^2+(b+a^2)^(1/2)+-1*x*2^(1/2)*((b+a^2)^(1/2)+-1a)^(1/2))+1//4*2^(1/2)*(a+(b+a^2)^(1/2))^-1//2*(b+a^2)^-1//2*arctan((a+(b+a^2)^(1/2))^-1//2*(((b+a^2)^(1/2)+-1a)^(1/2)+x*2^(1/2)))+1//8*2^(1/2)*(b+a^2)^-1//2*((b+a^2)^(1/2)+-1a)^-1//2*log(x^2+(b+a^2)^(1/2)+x*2^(1/2)*((b+a^2)^(1/2)+-1a)^(1/2)))
@test integrate((-1+a^2+x^4+2*a*x^2)^-1, x) == :(-1//2*(1+a)^-1//2*arctan(x*(1+a)^-1//2)+-1//2*(1+-1a)^-1//2*arctanh(x*(1+-1a)^-1//2))
@test integrate((1+a^2+x^4+2*a*x^2)^-1, x) == :(-1//4*2^(1/2)*(1+a^2)^-1//2*(a+(1+a^2)^(1/2))^-1//2*arctan((a+(1+a^2)^(1/2))^-1//2*(((1+a^2)^(1/2)+-1a)^(1/2)+-1*x*2^(1/2)))+-1//8*2^(1/2)*(1+a^2)^-1//2*((1+a^2)^(1/2)+-1a)^-1//2*log(x^2+(1+a^2)^(1/2)+-1*x*2^(1/2)*((1+a^2)^(1/2)+-1a)^(1/2))+1//4*2^(1/2)*(1+a^2)^-1//2*(a+(1+a^2)^(1/2))^-1//2*arctan((a+(1+a^2)^(1/2))^-1//2*(((1+a^2)^(1/2)+-1a)^(1/2)+x*2^(1/2)))+1//8*2^(1/2)*(1+a^2)^-1//2*((1+a^2)^(1/2)+-1a)^-1//2*log(x^2+(1+a^2)^(1/2)+x*2^(1/2)*((1+a^2)^(1/2)+-1a)^(1/2)))
@test integrate((4+x^4+-5*x^2)^-1, x) == :(-1//6*arctanh((1/2)*x)+1//3*arctanh(x))
@test integrate((3+x^4+4*x^2)^-1, x) == :((1/2)*arctan(x)+-1//6*3^(1/2)*arctan(1//3*x*3^(1/2)))
@test integrate((9+x^4+5*x^2)^-1, x) == :(-1//12*log(3+x^2+-1x)+1//12*log(3+x+x^2)+-1//66*11^(1/2)*arctan(1//11*11^(1/2)*(1+-2x))+1//66*11^(1/2)*arctan(1//11*11^(1/2)*(1+2x)))
@test integrate((1+x^4+-1*x^2)^-1, x) == :((1/2)*arctan(3^(1/2)+2x)+-1//2*arctan(3^(1/2)+-2x)+-1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+x*3^(1/2)))
@test integrate((2+x^4+2*x^2)^-1, x) == :(-1//4*(-1+2^(1/2))^(1/2)*arctan((2+2*2^(1/2))^-1//2*((-2+2*2^(1/2))^(1/2)+-2x))+-1//8*(-1+2^(1/2))^-1//2*log(2^(1/2)+x^2+-1*x*(-2+2*2^(1/2))^(1/2))+1//4*(-1+2^(1/2))^(1/2)*arctan((2+2*2^(1/2))^-1//2*((-2+2*2^(1/2))^(1/2)+2x))+1//8*(-1+2^(1/2))^-1//2*log(2^(1/2)+x^2+x*(-2+2*2^(1/2))^(1/2)))
@test integrate((2+-3*x^4+5*x^2)^-1//2, x) == :(Elliptic.F(arcsin((1/2)*x*2^(1/2)),-6))
@test integrate((2+-3*x^4+4*x^2)^-1//2, x) == :((1//3+1//6*10^(1/2))^(1/2)*Elliptic.F(arcsin(x*(-1+(1/2)*10^(1/2))^(1/2)),-7//3+-2//3*10^(1/2)))
@test integrate((2+-3*x^4+3*x^2)^-1//2, x) == :(2^(1/2)*(-3+33^(1/2))^-1//2*Elliptic.F(arcsin(x*6^(1/2)*(3+33^(1/2))^-1//2),-7//4+-1//4*33^(1/2)))
@test integrate((2+-3*x^4+2*x^2)^-1//2, x) == :((-1+7^(1/2))^-1//2*Elliptic.F(arcsin(x*3^(1/2)*(1+7^(1/2))^-1//2),-4//3+-1//3*7^(1/2)))
@test integrate((2+x^2+-3*x^4)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-3//2))
@test integrate((2+-3*x^4)^-1//2, x) == :(1//6*6^3//4*Elliptic.F(arcsin((1/2)*x*2^3//4*3^1//4),-1))
@test integrate((2+-1*x^2+-3*x^4)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.F(arcsin((1/2)*x*6^(1/2)),-2//3))
@test integrate((2+-3*x^4+-2*x^2)^-1//2, x) == :((1+7^(1/2))^-1//2*Elliptic.F(arcsin(x*3^(1/2)*(-1+7^(1/2))^-1//2),-4//3+1//3*7^(1/2)))
@test integrate((2+-3*x^2+-3*x^4)^-1//2, x) == :(2^(1/2)*(3+33^(1/2))^-1//2*Elliptic.F(arcsin(x*6^(1/2)*(-3+33^(1/2))^-1//2),-7//4+1//4*33^(1/2)))
@test integrate((2+-4*x^2+-3*x^4)^-1//2, x) == :((-1//3+1//6*10^(1/2))^(1/2)*Elliptic.F(arcsin(x*(1+(1/2)*10^(1/2))^(1/2)),-7//3+2//3*10^(1/2)))
@test integrate((2+-5*x^2+-3*x^4)^-1//2, x) == :(1//6*6^(1/2)*Elliptic.F(arcsin(x*3^(1/2)),-1//6))
@test integrate((3+-2*x^4+7*x^2)^-1//2, x) == :(2^(1/2)*(-7+73^(1/2))^-1//2*Elliptic.F(arcsin(2*x*(7+73^(1/2))^-1//2),-61//12+-7//12*73^(1/2)))
@test integrate((3+-2*x^4+6*x^2)^-1//2, x) == :((1/2+1//6*15^(1/2))^(1/2)*Elliptic.F(arcsin(x*(-1+1//3*15^(1/2))^(1/2)),-4+-1*15^(1/2)))
@test integrate((3+-2*x^4+5*x^2)^-1//2, x) == :(Elliptic.F(arcsin(1//3*x*3^(1/2)),-6))
@test integrate((3+-2*x^4+4*x^2)^-1//2, x) == :((-2+10^(1/2))^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(2+10^(1/2))^-1//2),-7//3+-2//3*10^(1/2)))
@test integrate((3+-2*x^4+3*x^2)^-1//2, x) == :(2^(1/2)*(-3+33^(1/2))^-1//2*Elliptic.F(arcsin(2*x*(3+33^(1/2))^-1//2),-7//4+-1//4*33^(1/2)))
@test integrate((3+-2*x^4+2*x^2)^-1//2, x) == :((-1+7^(1/2))^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(1+7^(1/2))^-1//2),-4//3+-1//3*7^(1/2)))
@test integrate((3+x^2+-2*x^4)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(1//3*x*6^(1/2)),-3//2))
@test integrate((3+-2*x^4)^-1//2, x) == :(1//6*6^3//4*Elliptic.F(arcsin(1//3*x*2^1//4*3^3//4),-1))
@test integrate((3+-1*x^2+-2*x^4)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.F(arcsin(x),-2//3))
@test integrate((3+-2*x^2+-2*x^4)^-1//2, x) == :((1+7^(1/2))^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-1+7^(1/2))^-1//2),-4//3+1//3*7^(1/2)))
@test integrate((3+-3*x^2+-2*x^4)^-1//2, x) == :(2^(1/2)*(3+33^(1/2))^-1//2*Elliptic.F(arcsin(2*x*(-3+33^(1/2))^-1//2),-7//4+1//4*33^(1/2)))
@test integrate((3+-4*x^2+-2*x^4)^-1//2, x) == :((2+10^(1/2))^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(-2+10^(1/2))^-1//2),-7//3+2//3*10^(1/2)))
@test integrate((3+-5*x^2+-2*x^4)^-1//2, x) == :(1//6*6^(1/2)*Elliptic.F(arcsin(x*2^(1/2)),-1//6))
@test integrate((3+-6*x^2+-2*x^4)^-1//2, x) == :((-1//2+1//6*15^(1/2))^(1/2)*Elliptic.F(arcsin(x*(1+1//3*15^(1/2))^(1/2)),-4+15^(1/2)))
@test integrate((3+-7*x^2+-2*x^4)^-1//2, x) == :(2^(1/2)*(7+73^(1/2))^-1//2*Elliptic.F(arcsin(2*x*(-7+73^(1/2))^-1//2),-61//12+7//12*73^(1/2)))
@test integrate((-2+3*x^4+5*x^2)^-1//2, x) == :(1//7*7^(1/2)*(-1+3*x^2)^(1/2)*(2+x^2)^(1/2)*(-2+3*x^4+5*x^2)^-1//2*Elliptic.F(arcsin((1/2)*x*14^(1/2)*(-1+3*x^2)^-1//2),6//7))
@test integrate((-2+3*x^4+4*x^2)^-1//2, x) == :(1//20*10^3//4*((2+-1*x^2*(2+10^(1/2)))^-1)^-1//2*((2+-1*x^2*(2+10^(1/2)))^-1*(2+-1*x^2*(2+-1*10^(1/2))))^(1/2)*(-2+x^2*(2+10^(1/2)))^(1/2)*(-2+3*x^4+4*x^2)^-1//2*Elliptic.F(arcsin(x*2^3//4*5^1//4*(-2+x^2*(2+10^(1/2)))^-1//2),1/2+1//10*10^(1/2)))
@test integrate((-2+3*x^2+3*x^4)^-1//2, x) == :(1//132*2^(1/2)*33^3//4*((4+-1*x^2*(3+33^(1/2)))^-1)^-1//2*((4+-1*x^2*(3+33^(1/2)))^-1*(4+-1*x^2*(3+-1*33^(1/2))))^(1/2)*(-4+x^2*(3+33^(1/2)))^(1/2)*(-2+3*x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*33^1//4*(-4+x^2*(3+33^(1/2)))^-1//2),1/2+1//22*33^(1/2)))
@test integrate((-2+2*x^2+3*x^4)^-1//2, x) == :(1//14*7^3//4*((2+-1*x^2*(1+7^(1/2)))^-1)^-1//2*((2+-1*x^2*(1+7^(1/2)))^-1*(2+-1*x^2*(1+-1*7^(1/2))))^(1/2)*(-2+x^2*(1+7^(1/2)))^(1/2)*(-2+2*x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*7^1//4*(-2+x^2*(1+7^(1/2)))^-1//2),1/2+1//14*7^(1/2)))
@test integrate((-2+x^2+3*x^4)^-1//2, x) == :(1//5*5^(1/2)*(1+x^2)^(1/2)*(-2+3*x^2)^(1/2)*(-2+x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*5^(1/2)*(-2+3*x^2)^-1//2),3//5))
@test integrate((-2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+-1*6^(1/2)*x^2)^-1)^-1//2*((2+-1*6^(1/2)*x^2)^-1*(2+6^(1/2)*x^2))^(1/2)*(-2+3*x^4)^-1//2*(-2+6^(1/2)*x^2)^(1/2)*Elliptic.F(arcsin(x*2^3//4*3^1//4*(-2+6^(1/2)*x^2)^-1//2),1/2))
@test integrate((-2+-1*x^2+3*x^4)^-1//2, x) == :(1//5*5^(1/2)*(-1+x^2)^(1/2)*(2+3*x^2)^(1/2)*(-2+-1*x^2+3*x^4)^-1//2*Elliptic.F(arcsin((1/2)*x*10^(1/2)*(-1+x^2)^-1//2),2//5))
@test integrate((-2+-2*x^2+3*x^4)^-1//2, x) == :(1//14*7^3//4*((2+x^2*(1+-1*7^(1/2)))^-1)^-1//2*((2+x^2*(1+-1*7^(1/2)))^-1*(2+x^2*(1+7^(1/2))))^(1/2)*(-2+-1*x^2*(1+-1*7^(1/2)))^(1/2)*(-2+-2*x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*7^1//4*(-2+-1*x^2*(1+-1*7^(1/2)))^-1//2),1/2+-1//14*7^(1/2)))
@test integrate((-2+-3*x^2+3*x^4)^-1//2, x) == :(1//132*2^(1/2)*33^3//4*((4+x^2*(3+-1*33^(1/2)))^-1)^-1//2*((4+x^2*(3+-1*33^(1/2)))^-1*(4+x^2*(3+33^(1/2))))^(1/2)*(-4+-1*x^2*(3+-1*33^(1/2)))^(1/2)*(-2+-3*x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*33^1//4*(-4+-1*x^2*(3+-1*33^(1/2)))^-1//2),1/2+-1//22*33^(1/2)))
@test integrate((-2+-4*x^2+3*x^4)^-1//2, x) == :(1//20*10^3//4*((2+x^2*(2+-1*10^(1/2)))^-1)^-1//2*((2+x^2*(2+-1*10^(1/2)))^-1*(2+x^2*(2+10^(1/2))))^(1/2)*(-2+-1*x^2*(2+-1*10^(1/2)))^(1/2)*(-2+-4*x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*2^3//4*5^1//4*(-2+-1*x^2*(2+-1*10^(1/2)))^-1//2),1/2+-1//10*10^(1/2)))
@test integrate((-2+-5*x^2+3*x^4)^-1//2, x) == :(1//7*7^(1/2)*(1+3*x^2)^(1/2)*(-2+x^2)^(1/2)*(-2+-5*x^2+3*x^4)^-1//2*Elliptic.F(arcsin(x*7^(1/2)*(-2+x^2)^-1//2),1//7))
@test integrate((-3+2*x^4+7*x^2)^-1//2, x) == :(1//438*3^(1/2)*73^3//4*((6+-1*x^2*(7+73^(1/2)))^-1)^-1//2*((6+-1*x^2*(7+73^(1/2)))^-1*(6+-1*x^2*(7+-1*73^(1/2))))^(1/2)*(-6+x^2*(7+73^(1/2)))^(1/2)*(-3+2*x^4+7*x^2)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*73^1//4*(-6+x^2*(7+73^(1/2)))^-1//2),1/2+7//146*73^(1/2)))
@test integrate((-3+2*x^4+6*x^2)^-1//2, x) == :(1//30*2^(1/2)*3^1//4*5^3//4*((3+-1*x^2*(3+15^(1/2)))^-1)^-1//2*((3+-1*x^2*(3+15^(1/2)))^-1*(3+-1*x^2*(3+-1*15^(1/2))))^(1/2)*(-3+x^2*(3+15^(1/2)))^(1/2)*(-3+2*x^4+6*x^2)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*15^1//4*(-3+x^2*(3+15^(1/2)))^-1//2),1/2+1//10*15^(1/2)))
@test integrate((-3+2*x^4+5*x^2)^-1//2, x) == :(1//7*7^(1/2)*(-1+2*x^2)^(1/2)*(3+x^2)^(1/2)*(-3+2*x^4+5*x^2)^-1//2*Elliptic.F(arcsin(1//3*x*21^(1/2)*(-1+2*x^2)^-1//2),6//7))
@test integrate((-3+2*x^4+4*x^2)^-1//2, x) == :(1//30*2^1//4*3^(1/2)*5^3//4*((3+-1*x^2*(2+10^(1/2)))^-1)^-1//2*((3+-1*x^2*(2+10^(1/2)))^-1*(3+-1*x^2*(2+-1*10^(1/2))))^(1/2)*(-3+x^2*(2+10^(1/2)))^(1/2)*(-3+2*x^4+4*x^2)^-1//2*Elliptic.F(arcsin(x*2^3//4*5^1//4*(-3+x^2*(2+10^(1/2)))^-1//2),1/2+1//10*10^(1/2)))
@test integrate((-3+2*x^4+3*x^2)^-1//2, x) == :(1//66*3^1//4*11^3//4*((6+-1*x^2*(3+33^(1/2)))^-1)^-1//2*((6+-1*x^2*(3+33^(1/2)))^-1*(6+-1*x^2*(3+-1*33^(1/2))))^(1/2)*(-6+x^2*(3+33^(1/2)))^(1/2)*(-3+2*x^4+3*x^2)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*33^1//4*(-6+x^2*(3+33^(1/2)))^-1//2),1/2+1//22*33^(1/2)))
@test integrate((-3+2*x^2+2*x^4)^-1//2, x) == :(1//42*6^(1/2)*7^3//4*((3+-1*x^2*(1+7^(1/2)))^-1)^-1//2*((3+-1*x^2*(1+7^(1/2)))^-1*(3+-1*x^2*(1+-1*7^(1/2))))^(1/2)*(-3+x^2*(1+7^(1/2)))^(1/2)*(-3+2*x^2+2*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*7^1//4*(-3+x^2*(1+7^(1/2)))^-1//2),1/2+1//14*7^(1/2)))
@test integrate((-3+x^2+2*x^4)^-1//2, x) == :(1//5*5^(1/2)*(-1+x^2)^(1/2)*(3+2*x^2)^(1/2)*(-3+x^2+2*x^4)^-1//2*Elliptic.F(arcsin(1//3*x*15^(1/2)*(-1+x^2)^-1//2),3//5))
@test integrate((-3+2*x^4)^-1//2, x) == :(1//6*6^1//4*((3+-1*6^(1/2)*x^2)^-1)^-1//2*((3+-1*6^(1/2)*x^2)^-1*(3+6^(1/2)*x^2))^(1/2)*(-3+2*x^4)^-1//2*(-3+6^(1/2)*x^2)^(1/2)*Elliptic.F(arcsin(x*2^3//4*3^1//4*(-3+6^(1/2)*x^2)^-1//2),1/2))
@test integrate((-3+-1*x^2+2*x^4)^-1//2, x) == :(1//5*5^(1/2)*(1+x^2)^(1/2)*(-3+2*x^2)^(1/2)*(-3+-1*x^2+2*x^4)^-1//2*Elliptic.F(arcsin(x*5^(1/2)*(-3+2*x^2)^-1//2),2//5))
@test integrate((-3+-2*x^2+2*x^4)^-1//2, x) == :(1//42*6^(1/2)*7^3//4*((3+x^2*(1+-1*7^(1/2)))^-1)^-1//2*((3+x^2*(1+-1*7^(1/2)))^-1*(3+x^2*(1+7^(1/2))))^(1/2)*(-3+-1*x^2*(1+-1*7^(1/2)))^(1/2)*(-3+-2*x^2+2*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*7^1//4*(-3+-1*x^2*(1+-1*7^(1/2)))^-1//2),1/2+-1//14*7^(1/2)))
@test integrate((-3+-3*x^2+2*x^4)^-1//2, x) == :(1//66*3^1//4*11^3//4*((6+x^2*(3+-1*33^(1/2)))^-1)^-1//2*((6+x^2*(3+-1*33^(1/2)))^-1*(6+x^2*(3+33^(1/2))))^(1/2)*(-6+-1*x^2*(3+-1*33^(1/2)))^(1/2)*(-3+-3*x^2+2*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*33^1//4*(-6+-1*x^2*(3+-1*33^(1/2)))^-1//2),1/2+-1//22*33^(1/2)))
@test integrate((-3+-4*x^2+2*x^4)^-1//2, x) == :(1//30*2^1//4*3^(1/2)*5^3//4*((3+x^2*(2+-1*10^(1/2)))^-1)^-1//2*((3+x^2*(2+-1*10^(1/2)))^-1*(3+x^2*(2+10^(1/2))))^(1/2)*(-3+-1*x^2*(2+-1*10^(1/2)))^(1/2)*(-3+-4*x^2+2*x^4)^-1//2*Elliptic.F(arcsin(x*2^3//4*5^1//4*(-3+-1*x^2*(2+-1*10^(1/2)))^-1//2),1/2+-1//10*10^(1/2)))
@test integrate((-3+-5*x^2+2*x^4)^-1//2, x) == :(1//7*7^(1/2)*(1+2*x^2)^(1/2)*(-3+x^2)^(1/2)*(-3+-5*x^2+2*x^4)^-1//2*Elliptic.F(arcsin(x*7^(1/2)*(-3+x^2)^-1//2),1//7))
@test integrate((2+3*x^4+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+3*x^2))^(1/2)*(2+3*x^4+5*x^2)^-1//2*(1+x^2)*Elliptic.F(arctan(x),-1//2))
@test integrate((2+3*x^4+4*x^2)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+3*x^4+4*x^2))^(1/2)*(2+3*x^4+4*x^2)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//6*6^(1/2)))
@test integrate((2+3*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+3*x^2+3*x^4))^(1/2)*(2+3*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//8*6^(1/2)))
@test integrate((2+2*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+2*x^2+3*x^4))^(1/2)*(2+2*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//12*6^(1/2)))
@test integrate((2+x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+x^2+3*x^4))^(1/2)*(2+x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//24*6^(1/2)))
@test integrate((2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+3*x^4))^(1/2)*(2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2))
@test integrate((2+-1*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-1*x^2+3*x^4))^(1/2)*(2+-1*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//24*6^(1/2)))
@test integrate((2+-2*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-2*x^2+3*x^4))^(1/2)*(2+-2*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//12*6^(1/2)))
@test integrate((2+-3*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-3*x^2+3*x^4))^(1/2)*(2+-3*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//8*6^(1/2)))
@test integrate((2+-4*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-4*x^2+3*x^4))^(1/2)*(2+-4*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//6*6^(1/2)))
@test integrate((2+-5*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-5*x^2+3*x^4))^(1/2)*(2+-5*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+5//24*6^(1/2)))
@test integrate((2+-6*x^2+3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-6*x^2+3*x^4))^(1/2)*(2+-6*x^2+3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//4*6^(1/2)))
@test integrate((3+2*x^4+9*x^2)^-1//2, x) == :(((6+x^2*(9+57^(1/2)))^-1*(6+x^2*(9+-1*57^(1/2))))^(1/2)*(54+6*57^(1/2))^-1//2*(3+2*x^4+9*x^2)^-1//2*(6+x^2*(9+57^(1/2)))*Elliptic.F(arctan(x*(3//2+1//6*57^(1/2))^(1/2)),-19//4+3//4*57^(1/2)))
@test integrate((3+2*x^4+8*x^2)^-1//2, x) == :(((3+x^2*(4+10^(1/2)))^-1*(3+x^2*(4+-1*10^(1/2))))^(1/2)*(12+3*10^(1/2))^-1//2*(3+2*x^4+8*x^2)^-1//2*(3+x^2*(4+10^(1/2)))*Elliptic.F(arctan(x*(4//3+1//3*10^(1/2))^(1/2)),-10//3+4//3*10^(1/2)))
@test integrate((3+2*x^4+7*x^2)^-1//2, x) == :(1//6*6^(1/2)*((1+2*x^2)^-1*(3+x^2))^(1/2)*(3+2*x^4+7*x^2)^-1//2*(1+2*x^2)*Elliptic.F(arctan(x*2^(1/2)),5//6))
@test integrate((3+2*x^4+6*x^2)^-1//2, x) == :(((3+x^2*(3+3^(1/2)))^-1*(3+x^2*(3+-1*3^(1/2))))^(1/2)*(9+3*3^(1/2))^-1//2*(3+2*x^4+6*x^2)^-1//2*(3+x^2*(3+3^(1/2)))*Elliptic.F(arctan(x*(1+1//3*3^(1/2))^(1/2)),-1+3^(1/2)))
@test integrate((3+2*x^4+5*x^2)^-1//2, x) == :(1//3*3^(1/2)*((1+x^2)^-1*(3+2*x^2))^(1/2)*(3+2*x^4+5*x^2)^-1//2*(1+x^2)*Elliptic.F(arctan(x),1//3))
@test integrate((3+2*x^4+4*x^2)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^4+4*x^2))^(1/2)*(3+2*x^4+4*x^2)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//6*6^(1/2)))
@test integrate((3+2*x^4+3*x^2)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^4+3*x^2))^(1/2)*(3+2*x^4+3*x^2)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//8*6^(1/2)))
@test integrate((3+2*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^2+2*x^4))^(1/2)*(3+2*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//12*6^(1/2)))
@test integrate((3+x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+x^2+2*x^4))^(1/2)*(3+x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//24*6^(1/2)))
@test integrate((3+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^4))^(1/2)*(3+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2))
@test integrate((3+-1*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-1*x^2+2*x^4))^(1/2)*(3+-1*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//24*6^(1/2)))
@test integrate((3+-2*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-2*x^2+2*x^4))^(1/2)*(3+-2*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//12*6^(1/2)))
@test integrate((3+-3*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-3*x^2+2*x^4))^(1/2)*(3+-3*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//8*6^(1/2)))
@test integrate((3+-4*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-4*x^2+2*x^4))^(1/2)*(3+-4*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//6*6^(1/2)))
@test integrate((3+-5*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-5*x^2+2*x^4))^(1/2)*(3+-5*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+5//24*6^(1/2)))
@test integrate((3+-6*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-6*x^2+2*x^4))^(1/2)*(3+-6*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//4*6^(1/2)))
@test integrate((3+-7*x^2+2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-7*x^2+2*x^4))^(1/2)*(3+-7*x^2+2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+7//24*6^(1/2)))
@test integrate((-3+-2*x^4+7*x^2)^-1//2, x) == :(-1//5*5^(1/2)*Elliptic.F(arccos(1//3*x*3^(1/2)),6//5))
@test integrate((-3+-2*x^4+6*x^2)^-1//2, x) == :(-1//6*2^(1/2)*3^3//4*Elliptic.F(arccos(x*(1+-1//3*3^(1/2))^(1/2)),1/2+(1/2)*3^(1/2)))
@test integrate((-3+-2*x^4+5*x^2)^-1//2, x) == :(-1*Elliptic.F(arccos(1//3*x*6^(1/2)),3))
@test integrate((-3+-2*x^4+4*x^2)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-4*x^2+2*x^4))^(1/2)*(-3+-2*x^4+4*x^2)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//6*6^(1/2)))
@test integrate((-3+-2*x^4+3*x^2)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-3*x^2+2*x^4))^(1/2)*(-3+-2*x^4+3*x^2)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//8*6^(1/2)))
@test integrate((-3+-2*x^4+2*x^2)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-2*x^2+2*x^4))^(1/2)*(-3+-2*x^4+2*x^2)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//12*6^(1/2)))
@test integrate((-3+x^2+-2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+-1*x^2+2*x^4))^(1/2)*(-3+x^2+-2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+1//24*6^(1/2)))
@test integrate((-3+-2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^4))^(1/2)*(-3+-2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2))
@test integrate((-3+-1*x^2+-2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+x^2+2*x^4))^(1/2)*(-3+-1*x^2+-2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//24*6^(1/2)))
@test integrate((-3+-2*x^2+-2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^2+2*x^4))^(1/2)*(-3+-2*x^2+-2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//12*6^(1/2)))
@test integrate((-3+-3*x^2+-2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^4+3*x^2))^(1/2)*(-3+-3*x^2+-2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//8*6^(1/2)))
@test integrate((-3+-4*x^2+-2*x^4)^-1//2, x) == :(1//12*6^3//4*((3+6^(1/2)*x^2)^-2*(3+2*x^4+4*x^2))^(1/2)*(-3+-4*x^2+-2*x^4)^-1//2*(3+6^(1/2)*x^2)*Elliptic.F(2*arctan(1//3*x*2^1//4*3^3//4),1/2+-1//6*6^(1/2)))
@test integrate((-3+-5*x^2+-2*x^4)^-1//2, x) == :(1//3*3^(1/2)*((1+x^2)^-1*(3+2*x^2))^-1//2*(-1+-1*x^2)^-1//2*(3+2*x^2)^(1/2)*Elliptic.F(arctan(x),1//3))
@test integrate((-2+-3*x^4+6*x^2)^-1//2, x) == :(-1//6*2^(1/2)*3^3//4*Elliptic.F(arccos(x*3^(1/2)*(3+3^(1/2))^-1//2),1/2+(1/2)*3^(1/2)))
@test integrate((-2+-3*x^4+5*x^2)^-1//2, x) == :(-1*Elliptic.F(arccos(x),3))
@test integrate((-2+-3*x^4+4*x^2)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-4*x^2+3*x^4))^(1/2)*(-2+-3*x^4+4*x^2)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//6*6^(1/2)))
@test integrate((-2+-3*x^4+3*x^2)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-3*x^2+3*x^4))^(1/2)*(-2+-3*x^4+3*x^2)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//8*6^(1/2)))
@test integrate((-2+-3*x^4+2*x^2)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-2*x^2+3*x^4))^(1/2)*(-2+-3*x^4+2*x^2)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//12*6^(1/2)))
@test integrate((-2+x^2+-3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+-1*x^2+3*x^4))^(1/2)*(-2+x^2+-3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+1//24*6^(1/2)))
@test integrate((-2+-3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+3*x^4))^(1/2)*(-2+-3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2))
@test integrate((-2+-1*x^2+-3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+x^2+3*x^4))^(1/2)*(-2+-1*x^2+-3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//24*6^(1/2)))
@test integrate((-2+-3*x^4+-2*x^2)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+2*x^2+3*x^4))^(1/2)*(-2+-3*x^4+-2*x^2)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//12*6^(1/2)))
@test integrate((-2+-3*x^2+-3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+3*x^2+3*x^4))^(1/2)*(-2+-3*x^2+-3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//8*6^(1/2)))
@test integrate((-2+-4*x^2+-3*x^4)^-1//2, x) == :(1//12*6^3//4*((2+6^(1/2)*x^2)^-2*(2+3*x^4+4*x^2))^(1/2)*(-2+-4*x^2+-3*x^4)^-1//2*(2+6^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*3^1//4),1/2+-1//6*6^(1/2)))
@test integrate((-2+-5*x^2+-3*x^4)^-1//2, x) == :(-1//2*2^(1/2)*((1+x^2)^-1*(2+3*x^2))^-1//2*(1+x^2)^-1//2*(-2+-3*x^2)^(1/2)*Elliptic.F(arctan(x),-1//2))
@test integrate((2+5*x^2+5*x^4)^-1//2, x) == :(1//20*10^3//4*((2+10^(1/2)*x^2)^-2*(2+5*x^2+5*x^4))^(1/2)*(2+5*x^2+5*x^4)^-1//2*(2+10^(1/2)*x^2)*Elliptic.F(2*arctan((1/2)*x*2^3//4*5^1//4),1/2+-1//8*10^(1/2)))
@test integrate((2+4*x^4+5*x^2)^-1//2, x) == :(1//4*2^1//4*((1+2^(1/2)*x^2)^-2*(2+4*x^4+5*x^2))^(1/2)*(2+4*x^4+5*x^2)^-1//2*(1+2^(1/2)*x^2)*Elliptic.F(2*arctan(x*2^1//4),1/2+-5//16*2^(1/2)))
@test integrate((2+3*x^4+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*((1+x^2)^-1*(2+3*x^2))^(1/2)*(2+3*x^4+5*x^2)^-1//2*(1+x^2)*Elliptic.F(arctan(x),-1//2))
@test integrate((2+2*x^4+5*x^2)^-1//2, x) == :((1/2)*((1+2*x^2)^-1*(2+x^2))^(1/2)*(2+2*x^4+5*x^2)^-1//2*(1+2*x^2)*Elliptic.F(arctan(x*2^(1/2)),3//4))
@test integrate((2+x^4+5*x^2)^-1//2, x) == :((1/2)*((4+x^2*(5+17^(1/2)))^-1*(4+x^2*(5+-1*17^(1/2))))^(1/2)*(5+17^(1/2))^-1//2*(2+x^4+5*x^2)^-1//2*(4+x^2*(5+17^(1/2)))*Elliptic.F(arctan((1/2)*x*(5+17^(1/2))^(1/2)),-17//4+5//4*17^(1/2)))
@test integrate((2+-1*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+33^(1/2))^-1//2*Elliptic.F(arcsin(x*2^(1/2)*(5+33^(1/2))^-1//2),-29//4+-5//4*33^(1/2)))
@test integrate((2+-2*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+41^(1/2))^-1//2*Elliptic.F(arcsin(2*x*(5+41^(1/2))^-1//2),-33//8+-5//8*41^(1/2)))
@test integrate((2+-3*x^4+5*x^2)^-1//2, x) == :(Elliptic.F(arcsin((1/2)*x*2^(1/2)),-6))
@test integrate((2+-4*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+57^(1/2))^-1//2*Elliptic.F(arcsin(2*x*2^(1/2)*(5+57^(1/2))^-1//2),-41//16+-5//16*57^(1/2)))
@test integrate((2+-5*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+65^(1/2))^-1//2*Elliptic.F(arcsin(x*10^(1/2)*(5+65^(1/2))^-1//2),-9//4+-1//4*65^(1/2)))
@test integrate((2+-6*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+73^(1/2))^-1//2*Elliptic.F(arcsin(2*x*3^(1/2)*(5+73^(1/2))^-1//2),-49//24+-5//24*73^(1/2)))
@test integrate((2+-7*x^4+5*x^2)^-1//2, x) == :((1/2)*2^(1/2)*Elliptic.F(arcsin(x),-7//2))
@test integrate((2+-8*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+89^(1/2))^-1//2*Elliptic.F(arcsin(4*x*(5+89^(1/2))^-1//2),-57//32+-5//32*89^(1/2)))
@test integrate((2+-9*x^4+5*x^2)^-1//2, x) == :(2^(1/2)*(-5+97^(1/2))^-1//2*Elliptic.F(arcsin(3*x*2^(1/2)*(5+97^(1/2))^-1//2),-61//36+-5//36*97^(1/2)))
@test integrate(x^2*(b*x^2+c*x^4), x) == :(1//5*b*x^5+1//7*c*x^7)
@test integrate(x*(b*x^2+c*x^4), x) == :(1//4*b*x^4+1//6*c*x^6)
@test integrate(b*x^2+c*x^4, x) == :(1//3*b*x^3+1//5*c*x^5)
@test integrate(x^-1*(b*x^2+c*x^4), x) == :((1/2)*b*x^2+1//4*c*x^4)
@test integrate(x^-2*(b*x^2+c*x^4), x) == :(b*x+1//3*c*x^3)
@test integrate(x^-3*(b*x^2+c*x^4), x) == :(b*log(x)+(1/2)*c*x^2)
@test integrate(x^-4*(b*x^2+c*x^4), x) == :(c*x+-1*b*x^-1)
@test integrate(x^-5*(b*x^2+c*x^4), x) == :(c*log(x)+-1//2*b*x^-2)
@test integrate(x^-6*(b*x^2+c*x^4), x) == :(-1*c*x^-1+-1//3*b*x^-3)
@test integrate(x^-7*(b*x^2+c*x^4), x) == :(-1//2*c*x^-2+-1//4*b*x^-4)
@test integrate(x^-8*(b*x^2+c*x^4), x) == :(-1//3*c*x^-3+-1//5*b*x^-5)
@test integrate((b*x^2+c*x^4)^2, x) == :(1//5*b^2*x^5+1//9*c^2*x^9+2//7*b*c*x^7)
@test integrate(x^-1*(b*x^2+c*x^4)^2, x) == :(1//4*b^2*x^4+1//8*c^2*x^8+1//3*b*c*x^6)
@test integrate(x^-2*(b*x^2+c*x^4)^2, x) == :(1//3*b^2*x^3+1//7*c^2*x^7+2//5*b*c*x^5)
@test integrate(x^-3*(b*x^2+c*x^4)^2, x) == :(1//6*c^-1*(b+c*x^2)^3)
@test integrate(x^-4*(b*x^2+c*x^4)^2, x) == :(x*b^2+1//5*c^2*x^5+2//3*b*c*x^3)
@test integrate(x^-5*(b*x^2+c*x^4)^2, x) == :(b^2*log(x)+1//4*c^2*x^4+b*c*x^2)
@test integrate(x^-6*(b*x^2+c*x^4)^2, x) == :(-1*b^2*x^-1+1//3*c^2*x^3+2*b*c*x)
@test integrate(x^-7*(b*x^2+c*x^4)^2, x) == :((1/2)*c^2*x^2+-1//2*b^2*x^-2+2*b*c*log(x))
@test integrate(x^-8*(b*x^2+c*x^4)^2, x) == :(x*c^2+-1//3*b^2*x^-3+-2*b*c*x^-1)
@test integrate(x^-9*(b*x^2+c*x^4)^2, x) == :(c^2*log(x)+-1//4*b^2*x^-4+-1*b*c*x^-2)
@test integrate(x^-10*(b*x^2+c*x^4)^2, x) == :(-1*c^2*x^-1+-1//5*b^2*x^-5+-2//3*b*c*x^-3)
@test integrate(x^-11*(b*x^2+c*x^4)^2, x) == :(-1//6*b^-1*x^-6*(b+c*x^2)^3)
@test integrate(x^-12*(b*x^2+c*x^4)^2, x) == :(-1//3*c^2*x^-3+-1//7*b^2*x^-7+-2//5*b*c*x^-5)
@test integrate(x^-2*(b*x^2+c*x^4)^3, x) == :(1//5*b^3*x^5+1//11*c^3*x^11+1//3*b*c^2*x^9+3//7*c*b^2*x^7)
@test integrate(x^-3*(b*x^2+c*x^4)^3, x) == :(1//10*c^-2*(b+c*x^2)^5+-1//8*b*c^-2*(b+c*x^2)^4)
@test integrate(x^-4*(b*x^2+c*x^4)^3, x) == :(1//3*b^3*x^3+1//9*c^3*x^9+3//5*c*b^2*x^5+3//7*b*c^2*x^7)
@test integrate(x^-5*(b*x^2+c*x^4)^3, x) == :(1//8*c^-1*(b+c*x^2)^4)
@test integrate(x^-6*(b*x^2+c*x^4)^3, x) == :(x*b^3+1//7*c^3*x^7+c*b^2*x^3+3//5*b*c^2*x^5)
@test integrate(x^-7*(b*x^2+c*x^4)^3, x) == :(b^3*log(x)+1//6*c^3*x^6+3//2*c*b^2*x^2+3//4*b*c^2*x^4)
@test integrate(x^-8*(b*x^2+c*x^4)^3, x) == :(-1*b^3*x^-1+1//5*c^3*x^5+b*c^2*x^3+3*c*x*b^2)
@test integrate(x^-9*(b*x^2+c*x^4)^3, x) == :(-1//2*b^3*x^-2+1//4*c^3*x^4+3*c*b^2*log(x)+3//2*b*c^2*x^2)
@test integrate(x^-10*(b*x^2+c*x^4)^3, x) == :(-1//3*b^3*x^-3+1//3*c^3*x^3+-3*c*b^2*x^-1+3*b*x*c^2)
@test integrate(x^-11*(b*x^2+c*x^4)^3, x) == :((1/2)*c^3*x^2+-1//4*b^3*x^-4+3*b*c^2*log(x)+-3//2*c*b^2*x^-2)
@test integrate(x^-12*(b*x^2+c*x^4)^3, x) == :(x*c^3+-1//5*b^3*x^-5+-1*c*b^2*x^-3+-3*b*c^2*x^-1)
@test integrate(x^-13*(b*x^2+c*x^4)^3, x) == :(c^3*log(x)+-1//6*b^3*x^-6+-3//2*b*c^2*x^-2+-3//4*c*b^2*x^-4)
@test integrate(x^-14*(b*x^2+c*x^4)^3, x) == :(-1*c^3*x^-1+-1//7*b^3*x^-7+-1*b*c^2*x^-3+-3//5*c*b^2*x^-5)
@test integrate(x^-15*(b*x^2+c*x^4)^3, x) == :(-1//8*b^-1*x^-8*(b+c*x^2)^4)
@test integrate(x^-16*(b*x^2+c*x^4)^3, x) == :(-1//3*c^3*x^-3+-1//9*b^3*x^-9+-3//5*b*c^2*x^-5+-3//7*c*b^2*x^-7)
@test integrate(x^-17*(b*x^2+c*x^4)^3, x) == :(-1//10*b^-1*x^-10*(b+c*x^2)^4+1//40*c*b^-2*x^-8*(b+c*x^2)^4)
@test integrate(x^10*(b*x^2+c*x^4)^-1, x) == :(1//7*c^-1*x^7+b^7//2*c^-9//2*arctan(x*b^-1//2*c^(1/2))+-1*x*b^3*c^-4+-1//5*b*c^-2*x^5+1//3*b^2*c^-3*x^3)
@test integrate(x^9*(b*x^2+c*x^4)^-1, x) == :(1//6*c^-1*x^6+(1/2)*b^2*c^-3*x^2+-1//2*b^3*c^-4*log(b+c*x^2)+-1//4*b*c^-2*x^4)
@test integrate(x^8*(b*x^2+c*x^4)^-1, x) == :(1//5*c^-1*x^5+x*b^2*c^-3+-1*b^5//2*c^-7//2*arctan(x*b^-1//2*c^(1/2))+-1//3*b*c^-2*x^3)
@test integrate(x^7*(b*x^2+c*x^4)^-1, x) == :(1//4*c^-1*x^4+(1/2)*b^2*c^-3*log(b+c*x^2)+-1//2*b*c^-2*x^2)
@test integrate(x^6*(b*x^2+c*x^4)^-1, x) == :(1//3*c^-1*x^3+b^3//2*c^-5//2*arctan(x*b^-1//2*c^(1/2))+-1*b*x*c^-2)
@test integrate(x^5*(b*x^2+c*x^4)^-1, x) == :((1/2)*c^-1*x^2+-1//2*b*c^-2*log(b+c*x^2))
@test integrate(x^4*(b*x^2+c*x^4)^-1, x) == :(x*c^-1+-1*b^(1/2)*c^-3//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^3*(b*x^2+c*x^4)^-1, x) == :((1/2)*c^-1*log(b+c*x^2))
@test integrate(x^2*(b*x^2+c*x^4)^-1, x) == :(b^-1//2*c^-1//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x*(b*x^2+c*x^4)^-1, x) == :(b^-1*log(x)+-1//2*b^-1*log(b+c*x^2))
@test integrate((b*x^2+c*x^4)^-1, x) == :(-1*b^-1*x^-1+-1*b^-3//2*c^(1/2)*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^-1*(b*x^2+c*x^4)^-1, x) == :(-1//2*b^-1*x^-2+(1/2)*c*b^-2*log(b+c*x^2)+-1*c*b^-2*log(x))
@test integrate(x^-2*(b*x^2+c*x^4)^-1, x) == :(-1//3*b^-1*x^-3+c*b^-2*x^-1+b^-5//2*c^3//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^-3*(b*x^2+c*x^4)^-1, x) == :(-1//4*b^-1*x^-4+b^-3*c^2*log(x)+(1/2)*c*b^-2*x^-2+-1//2*b^-3*c^2*log(b+c*x^2))
@test integrate(x^-4*(b*x^2+c*x^4)^-1, x) == :(-1//5*b^-1*x^-5+-1*b^-3*c^2*x^-1+-1*b^-7//2*c^5//2*arctan(x*b^-1//2*c^(1/2))+1//3*c*b^-2*x^-3)
@test integrate(x^-5*(b*x^2+c*x^4)^-1, x) == :(-1//6*b^-1*x^-6+(1/2)*b^-4*c^3*log(b+c*x^2)+-1*b^-4*c^3*log(x)+-1//2*b^-3*c^2*x^-2+1//4*c*b^-2*x^-4)
@test integrate(x^12*(b*x^2+c*x^4)^-2, x) == :(7//10*c^-2*x^5+-7//2*b^5//2*c^-9//2*arctan(x*b^-1//2*c^(1/2))+-7//6*b*c^-3*x^3+-1//2*c^-1*x^7*(b+c*x^2)^-1+7//2*x*b^2*c^-4)
@test integrate(x^11*(b*x^2+c*x^4)^-2, x) == :(1//4*c^-2*x^4+(1/2)*b^3*c^-4*(b+c*x^2)^-1+-1*b*c^-3*x^2+3//2*b^2*c^-4*log(b+c*x^2))
@test integrate(x^10*(b*x^2+c*x^4)^-2, x) == :(5//6*c^-2*x^3+-5//2*b*x*c^-3+-1//2*c^-1*x^5*(b+c*x^2)^-1+5//2*b^3//2*c^-7//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^9*(b*x^2+c*x^4)^-2, x) == :((1/2)*c^-2*x^2+-1*b*c^-3*log(b+c*x^2)+-1//2*b^2*c^-3*(b+c*x^2)^-1)
@test integrate(x^8*(b*x^2+c*x^4)^-2, x) == :(3//2*x*c^-2+-3//2*b^(1/2)*c^-5//2*arctan(x*b^-1//2*c^(1/2))+-1//2*c^-1*x^3*(b+c*x^2)^-1)
@test integrate(x^7*(b*x^2+c*x^4)^-2, x) == :((1/2)*c^-2*log(b+c*x^2)+(1/2)*b*c^-2*(b+c*x^2)^-1)
@test integrate(x^6*(b*x^2+c*x^4)^-2, x) == :((1/2)*b^-1//2*c^-3//2*arctan(x*b^-1//2*c^(1/2))+-1//2*x*c^-1*(b+c*x^2)^-1)
@test integrate(x^5*(b*x^2+c*x^4)^-2, x) == :(-1//2*c^-1*(b+c*x^2)^-1)
@test integrate(x^4*(b*x^2+c*x^4)^-2, x) == :((1/2)*x*b^-1*(b+c*x^2)^-1+(1/2)*b^-3//2*c^-1//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^3*(b*x^2+c*x^4)^-2, x) == :(b^-2*log(x)+(1/2)*b^-1*(b+c*x^2)^-1+-1//2*b^-2*log(b+c*x^2))
@test integrate(x^2*(b*x^2+c*x^4)^-2, x) == :(-3//2*b^-2*x^-1+(1/2)*b^-1*x^-1*(b+c*x^2)^-1+-3//2*b^-5//2*c^(1/2)*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x*(b*x^2+c*x^4)^-2, x) == :(-1//2*b^-2*x^-2+c*b^-3*log(b+c*x^2)+-2*c*b^-3*log(x)+-1//2*c*b^-2*(b+c*x^2)^-1)
@test integrate((b*x^2+c*x^4)^-2, x) == :(-5//6*b^-2*x^-3+(1/2)*b^-1*x^-3*(b+c*x^2)^-1+5//2*c*b^-3*x^-1+5//2*b^-7//2*c^3//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^-1*(b*x^2+c*x^4)^-2, x) == :(-1//4*b^-2*x^-4+c*b^-3*x^-2+(1/2)*b^-3*c^2*(b+c*x^2)^-1+3*b^-4*c^2*log(x)+-3//2*b^-4*c^2*log(b+c*x^2))
@test integrate(x^-2*(b*x^2+c*x^4)^-2, x) == :(-7//10*b^-2*x^-5+(1/2)*b^-1*x^-5*(b+c*x^2)^-1+-7//2*b^-4*c^2*x^-1+-7//2*b^-9//2*c^5//2*arctan(x*b^-1//2*c^(1/2))+7//6*c*b^-3*x^-3)
@test integrate(x^14*(b*x^2+c*x^4)^-3, x) == :(35//24*c^-3*x^3+-35//8*b*x*c^-4+-7//8*c^-2*x^5*(b+c*x^2)^-1+-1//4*c^-1*x^7*(b+c*x^2)^-2+35//8*b^3//2*c^-9//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^13*(b*x^2+c*x^4)^-3, x) == :((1/2)*c^-3*x^2+-3//2*b*c^-4*log(b+c*x^2)+-3//2*b^2*c^-4*(b+c*x^2)^-1+1//4*b^3*c^-4*(b+c*x^2)^-2)
@test integrate(x^12*(b*x^2+c*x^4)^-3, x) == :(15//8*x*c^-3+-15//8*b^(1/2)*c^-7//2*arctan(x*b^-1//2*c^(1/2))+-5//8*c^-2*x^3*(b+c*x^2)^-1+-1//4*c^-1*x^5*(b+c*x^2)^-2)
@test integrate(x^11*(b*x^2+c*x^4)^-3, x) == :((1/2)*c^-3*log(b+c*x^2)+b*c^-3*(b+c*x^2)^-1+-1//4*b^2*c^-3*(b+c*x^2)^-2)
@test integrate(x^10*(b*x^2+c*x^4)^-3, x) == :(-3//8*x*c^-2*(b+c*x^2)^-1+-1//4*c^-1*x^3*(b+c*x^2)^-2+3//8*b^-1//2*c^-5//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^9*(b*x^2+c*x^4)^-3, x) == :(1//4*b^-1*x^4*(b+c*x^2)^-2)
@test integrate(x^8*(b*x^2+c*x^4)^-3, x) == :(-1//4*x*c^-1*(b+c*x^2)^-2+1//8*b^-3//2*c^-3//2*arctan(x*b^-1//2*c^(1/2))+1//8*x*b^-1*c^-1*(b+c*x^2)^-1)
@test integrate(x^7*(b*x^2+c*x^4)^-3, x) == :(-1//4*c^-1*(b+c*x^2)^-2)
@test integrate(x^6*(b*x^2+c*x^4)^-3, x) == :(1//4*x*b^-1*(b+c*x^2)^-2+3//8*x*b^-2*(b+c*x^2)^-1+3//8*b^-5//2*c^-1//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x^5*(b*x^2+c*x^4)^-3, x) == :(b^-3*log(x)+(1/2)*b^-2*(b+c*x^2)^-1+-1//2*b^-3*log(b+c*x^2)+1//4*b^-1*(b+c*x^2)^-2)
@test integrate(x^4*(b*x^2+c*x^4)^-3, x) == :(-15//8*b^-3*x^-1+-15//8*b^-7//2*c^(1/2)*arctan(x*b^-1//2*c^(1/2))+1//4*b^-1*x^-1*(b+c*x^2)^-2+5//8*b^-2*x^-1*(b+c*x^2)^-1)
@test integrate(x^3*(b*x^2+c*x^4)^-3, x) == :(-1//2*b^-3*x^-2+-1*c*b^-3*(b+c*x^2)^-1+-3*c*b^-4*log(x)+-1//4*c*b^-2*(b+c*x^2)^-2+3//2*c*b^-4*log(b+c*x^2))
@test integrate(x^2*(b*x^2+c*x^4)^-3, x) == :(-35//24*b^-3*x^-3+1//4*b^-1*x^-3*(b+c*x^2)^-2+7//8*b^-2*x^-3*(b+c*x^2)^-1+35//8*c*b^-4*x^-1+35//8*b^-9//2*c^3//2*arctan(x*b^-1//2*c^(1/2)))
@test integrate(x*(b*x^2+c*x^4)^-3, x) == :(-1//4*b^-3*x^-4+-3*b^-5*c^2*log(b+c*x^2)+6*b^-5*c^2*log(x)+1//4*b^-3*c^2*(b+c*x^2)^-2+3//2*c*b^-4*x^-2+3//2*b^-4*c^2*(b+c*x^2)^-1)
@test integrate((b*x^2+c*x^4)^-3, x) == :(-63//40*b^-3*x^-5+-63//8*b^-5*c^2*x^-1+-63//8*b^-11//2*c^5//2*arctan(x*b^-1//2*c^(1/2))+1//4*b^-1*x^-5*(b+c*x^2)^-2+9//8*b^-2*x^-5*(b+c*x^2)^-1+21//8*c*b^-4*x^-3)
@test integrate(x^-1*(b*x^2+c*x^4)^-3, x) == :(-1//6*b^-3*x^-6+-10*b^-6*c^3*log(x)+-3*b^-5*c^2*x^-2+-2*b^-5*c^3*(b+c*x^2)^-1+5*b^-6*c^3*log(b+c*x^2)+-1//4*b^-4*c^3*(b+c*x^2)^-2+3//4*c*b^-4*x^-4)
@test integrate(x^5*(b*x^2+c*x^4)^(1/2), x) == :(-5//48*b*c^-2*(b*x^2+c*x^4)^3//2+-5//128*b^4*c^-7//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+1//8*c^-1*x^2*(b*x^2+c*x^4)^3//2+5//128*b^2*c^-3*(b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x^3*(b*x^2+c*x^4)^(1/2), x) == :(1//6*c^-1*(b*x^2+c*x^4)^3//2+1//16*b^3*c^-5//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+-1//16*b*c^-2*(b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x*(b*x^2+c*x^4)^(1/2), x) == :(-1//8*b^2*c^-3//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+1//8*c^-1*(b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x^-1*(b*x^2+c*x^4)^(1/2), x) == :((1/2)*(b*x^2+c*x^4)^(1/2)+(1/2)*b*c^-1//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-3*(b*x^2+c*x^4)^(1/2), x) == :(c^(1/2)*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+-1*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-5*(b*x^2+c*x^4)^(1/2), x) == :(-1//3*b^-1*x^-6*(b*x^2+c*x^4)^3//2)
@test integrate(x^-7*(b*x^2+c*x^4)^(1/2), x) == :(-1//5*b^-1*x^-8*(b*x^2+c*x^4)^3//2+2//15*c*b^-2*x^-6*(b*x^2+c*x^4)^3//2)
@test integrate(x^-9*(b*x^2+c*x^4)^(1/2), x) == :(-1//7*b^-1*x^-10*(b*x^2+c*x^4)^3//2+-8//105*b^-3*c^2*x^-6*(b*x^2+c*x^4)^3//2+4//35*c*b^-2*x^-8*(b*x^2+c*x^4)^3//2)
@test integrate(x^-11*(b*x^2+c*x^4)^(1/2), x) == :(-1//9*b^-1*x^-12*(b*x^2+c*x^4)^3//2+-8//105*b^-3*c^2*x^-8*(b*x^2+c*x^4)^3//2+2//21*c*b^-2*x^-10*(b*x^2+c*x^4)^3//2+16//315*b^-4*c^3*x^-6*(b*x^2+c*x^4)^3//2)
@test integrate(x^-13*(b*x^2+c*x^4)^(1/2), x) == :(-1//11*b^-1*x^-14*(b*x^2+c*x^4)^3//2+-128//3465*b^-5*c^4*x^-6*(b*x^2+c*x^4)^3//2+-16//231*b^-3*c^2*x^-10*(b*x^2+c*x^4)^3//2+8//99*c*b^-2*x^-12*(b*x^2+c*x^4)^3//2+64//1155*b^-4*c^3*x^-8*(b*x^2+c*x^4)^3//2)
@test integrate(x^4*(b*x^2+c*x^4)^(1/2), x) == :(1//7*x*c^-1*(b*x^2+c*x^4)^3//2+-4//35*b*c^-2*x^-1*(b*x^2+c*x^4)^3//2+8//105*b^2*c^-3*x^-3*(b*x^2+c*x^4)^3//2)
@test integrate(x^2*(b*x^2+c*x^4)^(1/2), x) == :(1//5*c^-1*x^-1*(b*x^2+c*x^4)^3//2+-2//15*b*c^-2*x^-3*(b*x^2+c*x^4)^3//2)
@test integrate((b*x^2+c*x^4)^(1/2), x) == :(1//3*c^-1*x^-3*(b*x^2+c*x^4)^3//2)
@test integrate(x^-2*(b*x^2+c*x^4)^(1/2), x) == :(x^-1*(b*x^2+c*x^4)^(1/2)+-1*b^(1/2)*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-4*(b*x^2+c*x^4)^(1/2), x) == :(-1//2*x^-3*(b*x^2+c*x^4)^(1/2)+-1//2*c*b^-1//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-6*(b*x^2+c*x^4)^(1/2), x) == :(-1//4*x^-5*(b*x^2+c*x^4)^(1/2)+1//8*b^-3//2*c^2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//8*c*b^-1*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-8*(b*x^2+c*x^4)^(1/2), x) == :(-1//6*x^-7*(b*x^2+c*x^4)^(1/2)+-1//16*b^-5//2*c^3*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//24*c*b^-1*x^-5*(b*x^2+c*x^4)^(1/2)+1//16*b^-2*c^2*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^3*(b*x^2+c*x^4)^3//2, x) == :(1//10*c^-1*(b*x^2+c*x^4)^5//2+-3//256*b^5*c^-7//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+-1//32*b*c^-2*(b*x^2+c*x^4)^3//2*(b+2*c*x^2)+3//256*b^3*c^-3*(b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x*(b*x^2+c*x^4)^3//2, x) == :(1//16*c^-1*(b*x^2+c*x^4)^3//2*(b+2*c*x^2)+3//128*b^4*c^-5//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+-3//128*b^2*c^-2*(b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x^-1*(b*x^2+c*x^4)^3//2, x) == :(1//6*(b*x^2+c*x^4)^3//2+-1//16*b^3*c^-3//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+1//16*b*c^-1*(b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x^-3*(b*x^2+c*x^4)^3//2, x) == :(1//4*x^-2*(b*x^2+c*x^4)^3//2+3//8*b*(b*x^2+c*x^4)^(1/2)+3//8*b^2*c^-1//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-5*(b*x^2+c*x^4)^3//2, x) == :(-1*x^-4*(b*x^2+c*x^4)^3//2+3//2*c*(b*x^2+c*x^4)^(1/2)+3//2*b*c^(1/2)*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-7*(b*x^2+c*x^4)^3//2, x) == :(c^3//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+-1//3*x^-6*(b*x^2+c*x^4)^3//2+-1*c*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-9*(b*x^2+c*x^4)^3//2, x) == :(-1//5*b^-1*x^-10*(b*x^2+c*x^4)^5//2)
@test integrate(x^-11*(b*x^2+c*x^4)^3//2, x) == :(-1//7*b^-1*x^-12*(b*x^2+c*x^4)^5//2+2//35*c*b^-2*x^-10*(b*x^2+c*x^4)^5//2)
@test integrate(x^-13*(b*x^2+c*x^4)^3//2, x) == :(-1//9*b^-1*x^-14*(b*x^2+c*x^4)^5//2+-8//315*b^-3*c^2*x^-10*(b*x^2+c*x^4)^5//2+4//63*c*b^-2*x^-12*(b*x^2+c*x^4)^5//2)
@test integrate(x^-15*(b*x^2+c*x^4)^3//2, x) == :(-1//11*b^-1*x^-16*(b*x^2+c*x^4)^5//2+-8//231*b^-3*c^2*x^-12*(b*x^2+c*x^4)^5//2+2//33*c*b^-2*x^-14*(b*x^2+c*x^4)^5//2+16//1155*b^-4*c^3*x^-10*(b*x^2+c*x^4)^5//2)
@test integrate(x^-17*(b*x^2+c*x^4)^3//2, x) == :(-1//13*b^-1*x^-18*(b*x^2+c*x^4)^5//2+-128//15015*b^-5*c^4*x^-10*(b*x^2+c*x^4)^5//2+-16//429*b^-3*c^2*x^-14*(b*x^2+c*x^4)^5//2+8//143*c*b^-2*x^-16*(b*x^2+c*x^4)^5//2+64//3003*b^-4*c^3*x^-12*(b*x^2+c*x^4)^5//2)
@test integrate(x^6*(b*x^2+c*x^4)^3//2, x) == :(1//13*c^-1*x^3*(b*x^2+c*x^4)^5//2+-64//3003*b^3*c^-4*x^-3*(b*x^2+c*x^4)^5//2+-8//143*b*x*c^-2*(b*x^2+c*x^4)^5//2+16//429*b^2*c^-3*x^-1*(b*x^2+c*x^4)^5//2+128//15015*b^4*c^-5*x^-5*(b*x^2+c*x^4)^5//2)
@test integrate(x^4*(b*x^2+c*x^4)^3//2, x) == :(1//11*x*c^-1*(b*x^2+c*x^4)^5//2+-16//1155*b^3*c^-4*x^-5*(b*x^2+c*x^4)^5//2+-2//33*b*c^-2*x^-1*(b*x^2+c*x^4)^5//2+8//231*b^2*c^-3*x^-3*(b*x^2+c*x^4)^5//2)
@test integrate(x^2*(b*x^2+c*x^4)^3//2, x) == :(1//9*c^-1*x^-1*(b*x^2+c*x^4)^5//2+-4//63*b*c^-2*x^-3*(b*x^2+c*x^4)^5//2+8//315*b^2*c^-3*x^-5*(b*x^2+c*x^4)^5//2)
@test integrate((b*x^2+c*x^4)^3//2, x) == :(1//7*c^-1*x^-3*(b*x^2+c*x^4)^5//2+-2//35*b*c^-2*x^-5*(b*x^2+c*x^4)^5//2)
@test integrate(x^-2*(b*x^2+c*x^4)^3//2, x) == :(1//5*c^-1*x^-5*(b*x^2+c*x^4)^5//2)
@test integrate(x^-4*(b*x^2+c*x^4)^3//2, x) == :(-1*b^3//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+1//3*x^-3*(b*x^2+c*x^4)^3//2+b*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-6*(b*x^2+c*x^4)^3//2, x) == :(-1//2*x^-5*(b*x^2+c*x^4)^3//2+-3//2*c*b^(1/2)*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+3//2*c*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-8*(b*x^2+c*x^4)^3//2, x) == :(-1//4*x^-7*(b*x^2+c*x^4)^3//2+-3//8*c*x^-3*(b*x^2+c*x^4)^(1/2)+-3//8*b^-1//2*c^2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-10*(b*x^2+c*x^4)^3//2, x) == :(-1//6*x^-9*(b*x^2+c*x^4)^3//2+-1//8*c*x^-5*(b*x^2+c*x^4)^(1/2)+1//16*b^-3//2*c^3*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//16*b^-1*c^2*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-12*(b*x^2+c*x^4)^3//2, x) == :(-1//8*x^-11*(b*x^2+c*x^4)^3//2+-3//128*b^-5//2*c^4*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//16*c*x^-7*(b*x^2+c*x^4)^(1/2)+-1//64*b^-1*c^2*x^-5*(b*x^2+c*x^4)^(1/2)+3//128*b^-2*c^3*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-14*(b*x^2+c*x^4)^3//2, x) == :(-1//10*x^-13*(b*x^2+c*x^4)^3//2+-3//80*c*x^-9*(b*x^2+c*x^4)^(1/2)+3//256*b^-7//2*c^5*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-3//256*b^-3*c^4*x^-3*(b*x^2+c*x^4)^(1/2)+-1//160*b^-1*c^2*x^-7*(b*x^2+c*x^4)^(1/2)+1//128*b^-2*c^3*x^-5*(b*x^2+c*x^4)^(1/2))
@test integrate(x^7*(b*x^2+c*x^4)^-1//2, x) == :(-5//16*b^3*c^-7//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+1//6*c^-1*x^4*(b*x^2+c*x^4)^(1/2)+5//16*b^2*c^-3*(b*x^2+c*x^4)^(1/2)+-5//24*b*c^-2*x^2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^5*(b*x^2+c*x^4)^-1//2, x) == :(-3//8*b*c^-2*(b*x^2+c*x^4)^(1/2)+1//4*c^-1*x^2*(b*x^2+c*x^4)^(1/2)+3//8*b^2*c^-5//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^3*(b*x^2+c*x^4)^-1//2, x) == :((1/2)*c^-1*(b*x^2+c*x^4)^(1/2)+-1//2*b*c^-3//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x*(b*x^2+c*x^4)^-1//2, x) == :(c^-1//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-1*(b*x^2+c*x^4)^-1//2, x) == :(-1*b^-1*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-3*(b*x^2+c*x^4)^-1//2, x) == :(-1//3*b^-1*x^-4*(b*x^2+c*x^4)^(1/2)+2//3*c*b^-2*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-5*(b*x^2+c*x^4)^-1//2, x) == :(-1//5*b^-1*x^-6*(b*x^2+c*x^4)^(1/2)+-8//15*b^-3*c^2*x^-2*(b*x^2+c*x^4)^(1/2)+4//15*c*b^-2*x^-4*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-7*(b*x^2+c*x^4)^-1//2, x) == :(-1//7*b^-1*x^-8*(b*x^2+c*x^4)^(1/2)+-8//35*b^-3*c^2*x^-4*(b*x^2+c*x^4)^(1/2)+6//35*c*b^-2*x^-6*(b*x^2+c*x^4)^(1/2)+16//35*b^-4*c^3*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^4*(b*x^2+c*x^4)^-1//2, x) == :(1//3*x*c^-1*(b*x^2+c*x^4)^(1/2)+-2//3*b*c^-2*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate(x^2*(b*x^2+c*x^4)^-1//2, x) == :(c^-1*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate((b*x^2+c*x^4)^-1//2, x) == :(-1*b^-1//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-2*(b*x^2+c*x^4)^-1//2, x) == :((1/2)*c*b^-3//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//2*b^-1*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-4*(b*x^2+c*x^4)^-1//2, x) == :(-3//8*b^-5//2*c^2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//4*b^-1*x^-5*(b*x^2+c*x^4)^(1/2)+3//8*c*b^-2*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^9*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^6*(b*x^2+c*x^4)^-1//2+-15//8*b*c^-3*(b*x^2+c*x^4)^(1/2)+5//4*c^-2*x^2*(b*x^2+c*x^4)^(1/2)+15//8*b^2*c^-7//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^7*(b*x^2+c*x^4)^-3//2, x) == :(3//2*c^-2*(b*x^2+c*x^4)^(1/2)+-1*c^-1*x^4*(b*x^2+c*x^4)^-1//2+-3//2*b*c^-5//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^5*(b*x^2+c*x^4)^-3//2, x) == :(c^-3//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2)+-1*c^-1*x^2*(b*x^2+c*x^4)^-1//2)
@test integrate(x^3*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^2*(b*x^2+c*x^4)^-1//2)
@test integrate(x*(b*x^2+c*x^4)^-3//2, x) == :(-1*b^-2*(b*x^2+c*x^4)^-1//2*(b+2*c*x^2))
@test integrate(x^-1*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-2*(b*x^2+c*x^4)^-1//2+-4//3*b^-2*x^-4*(b*x^2+c*x^4)^(1/2)+8//3*c*b^-3*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-3*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-4*(b*x^2+c*x^4)^-1//2+-6//5*b^-2*x^-6*(b*x^2+c*x^4)^(1/2)+-16//5*b^-4*c^2*x^-2*(b*x^2+c*x^4)^(1/2)+8//5*c*b^-3*x^-4*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-5*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-6*(b*x^2+c*x^4)^-1//2+-8//7*b^-2*x^-8*(b*x^2+c*x^4)^(1/2)+-64//35*b^-4*c^2*x^-4*(b*x^2+c*x^4)^(1/2)+48//35*c*b^-3*x^-6*(b*x^2+c*x^4)^(1/2)+128//35*b^-5*c^3*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^6*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^3*(b*x^2+c*x^4)^-1//2+2*c^-2*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate(x^4*(b*x^2+c*x^4)^-3//2, x) == :(-1*x*c^-1*(b*x^2+c*x^4)^-1//2)
@test integrate(x^2*(b*x^2+c*x^4)^-3//2, x) == :(-1*b^-3//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+x*b^-1*(b*x^2+c*x^4)^-1//2)
@test integrate((b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-1*(b*x^2+c*x^4)^-1//2+-3//2*b^-2*x^-3*(b*x^2+c*x^4)^(1/2)+3//2*c*b^-5//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-3*(b*x^2+c*x^4)^-1//2+-15//8*b^-7//2*c^2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-5//4*b^-2*x^-5*(b*x^2+c*x^4)^(1/2)+15//8*c*b^-3*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^3*(-4*x^4+3*x^2)^-1//2, x) == :(-3//32*arcsin(1+-8//3*x^2)+-1//8*(-4*x^4+3*x^2)^(1/2))
@test integrate(x^3*(-4*x^4+-3*x^2)^-1//2, x) == :(-3//32*arcsin(1+8//3*x^2)+-1//8*(-4*x^4+-3*x^2)^(1/2))
@test integrate(x^3*(3*x^2+4*x^4)^-1//2, x) == :(-3//16*arctanh(2*x^2*(3*x^2+4*x^4)^-1//2)+1//8*(3*x^2+4*x^4)^(1/2))
@test integrate(x^3*(-3*x^2+4*x^4)^-1//2, x) == :(1//8*(-3*x^2+4*x^4)^(1/2)+3//16*arctanh(2*x^2*(-3*x^2+4*x^4)^-1//2))
@test integrate(x^3*(a*x^2+b*x^4)^-1//2, x) == :((1/2)*b^-1*(a*x^2+b*x^4)^(1/2)+-1//2*a*b^-3//2*arctanh(b^(1/2)*x^2*(a*x^2+b*x^4)^-1//2))
@test integrate(x^3*(a*x^2+-1*b*x^4)^-1//2, x) == :(-1//2*b^-1*(a*x^2+-1*b*x^4)^(1/2)+(1/2)*a*b^-3//2*arctan(b^(1/2)*x^2*(a*x^2+-1*b*x^4)^-1//2))
@test integrate(x^7//2*(b*x^2+c*x^4), x) == :(2//13*b*x^13//2+2//17*c*x^17//2)
@test integrate(x^5//2*(b*x^2+c*x^4), x) == :(2//11*b*x^11//2+2//15*c*x^15//2)
@test integrate(x^3//2*(b*x^2+c*x^4), x) == :(2//9*b*x^9//2+2//13*c*x^13//2)
@test integrate(x^(1/2)*(b*x^2+c*x^4), x) == :(2//7*b*x^7//2+2//11*c*x^11//2)
@test integrate(x^-1//2*(b*x^2+c*x^4), x) == :(2//5*b*x^5//2+2//9*c*x^9//2)
@test integrate(x^-3//2*(b*x^2+c*x^4), x) == :(2//3*b*x^3//2+2//7*c*x^7//2)
@test integrate(x^-5//2*(b*x^2+c*x^4), x) == :(2*b*x^(1/2)+2//5*c*x^5//2)
@test integrate(x^-7//2*(b*x^2+c*x^4), x) == :(-2*b*x^-1//2+2//3*c*x^3//2)
@test integrate(x^7//2*(b*x^2+c*x^4)^2, x) == :(2//17*b^2*x^17//2+2//25*c^2*x^25//2+4//21*b*c*x^21//2)
@test integrate(x^5//2*(b*x^2+c*x^4)^2, x) == :(2//15*b^2*x^15//2+2//23*c^2*x^23//2+4//19*b*c*x^19//2)
@test integrate(x^3//2*(b*x^2+c*x^4)^2, x) == :(2//13*b^2*x^13//2+2//21*c^2*x^21//2+4//17*b*c*x^17//2)
@test integrate(x^(1/2)*(b*x^2+c*x^4)^2, x) == :(2//11*b^2*x^11//2+2//19*c^2*x^19//2+4//15*b*c*x^15//2)
@test integrate(x^-1//2*(b*x^2+c*x^4)^2, x) == :(2//9*b^2*x^9//2+2//17*c^2*x^17//2+4//13*b*c*x^13//2)
@test integrate(x^-3//2*(b*x^2+c*x^4)^2, x) == :(2//7*b^2*x^7//2+2//15*c^2*x^15//2+4//11*b*c*x^11//2)
@test integrate(x^-5//2*(b*x^2+c*x^4)^2, x) == :(2//5*b^2*x^5//2+2//13*c^2*x^13//2+4//9*b*c*x^9//2)
@test integrate(x^-7//2*(b*x^2+c*x^4)^2, x) == :(2//3*b^2*x^3//2+2//11*c^2*x^11//2+4//7*b*c*x^7//2)
@test integrate(x^7//2*(b*x^2+c*x^4)^3, x) == :(2//21*b^3*x^21//2+2//33*c^3*x^33//2+6//25*c*b^2*x^25//2+6//29*b*c^2*x^29//2)
@test integrate(x^5//2*(b*x^2+c*x^4)^3, x) == :(2//19*b^3*x^19//2+2//31*c^3*x^31//2+2//9*b*c^2*x^27//2+6//23*c*b^2*x^23//2)
@test integrate(x^3//2*(b*x^2+c*x^4)^3, x) == :(2//17*b^3*x^17//2+2//29*c^3*x^29//2+2//7*c*b^2*x^21//2+6//25*b*c^2*x^25//2)
@test integrate(x^(1/2)*(b*x^2+c*x^4)^3, x) == :(2//15*b^3*x^15//2+2//27*c^3*x^27//2+6//19*c*b^2*x^19//2+6//23*b*c^2*x^23//2)
@test integrate(x^-1//2*(b*x^2+c*x^4)^3, x) == :(2//13*b^3*x^13//2+2//25*c^3*x^25//2+2//7*b*c^2*x^21//2+6//17*c*b^2*x^17//2)
@test integrate(x^-3//2*(b*x^2+c*x^4)^3, x) == :(2//11*b^3*x^11//2+2//23*c^3*x^23//2+2//5*c*b^2*x^15//2+6//19*b*c^2*x^19//2)
@test integrate(x^-5//2*(b*x^2+c*x^4)^3, x) == :(2//9*b^3*x^9//2+2//21*c^3*x^21//2+6//13*c*b^2*x^13//2+6//17*b*c^2*x^17//2)
@test integrate(x^-7//2*(b*x^2+c*x^4)^3, x) == :(2//7*b^3*x^7//2+2//19*c^3*x^19//2+2//5*b*c^2*x^15//2+6//11*c*b^2*x^11//2)
@test integrate(x^13//2*(b*x^2+c*x^4)^-1, x) == :(2//7*c^-1*x^7//2+-2//3*b*c^-2*x^3//2+(1/2)*2^(1/2)*b^7//4*c^-11//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^7//4*c^-11//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^7//4*c^-11//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^7//4*c^-11//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^11//2*(b*x^2+c*x^4)^-1, x) == :(2//5*c^-1*x^5//2+-2*b*c^-2*x^(1/2)+(1/2)*2^(1/2)*b^5//4*c^-9//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^5//4*c^-9//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^5//4*c^-9//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^5//4*c^-9//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^9//2*(b*x^2+c*x^4)^-1, x) == :(2//3*c^-1*x^3//2+(1/2)*2^(1/2)*b^3//4*c^-7//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^3//4*c^-7//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^3//4*c^-7//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^3//4*c^-7//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^7//2*(b*x^2+c*x^4)^-1, x) == :(2*c^-1*x^(1/2)+(1/2)*2^(1/2)*b^1//4*c^-5//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^1//4*c^-5//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^1//4*c^-5//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^1//4*c^-5//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^5//2*(b*x^2+c*x^4)^-1, x) == :((1/2)*2^(1/2)*b^-1//4*c^-3//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-1//4*c^-3//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-1//4*c^-3//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-1//4*c^-3//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^3//2*(b*x^2+c*x^4)^-1, x) == :((1/2)*2^(1/2)*b^-3//4*c^-1//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-3//4*c^-1//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-3//4*c^-1//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-3//4*c^-1//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^-1, x) == :(-2*b^-1*x^-1//2+(1/2)*2^(1/2)*b^-5//4*c^1//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-5//4*c^1//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-5//4*c^1//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-5//4*c^1//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-1//2*(b*x^2+c*x^4)^-1, x) == :(-2//3*b^-1*x^-3//2+(1/2)*2^(1/2)*b^-7//4*c^3//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-7//4*c^3//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-7//4*c^3//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-7//4*c^3//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-3//2*(b*x^2+c*x^4)^-1, x) == :(-2//5*b^-1*x^-5//2+2*c*b^-2*x^-1//2+(1/2)*2^(1/2)*b^-9//4*c^5//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-9//4*c^5//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-9//4*c^5//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-9//4*c^5//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-5//2*(b*x^2+c*x^4)^-1, x) == :(-2//7*b^-1*x^-7//2+2//3*c*b^-2*x^-3//2+(1/2)*2^(1/2)*b^-11//4*c^7//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-11//4*c^7//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-11//4*c^7//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-11//4*c^7//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-7//2*(b*x^2+c*x^4)^-1, x) == :(-2//9*b^-1*x^-9//2+-2*b^-3*c^2*x^-1//2+2//5*c*b^-2*x^-5//2+(1/2)*2^(1/2)*b^-13//4*c^9//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//2*2^(1/2)*b^-13//4*c^9//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//4*2^(1/2)*b^-13//4*c^9//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//4*2^(1/2)*b^-13//4*c^9//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^19//2*(b*x^2+c*x^4)^-2, x) == :(9//10*c^-2*x^5//2+-9//2*b*c^-3*x^(1/2)+-1//2*c^-1*x^9//2*(b+c*x^2)^-1+-9//8*2^(1/2)*b^5//4*c^-13//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-9//16*2^(1/2)*b^5//4*c^-13//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+9//8*2^(1/2)*b^5//4*c^-13//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+9//16*2^(1/2)*b^5//4*c^-13//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^17//2*(b*x^2+c*x^4)^-2, x) == :(7//6*c^-2*x^3//2+-1//2*c^-1*x^7//2*(b+c*x^2)^-1+-7//8*2^(1/2)*b^3//4*c^-11//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-7//16*2^(1/2)*b^3//4*c^-11//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+7//8*2^(1/2)*b^3//4*c^-11//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+7//16*2^(1/2)*b^3//4*c^-11//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^15//2*(b*x^2+c*x^4)^-2, x) == :(5//2*c^-2*x^(1/2)+-1//2*c^-1*x^5//2*(b+c*x^2)^-1+-5//8*2^(1/2)*b^1//4*c^-9//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-5//16*2^(1/2)*b^1//4*c^-9//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+5//8*2^(1/2)*b^1//4*c^-9//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+5//16*2^(1/2)*b^1//4*c^-9//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^13//2*(b*x^2+c*x^4)^-2, x) == :(-1//2*c^-1*x^3//2*(b+c*x^2)^-1+-3//8*2^(1/2)*b^-1//4*c^-7//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-3//16*2^(1/2)*b^-1//4*c^-7//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+3//8*2^(1/2)*b^-1//4*c^-7//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+3//16*2^(1/2)*b^-1//4*c^-7//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^11//2*(b*x^2+c*x^4)^-2, x) == :(-1//2*c^-1*x^(1/2)*(b+c*x^2)^-1+-1//8*2^(1/2)*b^-3//4*c^-5//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//16*2^(1/2)*b^-3//4*c^-5//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//8*2^(1/2)*b^-3//4*c^-5//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+1//16*2^(1/2)*b^-3//4*c^-5//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^9//2*(b*x^2+c*x^4)^-2, x) == :((1/2)*b^-1*x^3//2*(b+c*x^2)^-1+-1//8*2^(1/2)*b^-5//4*c^-3//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-1//16*2^(1/2)*b^-5//4*c^-3//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//8*2^(1/2)*b^-5//4*c^-3//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+1//16*2^(1/2)*b^-5//4*c^-3//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^7//2*(b*x^2+c*x^4)^-2, x) == :((1/2)*b^-1*x^(1/2)*(b+c*x^2)^-1+-3//8*2^(1/2)*b^-7//4*c^-1//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-3//16*2^(1/2)*b^-7//4*c^-1//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+3//8*2^(1/2)*b^-7//4*c^-1//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+3//16*2^(1/2)*b^-7//4*c^-1//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^5//2*(b*x^2+c*x^4)^-2, x) == :(-5//2*b^-2*x^-1//2+(1/2)*b^-1*x^-1//2*(b+c*x^2)^-1+-5//8*2^(1/2)*b^-9//4*c^1//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-5//16*2^(1/2)*b^-9//4*c^1//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+5//8*2^(1/2)*b^-9//4*c^1//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+5//16*2^(1/2)*b^-9//4*c^1//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^3//2*(b*x^2+c*x^4)^-2, x) == :(-7//6*b^-2*x^-3//2+(1/2)*b^-1*x^-3//2*(b+c*x^2)^-1+-7//8*2^(1/2)*b^-11//4*c^3//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-7//16*2^(1/2)*b^-11//4*c^3//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+7//8*2^(1/2)*b^-11//4*c^3//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+7//16*2^(1/2)*b^-11//4*c^3//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^-2, x) == :(-9//10*b^-2*x^-5//2+(1/2)*b^-1*x^-5//2*(b+c*x^2)^-1+9//2*c*b^-3*x^-1//2+-9//8*2^(1/2)*b^-13//4*c^5//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-9//16*2^(1/2)*b^-13//4*c^5//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+9//8*2^(1/2)*b^-13//4*c^5//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+9//16*2^(1/2)*b^-13//4*c^5//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-1//2*(b*x^2+c*x^4)^-2, x) == :(-11//14*b^-2*x^-7//2+(1/2)*b^-1*x^-7//2*(b+c*x^2)^-1+11//6*c*b^-3*x^-3//2+-11//8*2^(1/2)*b^-15//4*c^7//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-11//16*2^(1/2)*b^-15//4*c^7//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+11//8*2^(1/2)*b^-15//4*c^7//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+11//16*2^(1/2)*b^-15//4*c^7//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-3//2*(b*x^2+c*x^4)^-2, x) == :(-13//18*b^-2*x^-9//2+(1/2)*b^-1*x^-9//2*(b+c*x^2)^-1+-13//2*b^-4*c^2*x^-1//2+13//10*c*b^-3*x^-5//2+-13//8*2^(1/2)*b^-17//4*c^9//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-13//16*2^(1/2)*b^-17//4*c^9//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+13//8*2^(1/2)*b^-17//4*c^9//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+13//16*2^(1/2)*b^-17//4*c^9//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^23//2*(b*x^2+c*x^4)^-3, x) == :(45//16*c^-3*x^(1/2)+-9//16*c^-2*x^5//2*(b+c*x^2)^-1+-1//4*c^-1*x^9//2*(b+c*x^2)^-2+-45//64*2^(1/2)*b^1//4*c^-13//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-45//128*2^(1/2)*b^1//4*c^-13//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+45//64*2^(1/2)*b^1//4*c^-13//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+45//128*2^(1/2)*b^1//4*c^-13//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^21//2*(b*x^2+c*x^4)^-3, x) == :(-7//16*c^-2*x^3//2*(b+c*x^2)^-1+-1//4*c^-1*x^7//2*(b+c*x^2)^-2+-21//64*2^(1/2)*b^-1//4*c^-11//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-21//128*2^(1/2)*b^-1//4*c^-11//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+21//64*2^(1/2)*b^-1//4*c^-11//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+21//128*2^(1/2)*b^-1//4*c^-11//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^19//2*(b*x^2+c*x^4)^-3, x) == :(-5//16*c^-2*x^(1/2)*(b+c*x^2)^-1+-1//4*c^-1*x^5//2*(b+c*x^2)^-2+-5//64*2^(1/2)*b^-3//4*c^-9//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-5//128*2^(1/2)*b^-3//4*c^-9//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+5//64*2^(1/2)*b^-3//4*c^-9//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+5//128*2^(1/2)*b^-3//4*c^-9//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^17//2*(b*x^2+c*x^4)^-3, x) == :(-1//4*c^-1*x^3//2*(b+c*x^2)^-2+-3//64*2^(1/2)*b^-5//4*c^-7//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-3//128*2^(1/2)*b^-5//4*c^-7//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+3//16*b^-1*c^-1*x^3//2*(b+c*x^2)^-1+3//64*2^(1/2)*b^-5//4*c^-7//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+3//128*2^(1/2)*b^-5//4*c^-7//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^15//2*(b*x^2+c*x^4)^-3, x) == :(-1//4*c^-1*x^(1/2)*(b+c*x^2)^-2+-3//64*2^(1/2)*b^-7//4*c^-5//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-3//128*2^(1/2)*b^-7//4*c^-5//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+1//16*b^-1*c^-1*x^(1/2)*(b+c*x^2)^-1+3//64*2^(1/2)*b^-7//4*c^-5//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+3//128*2^(1/2)*b^-7//4*c^-5//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^13//2*(b*x^2+c*x^4)^-3, x) == :(1//4*b^-1*x^3//2*(b+c*x^2)^-2+5//16*b^-2*x^3//2*(b+c*x^2)^-1+-5//64*2^(1/2)*b^-9//4*c^-3//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-5//128*2^(1/2)*b^-9//4*c^-3//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+5//64*2^(1/2)*b^-9//4*c^-3//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+5//128*2^(1/2)*b^-9//4*c^-3//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^11//2*(b*x^2+c*x^4)^-3, x) == :(1//4*b^-1*x^(1/2)*(b+c*x^2)^-2+7//16*b^-2*x^(1/2)*(b+c*x^2)^-1+-21//64*2^(1/2)*b^-11//4*c^-1//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-21//128*2^(1/2)*b^-11//4*c^-1//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+21//64*2^(1/2)*b^-11//4*c^-1//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+21//128*2^(1/2)*b^-11//4*c^-1//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^9//2*(b*x^2+c*x^4)^-3, x) == :(-45//16*b^-3*x^-1//2+1//4*b^-1*x^-1//2*(b+c*x^2)^-2+9//16*b^-2*x^-1//2*(b+c*x^2)^-1+-45//64*2^(1/2)*b^-13//4*c^1//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-45//128*2^(1/2)*b^-13//4*c^1//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+45//64*2^(1/2)*b^-13//4*c^1//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+45//128*2^(1/2)*b^-13//4*c^1//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^7//2*(b*x^2+c*x^4)^-3, x) == :(-77//48*b^-3*x^-3//2+1//4*b^-1*x^-3//2*(b+c*x^2)^-2+11//16*b^-2*x^-3//2*(b+c*x^2)^-1+-77//64*2^(1/2)*b^-15//4*c^3//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-77//128*2^(1/2)*b^-15//4*c^3//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+77//64*2^(1/2)*b^-15//4*c^3//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+77//128*2^(1/2)*b^-15//4*c^3//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^5//2*(b*x^2+c*x^4)^-3, x) == :(-117//80*b^-3*x^-5//2+1//4*b^-1*x^-5//2*(b+c*x^2)^-2+13//16*b^-2*x^-5//2*(b+c*x^2)^-1+117//16*c*b^-4*x^-1//2+-117//64*2^(1/2)*b^-17//4*c^5//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-117//128*2^(1/2)*b^-17//4*c^5//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+117//64*2^(1/2)*b^-17//4*c^5//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+117//128*2^(1/2)*b^-17//4*c^5//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^3//2*(b*x^2+c*x^4)^-3, x) == :(-165//112*b^-3*x^-7//2+1//4*b^-1*x^-7//2*(b+c*x^2)^-2+15//16*b^-2*x^-7//2*(b+c*x^2)^-1+55//16*c*b^-4*x^-3//2+-165//64*2^(1/2)*b^-19//4*c^7//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-165//128*2^(1/2)*b^-19//4*c^7//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+165//64*2^(1/2)*b^-19//4*c^7//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+165//128*2^(1/2)*b^-19//4*c^7//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^-3, x) == :(-221//144*b^-3*x^-9//2+-221//16*b^-5*c^2*x^-1//2+1//4*b^-1*x^-9//2*(b+c*x^2)^-2+17//16*b^-2*x^-9//2*(b+c*x^2)^-1+221//80*c*b^-4*x^-5//2+-221//64*2^(1/2)*b^-21//4*c^9//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-221//128*2^(1/2)*b^-21//4*c^9//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2))+221//64*2^(1/2)*b^-21//4*c^9//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+221//128*2^(1/2)*b^-21//4*c^9//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^-1//2*(b*x^2+c*x^4)^-3, x) == :(-285//176*b^-3*x^-11//2+-95//16*b^-5*c^2*x^-3//2+1//4*b^-1*x^-11//2*(b+c*x^2)^-2+19//16*b^-2*x^-11//2*(b+c*x^2)^-1+285//112*c*b^-4*x^-7//2+-285//64*2^(1/2)*b^-23//4*c^11//4*arctan(1+2^(1/2)*b^-1//4*c^1//4*x^(1/2))+-285//128*2^(1/2)*b^-23//4*c^11//4*log(b^(1/2)+x*c^(1/2)+2^(1/2)*b^1//4*c^1//4*x^(1/2))+285//64*2^(1/2)*b^-23//4*c^11//4*arctan(1+-1*2^(1/2)*b^-1//4*c^1//4*x^(1/2))+285//128*2^(1/2)*b^-23//4*c^11//4*log(b^(1/2)+x*c^(1/2)+-1*2^(1/2)*b^1//4*c^1//4*x^(1/2)))
@test integrate(x^7//2*(b*x^2+c*x^4)^(1/2), x) == :(2//13*x^9//2*(b*x^2+c*x^4)^(1/2)+-28//585*b^2*c^-2*x^(1/2)*(b*x^2+c*x^4)^(1/2)+4//117*b*c^-1*x^5//2*(b*x^2+c*x^4)^(1/2)+28//195*b^3*c^-5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-28//195*x*b^13//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+14//195*x*b^13//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^5//2*(b*x^2+c*x^4)^(1/2), x) == :(2//11*x^7//2*(b*x^2+c*x^4)^(1/2)+-20//231*b^2*c^-2*x^-1//2*(b*x^2+c*x^4)^(1/2)+4//77*b*c^-1*x^3//2*(b*x^2+c*x^4)^(1/2)+10//231*x*b^11//4*c^-9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^3//2*(b*x^2+c*x^4)^(1/2), x) == :(2//9*x^5//2*(b*x^2+c*x^4)^(1/2)+4//45*b*c^-1*x^(1/2)*(b*x^2+c*x^4)^(1/2)+-4//15*b^2*c^-3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-2//15*x*b^9//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+4//15*x*b^9//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^(1/2), x) == :(2//7*x^3//2*(b*x^2+c*x^4)^(1/2)+4//21*b*c^-1*x^-1//2*(b*x^2+c*x^4)^(1/2)+-2//21*x*b^7//4*c^-5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-1//2*(b*x^2+c*x^4)^(1/2), x) == :(2//5*x^(1/2)*(b*x^2+c*x^4)^(1/2)+4//5*b*c^-1//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-4//5*x*b^5//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+2//5*x*b^5//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-3//2*(b*x^2+c*x^4)^(1/2), x) == :(2//3*x^-1//2*(b*x^2+c*x^4)^(1/2)+2//3*x*b^3//4*c^-1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-5//2*(b*x^2+c*x^4)^(1/2), x) == :(-2*x^-3//2*(b*x^2+c*x^4)^(1/2)+4*c^(1/2)*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-4*x*b^1//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+2*x*b^1//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-7//2*(b*x^2+c*x^4)^(1/2), x) == :(-2//3*x^-5//2*(b*x^2+c*x^4)^(1/2)+2//3*x*b^-1//4*c^3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-9//2*(b*x^2+c*x^4)^(1/2), x) == :(-2//5*x^-7//2*(b*x^2+c*x^4)^(1/2)+-4//5*c*b^-1*x^-3//2*(b*x^2+c*x^4)^(1/2)+4//5*b^-1*c^3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-4//5*x*b^-3//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+2//5*x*b^-3//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-11//2*(b*x^2+c*x^4)^(1/2), x) == :(-2//7*x^-9//2*(b*x^2+c*x^4)^(1/2)+-4//21*c*b^-1*x^-5//2*(b*x^2+c*x^4)^(1/2)+-2//21*x*b^-5//4*c^7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-13//2*(b*x^2+c*x^4)^(1/2), x) == :(-2//9*x^-11//2*(b*x^2+c*x^4)^(1/2)+-4//45*c*b^-1*x^-7//2*(b*x^2+c*x^4)^(1/2)+4//15*b^-2*c^2*x^-3//2*(b*x^2+c*x^4)^(1/2)+-4//15*b^-2*c^5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-2//15*x*b^-7//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+4//15*x*b^-7//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-15//2*(b*x^2+c*x^4)^(1/2), x) == :(-2//11*x^-13//2*(b*x^2+c*x^4)^(1/2)+-4//77*c*b^-1*x^-9//2*(b*x^2+c*x^4)^(1/2)+20//231*b^-2*c^2*x^-5//2*(b*x^2+c*x^4)^(1/2)+10//231*x*b^-9//4*c^11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^3//2*(b*x^2+c*x^4)^3//2, x) == :(2//17*x^5//2*(b*x^2+c*x^4)^3//2+12//221*b*x^9//2*(b*x^2+c*x^4)^(1/2)+-56//3315*b^3*c^-2*x^(1/2)*(b*x^2+c*x^4)^(1/2)+8//663*b^2*c^-1*x^5//2*(b*x^2+c*x^4)^(1/2)+56//1105*b^4*c^-5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-56//1105*x*b^17//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+28//1105*x*b^17//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^3//2, x) == :(2//15*x^3//2*(b*x^2+c*x^4)^3//2+4//55*b*x^7//2*(b*x^2+c*x^4)^(1/2)+-8//231*b^3*c^-2*x^-1//2*(b*x^2+c*x^4)^(1/2)+8//385*b^2*c^-1*x^3//2*(b*x^2+c*x^4)^(1/2)+4//231*x*b^15//4*c^-9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-1//2*(b*x^2+c*x^4)^3//2, x) == :(2//13*x^(1/2)*(b*x^2+c*x^4)^3//2+4//39*b*x^5//2*(b*x^2+c*x^4)^(1/2)+8//195*b^2*c^-1*x^(1/2)*(b*x^2+c*x^4)^(1/2)+-8//65*b^3*c^-3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-4//65*x*b^13//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+8//65*x*b^13//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-3//2*(b*x^2+c*x^4)^3//2, x) == :(2//11*x^-1//2*(b*x^2+c*x^4)^3//2+12//77*b*x^3//2*(b*x^2+c*x^4)^(1/2)+8//77*b^2*c^-1*x^-1//2*(b*x^2+c*x^4)^(1/2)+-4//77*x*b^11//4*c^-5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-5//2*(b*x^2+c*x^4)^3//2, x) == :(2//9*x^-3//2*(b*x^2+c*x^4)^3//2+4//15*b*x^(1/2)*(b*x^2+c*x^4)^(1/2)+8//15*b^2*c^-1//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-8//15*x*b^9//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+4//15*x*b^9//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-7//2*(b*x^2+c*x^4)^3//2, x) == :(2//7*x^-5//2*(b*x^2+c*x^4)^3//2+4//7*b*x^-1//2*(b*x^2+c*x^4)^(1/2)+4//7*x*b^7//4*c^-1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-9//2*(b*x^2+c*x^4)^3//2, x) == :(-2*x^-7//2*(b*x^2+c*x^4)^3//2+12//5*c*x^(1/2)*(b*x^2+c*x^4)^(1/2)+24*b*c^(1/2)*x^3//2*(5*b^(1/2)+5*x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-24//5*x*b^5//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+12//5*x*b^5//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-11//2*(b*x^2+c*x^4)^3//2, x) == :(-2//3*x^-9//2*(b*x^2+c*x^4)^3//2+4//3*c*x^-1//2*(b*x^2+c*x^4)^(1/2)+4//3*x*b^3//4*c^3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-13//2*(b*x^2+c*x^4)^3//2, x) == :(-2//5*x^-11//2*(b*x^2+c*x^4)^3//2+-12//5*c*x^-3//2*(b*x^2+c*x^4)^(1/2)+24*c^3//2*x^3//2*(5*b^(1/2)+5*x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-24//5*x*b^1//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+12//5*x*b^1//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-15//2*(b*x^2+c*x^4)^3//2, x) == :(-2//7*x^-13//2*(b*x^2+c*x^4)^3//2+-4//7*c*x^-5//2*(b*x^2+c*x^4)^(1/2)+4//7*x*b^-1//4*c^7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-17//2*(b*x^2+c*x^4)^3//2, x) == :(-2//9*x^-15//2*(b*x^2+c*x^4)^3//2+-4//15*c*x^-7//2*(b*x^2+c*x^4)^(1/2)+-8//15*b^-1*c^2*x^-3//2*(b*x^2+c*x^4)^(1/2)+8//15*b^-1*c^5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-8//15*x*b^-3//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+4//15*x*b^-3//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-19//2*(b*x^2+c*x^4)^3//2, x) == :(-2//11*x^-17//2*(b*x^2+c*x^4)^3//2+-12//77*c*x^-9//2*(b*x^2+c*x^4)^(1/2)+-8//77*b^-1*c^2*x^-5//2*(b*x^2+c*x^4)^(1/2)+-4//77*x*b^-5//4*c^11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-21//2*(b*x^2+c*x^4)^3//2, x) == :(-2//13*x^-19//2*(b*x^2+c*x^4)^3//2+-4//39*c*x^-11//2*(b*x^2+c*x^4)^(1/2)+-8//195*b^-1*c^2*x^-7//2*(b*x^2+c*x^4)^(1/2)+8//65*b^-2*c^3*x^-3//2*(b*x^2+c*x^4)^(1/2)+-8//65*b^-2*c^7//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-4//65*x*b^-7//4*c^13//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+8//65*x*b^-7//4*c^13//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-23//2*(b*x^2+c*x^4)^3//2, x) == :(-2//15*x^-21//2*(b*x^2+c*x^4)^3//2+-4//55*c*x^-13//2*(b*x^2+c*x^4)^(1/2)+-8//385*b^-1*c^2*x^-9//2*(b*x^2+c*x^4)^(1/2)+8//231*b^-2*c^3*x^-5//2*(b*x^2+c*x^4)^(1/2)+4//231*x*b^-9//4*c^15//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^13//2*(b*x^2+c*x^4)^-1//2, x) == :(2//11*c^-1*x^7//2*(b*x^2+c*x^4)^(1/2)+-18//77*b*c^-2*x^3//2*(b*x^2+c*x^4)^(1/2)+30//77*b^2*c^-3*x^-1//2*(b*x^2+c*x^4)^(1/2)+-15//77*x*b^11//4*c^-13//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^11//2*(b*x^2+c*x^4)^-1//2, x) == :(2//9*c^-1*x^5//2*(b*x^2+c*x^4)^(1/2)+-14//45*b*c^-2*x^(1/2)*(b*x^2+c*x^4)^(1/2)+14//15*b^2*c^-5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-14//15*x*b^9//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+7//15*x*b^9//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^9//2*(b*x^2+c*x^4)^-1//2, x) == :(2//7*c^-1*x^3//2*(b*x^2+c*x^4)^(1/2)+-10//21*b*c^-2*x^-1//2*(b*x^2+c*x^4)^(1/2)+5//21*x*b^7//4*c^-9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^7//2*(b*x^2+c*x^4)^-1//2, x) == :(2//5*c^-1*x^(1/2)*(b*x^2+c*x^4)^(1/2)+-6//5*b*c^-3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-3//5*x*b^5//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+6//5*x*b^5//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^5//2*(b*x^2+c*x^4)^-1//2, x) == :(2//3*c^-1*x^-1//2*(b*x^2+c*x^4)^(1/2)+-1//3*x*b^3//4*c^-5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^3//2*(b*x^2+c*x^4)^-1//2, x) == :(2*c^-1//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+x*b^1//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+-2*x*b^1//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^-1//2, x) == :(x*b^-1//4*c^-1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-1//2*(b*x^2+c*x^4)^-1//2, x) == :(-2*b^-1*x^-3//2*(b*x^2+c*x^4)^(1/2)+2*b^-1*c^(1/2)*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+x*b^-3//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+-2*x*b^-3//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-3//2*(b*x^2+c*x^4)^-1//2, x) == :(-2//3*b^-1*x^-5//2*(b*x^2+c*x^4)^(1/2)+-1//3*x*b^-5//4*c^3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-5//2*(b*x^2+c*x^4)^-1//2, x) == :(-2//5*b^-1*x^-7//2*(b*x^2+c*x^4)^(1/2)+6//5*c*b^-2*x^-3//2*(b*x^2+c*x^4)^(1/2)+-6//5*b^-2*c^3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-3//5*x*b^-7//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+6//5*x*b^-7//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-7//2*(b*x^2+c*x^4)^-1//2, x) == :(-2//7*b^-1*x^-9//2*(b*x^2+c*x^4)^(1/2)+10//21*c*b^-2*x^-5//2*(b*x^2+c*x^4)^(1/2)+5//21*x*b^-9//4*c^7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-9//2*(b*x^2+c*x^4)^-1//2, x) == :(-2//9*b^-1*x^-11//2*(b*x^2+c*x^4)^(1/2)+-14//15*b^-3*c^2*x^-3//2*(b*x^2+c*x^4)^(1/2)+14//45*c*b^-2*x^-7//2*(b*x^2+c*x^4)^(1/2)+14//15*b^-3*c^5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-14//15*x*b^-11//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+7//15*x*b^-11//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-11//2*(b*x^2+c*x^4)^-1//2, x) == :(-2//11*b^-1*x^-13//2*(b*x^2+c*x^4)^(1/2)+-30//77*b^-3*c^2*x^-5//2*(b*x^2+c*x^4)^(1/2)+18//77*c*b^-2*x^-9//2*(b*x^2+c*x^4)^(1/2)+-15//77*x*b^-13//4*c^11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^17//2*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^11//2*(b*x^2+c*x^4)^-1//2+9//7*c^-2*x^3//2*(b*x^2+c*x^4)^(1/2)+-15//7*b*c^-3*x^-1//2*(b*x^2+c*x^4)^(1/2)+15//14*x*b^7//4*c^-13//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^15//2*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^9//2*(b*x^2+c*x^4)^-1//2+7//5*c^-2*x^(1/2)*(b*x^2+c*x^4)^(1/2)+-21//5*b*c^-5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-21//10*x*b^5//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+21//5*x*b^5//4*c^-11//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^13//2*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^7//2*(b*x^2+c*x^4)^-1//2+5//3*c^-2*x^-1//2*(b*x^2+c*x^4)^(1/2)+-5//6*x*b^3//4*c^-9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^11//2*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^5//2*(b*x^2+c*x^4)^-1//2+3*c^-3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-3*x*b^1//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+3//2*x*b^1//4*c^-7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^9//2*(b*x^2+c*x^4)^-3//2, x) == :(-1*c^-1*x^3//2*(b*x^2+c*x^4)^-1//2+(1/2)*x*b^-1//4*c^-5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^7//2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^5//2*(b*x^2+c*x^4)^-1//2+-1*b^-1*c^-1//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+x*b^-3//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+-1//2*x*b^-3//4*c^-3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^5//2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^3//2*(b*x^2+c*x^4)^-1//2+(1/2)*x*b^-5//4*c^-1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^3//2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^(1/2)*(b*x^2+c*x^4)^-1//2+-3*b^-2*x^-3//2*(b*x^2+c*x^4)^(1/2)+3*b^-2*c^(1/2)*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-3*x*b^-7//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+3//2*x*b^-7//4*c^1//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^(1/2)*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-1//2*(b*x^2+c*x^4)^-1//2+-5//3*b^-2*x^-5//2*(b*x^2+c*x^4)^(1/2)+-5//6*x*b^-9//4*c^3//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-1//2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-3//2*(b*x^2+c*x^4)^-1//2+-7//5*b^-2*x^-7//2*(b*x^2+c*x^4)^(1/2)+21//5*c*b^-3*x^-3//2*(b*x^2+c*x^4)^(1/2)+-21//5*b^-3*c^3//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-21//10*x*b^-11//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+21//5*x*b^-11//4*c^5//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-3//2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-5//2*(b*x^2+c*x^4)^-1//2+-9//7*b^-2*x^-9//2*(b*x^2+c*x^4)^(1/2)+15//7*c*b^-3*x^-5//2*(b*x^2+c*x^4)^(1/2)+15//14*x*b^-13//4*c^7//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate(x^-5//2*(b*x^2+c*x^4)^-3//2, x) == :(b^-1*x^-7//2*(b*x^2+c*x^4)^-1//2+-11//9*b^-2*x^-11//2*(b*x^2+c*x^4)^(1/2)+-77//15*b^-4*c^2*x^-3//2*(b*x^2+c*x^4)^(1/2)+77//45*c*b^-3*x^-7//2*(b*x^2+c*x^4)^(1/2)+77//15*b^-4*c^5//2*x^3//2*(b^(1/2)+x*c^(1/2))^-1*(b*x^2+c*x^4)^-1//2*(b+c*x^2)+-77//15*x*b^-15//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.E(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2)+77//30*x*b^-15//4*c^9//4*((b^(1/2)+x*c^(1/2))^-2*(b+c*x^2))^(1/2)*(b*x^2+c*x^4)^-1//2*(b^(1/2)+x*c^(1/2))*Elliptic.F(2*arctan(b^-1//4*c^1//4*x^(1/2)),1/2))
@test integrate((c*x)^m*(b*x^2+c*x^4)^3, x) == :(b^3*x^7*(c*x)^m*(7+m)^-1+c^3*x^13*(c*x)^m*(13+m)^-1+3*b*c^2*x^11*(c*x)^m*(11+m)^-1+3*c*b^2*x^9*(c*x)^m*(9+m)^-1)
@test integrate((c*x)^m*(b*x^2+c*x^4)^2, x) == :(b^2*x^5*(c*x)^m*(5+m)^-1+c^2*x^9*(c*x)^m*(9+m)^-1+2*b*c*x^7*(c*x)^m*(7+m)^-1)
@test integrate((c*x)^m*(b*x^2+c*x^4), x) == :(c^-4*(c*x)^(5+m)*(5+m)^-1+b*c^-3*(c*x)^(3+m)*(3+m)^-1)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2), x) == :(1//4*a^2*x^4+1//8*b^2*x^8+1//3*a*b*x^6)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(1//3*a^2*x^3+1//7*b^2*x^7+2//5*a*b*x^5)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2), x) == :((1/2)*a^2*x^2+1//6*b^2*x^6+(1/2)*a*b*x^4)
@test integrate(a^2+b^2*x^4+2*a*b*x^2, x) == :(x*a^2+1//5*b^2*x^5+2//3*a*b*x^3)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2), x) == :(a^2*log(x)+1//4*b^2*x^4+a*b*x^2)
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-1*a^2*x^-1+1//3*b^2*x^3+2*a*b*x)
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2), x) == :((1/2)*b^2*x^2+-1//2*a^2*x^-2+2*a*b*log(x))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2), x) == :(x*b^2+-1//3*a^2*x^-3+-2*a*b*x^-1)
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2), x) == :(b^2*log(x)+-1//4*a^2*x^-4+-1*a*b*x^-2)
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-1*b^2*x^-1+-1//5*a^2*x^-5+-2//3*a*b*x^-3)
@test integrate(x^-7*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-1//2*b^2*x^-2+-1//6*a^2*x^-6+-1//2*a*b*x^-4)
@test integrate(x^-8*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-1//3*b^2*x^-3+-1//7*a^2*x^-7+-2//5*a*b*x^-5)
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(1//7*a^4*x^7+1//15*b^4*x^15+4//9*b*a^3*x^9+4//13*a*b^3*x^13+6//11*a^2*b^2*x^11)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(1//14*b^-3*(a+b*x^2)^7+-1//6*a*b^-3*(a+b*x^2)^6+1//10*a^2*b^-3*(a+b*x^2)^5)
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(1//5*a^4*x^5+1//13*b^4*x^13+2//3*a^2*b^2*x^9+4//7*b*a^3*x^7+4//11*a*b^3*x^11)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(1//12*b^-2*(a+b*x^2)^6+-1//10*a*b^-2*(a+b*x^2)^5)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(1//3*a^4*x^3+1//11*b^4*x^11+4//5*b*a^3*x^5+4//9*a*b^3*x^9+6//7*a^2*b^2*x^7)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(1//10*b^-1*(a+b*x^2)^5)
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(x*a^4+1//9*b^4*x^9+4//3*b*a^3*x^3+4//7*a*b^3*x^7+6//5*a^2*b^2*x^5)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(a^4*log(x)+1//8*b^4*x^8+2*b*a^3*x^2+2//3*a*b^3*x^6+3//2*a^2*b^2*x^4)
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1*a^4*x^-1+1//7*b^4*x^7+2*a^2*b^2*x^3+4*b*x*a^3+4//5*a*b^3*x^5)
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//2*a^4*x^-2+1//6*b^4*x^6+a*b^3*x^4+3*a^2*b^2*x^2+4*b*a^3*log(x))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//3*a^4*x^-3+1//5*b^4*x^5+-4*b*a^3*x^-1+6*x*a^2*b^2+4//3*a*b^3*x^3)
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//4*a^4*x^-4+1//4*b^4*x^4+-2*b*a^3*x^-2+2*a*b^3*x^2+6*a^2*b^2*log(x))
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//5*a^4*x^-5+1//3*b^4*x^3+-6*a^2*b^2*x^-1+4*a*x*b^3+-4//3*b*a^3*x^-3)
@test integrate(x^-7*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :((1/2)*b^4*x^2+-1//6*a^4*x^-6+-1*b*a^3*x^-4+-3*a^2*b^2*x^-2+4*a*b^3*log(x))
@test integrate(x^-8*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(x*b^4+-1//7*a^4*x^-7+-4*a*b^3*x^-1+-2*a^2*b^2*x^-3+-4//5*b*a^3*x^-5)
@test integrate(x^-9*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(b^4*log(x)+-1//8*a^4*x^-8+-2*a*b^3*x^-2+-3//2*a^2*b^2*x^-4+-2//3*b*a^3*x^-6)
@test integrate(x^-10*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1*b^4*x^-1+-1//9*a^4*x^-9+-6//5*a^2*b^2*x^-5+-4//3*a*b^3*x^-3+-4//7*b*a^3*x^-7)
@test integrate(x^-11*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//10*a^-1*x^-10*(a+b*x^2)^5)
@test integrate(x^-12*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//3*b^4*x^-3+-1//11*a^4*x^-11+-6//7*a^2*b^2*x^-7+-4//5*a*b^3*x^-5+-4//9*b*a^3*x^-9)
@test integrate(x^-13*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//12*a^-1*x^-12*(a+b*x^2)^5+1//60*b*a^-2*x^-10*(a+b*x^2)^5)
@test integrate(x^-14*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//5*b^4*x^-5+-1//13*a^4*x^-13+-4//7*a*b^3*x^-7+-4//11*b*a^3*x^-11+-2//3*a^2*b^2*x^-9)
@test integrate(x^-15*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//6*b^4*x^-6+-1//14*a^4*x^-14+-3//5*a^2*b^2*x^-10+-1//2*a*b^3*x^-8+-1//3*b*a^3*x^-12)
@test integrate(x^-16*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-1//7*b^4*x^-7+-1//15*a^4*x^-15+-6//11*a^2*b^2*x^-11+-4//9*a*b^3*x^-9+-4//13*b*a^3*x^-13)
@test integrate(x^8*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//9*a^6*x^9+1//21*b^6*x^21+4//3*a^3*b^3*x^15+6//11*b*a^5*x^11+6//19*a*b^5*x^19+15//13*a^4*b^2*x^13+15//17*a^2*b^4*x^17)
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//20*b^-4*(a+b*x^2)^10+-1//6*a*b^-4*(a+b*x^2)^9+-1//14*a^3*b^-4*(a+b*x^2)^7+3//16*a^2*b^-4*(a+b*x^2)^8)
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//7*a^6*x^7+1//19*b^6*x^19+a^2*b^4*x^15+2//3*b*a^5*x^9+6//17*a*b^5*x^17+15//11*a^4*b^2*x^11+20//13*a^3*b^3*x^13)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//18*b^-3*(a+b*x^2)^9+-1//8*a*b^-3*(a+b*x^2)^8+1//14*a^2*b^-3*(a+b*x^2)^7)
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//5*a^6*x^5+1//17*b^6*x^17+2//5*a*b^5*x^15+5//3*a^4*b^2*x^9+6//7*b*a^5*x^7+15//13*a^2*b^4*x^13+20//11*a^3*b^3*x^11)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//16*b^-2*(a+b*x^2)^8+-1//14*a*b^-2*(a+b*x^2)^7)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//3*a^6*x^3+1//15*b^6*x^15+6//5*b*a^5*x^5+6//13*a*b^5*x^13+15//7*a^4*b^2*x^7+15//11*a^2*b^4*x^11+20//9*a^3*b^3*x^9)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(1//14*b^-1*(a+b*x^2)^7)
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(x*a^6+1//13*b^6*x^13+2*b*a^5*x^3+3*a^4*b^2*x^5+5//3*a^2*b^4*x^9+6//11*a*b^5*x^11+20//7*a^3*b^3*x^7)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(a^6*log(x)+1//12*b^6*x^12+3*b*a^5*x^2+3//5*a*b^5*x^10+10//3*a^3*b^3*x^6+15//4*a^4*b^2*x^4+15//8*a^2*b^4*x^8)
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1*a^6*x^-1+1//11*b^6*x^11+4*a^3*b^3*x^5+5*a^4*b^2*x^3+6*b*x*a^5+2//3*a*b^5*x^9+15//7*a^2*b^4*x^7)
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//2*a^6*x^-2+1//10*b^6*x^10+5*a^3*b^3*x^4+6*b*a^5*log(x)+3//4*a*b^5*x^8+5//2*a^2*b^4*x^6+15//2*a^4*b^2*x^2)
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//3*a^6*x^-3+1//9*b^6*x^9+-6*b*a^5*x^-1+3*a^2*b^4*x^5+15*x*a^4*b^2+6//7*a*b^5*x^7+20//3*a^3*b^3*x^3)
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//4*a^6*x^-4+1//8*b^6*x^8+a*b^5*x^6+-3*b*a^5*x^-2+10*a^3*b^3*x^2+15*a^4*b^2*log(x)+15//4*a^2*b^4*x^4)
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//5*a^6*x^-5+1//7*b^6*x^7+-15*a^4*b^2*x^-1+-2*b*a^5*x^-3+5*a^2*b^4*x^3+20*x*a^3*b^3+6//5*a*b^5*x^5)
@test integrate(x^-7*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//6*a^6*x^-6+1//6*b^6*x^6+20*a^3*b^3*log(x)+-15//2*a^4*b^2*x^-2+-3//2*b*a^5*x^-4+3//2*a*b^5*x^4+15//2*a^2*b^4*x^2)
@test integrate(x^-8*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//7*a^6*x^-7+1//5*b^6*x^5+-20*a^3*b^3*x^-1+-5*a^4*b^2*x^-3+2*a*b^5*x^3+15*x*a^2*b^4+-6//5*b*a^5*x^-5)
@test integrate(x^-9*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//8*a^6*x^-8+1//4*b^6*x^4+-1*b*a^5*x^-6+-10*a^3*b^3*x^-2+3*a*b^5*x^2+15*a^2*b^4*log(x)+-15//4*a^4*b^2*x^-4)
@test integrate(x^-10*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//9*a^6*x^-9+1//3*b^6*x^3+-15*a^2*b^4*x^-1+-3*a^4*b^2*x^-5+6*a*x*b^5+-20//3*a^3*b^3*x^-3+-6//7*b*a^5*x^-7)
@test integrate(x^-11*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :((1/2)*b^6*x^2+-1//10*a^6*x^-10+-5*a^3*b^3*x^-4+6*a*b^5*log(x)+-15//2*a^2*b^4*x^-2+-5//2*a^4*b^2*x^-6+-3//4*b*a^5*x^-8)
@test integrate(x^-12*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(x*b^6+-1//11*a^6*x^-11+-6*a*b^5*x^-1+-5*a^2*b^4*x^-3+-4*a^3*b^3*x^-5+-15//7*a^4*b^2*x^-7+-2//3*b*a^5*x^-9)
@test integrate(x^-13*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(b^6*log(x)+-1//12*a^6*x^-12+-3*a*b^5*x^-2+-15//4*a^2*b^4*x^-4+-15//8*a^4*b^2*x^-8+-10//3*a^3*b^3*x^-6+-3//5*b*a^5*x^-10)
@test integrate(x^-14*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1*b^6*x^-1+-1//13*a^6*x^-13+-3*a^2*b^4*x^-5+-2*a*b^5*x^-3+-20//7*a^3*b^3*x^-7+-6//11*b*a^5*x^-11+-5//3*a^4*b^2*x^-9)
@test integrate(x^-15*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//14*a^-1*x^-14*(a+b*x^2)^7)
@test integrate(x^-16*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//3*b^6*x^-3+-1//15*a^6*x^-15+-20//9*a^3*b^3*x^-9+-15//7*a^2*b^4*x^-7+-15//11*a^4*b^2*x^-11+-6//5*a*b^5*x^-5+-6//13*b*a^5*x^-13)
@test integrate(x^-17*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//16*a^-1*x^-16*(a+b*x^2)^7+1//112*b*a^-2*x^-14*(a+b*x^2)^7)
@test integrate(x^-18*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//5*b^6*x^-5+-1//17*a^6*x^-17+-20//11*a^3*b^3*x^-11+-15//13*a^4*b^2*x^-13+-6//7*a*b^5*x^-7+-5//3*a^2*b^4*x^-9+-2//5*b*a^5*x^-15)
@test integrate(x^-19*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//18*a^-1*x^-18*(a+b*x^2)^7+-1//504*a^-3*b^2*x^-14*(a+b*x^2)^7+1//72*b*a^-2*x^-16*(a+b*x^2)^7)
@test integrate(x^-20*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//7*b^6*x^-7+-1//19*a^6*x^-19+-1*a^4*b^2*x^-15+-20//13*a^3*b^3*x^-13+-15//11*a^2*b^4*x^-11+-6//17*b*a^5*x^-17+-2//3*a*b^5*x^-9)
@test integrate(x^-21*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//20*a^-1*x^-20*(a+b*x^2)^7+-1//240*a^-3*b^2*x^-16*(a+b*x^2)^7+1//60*b*a^-2*x^-18*(a+b*x^2)^7+1//1680*a^-4*b^3*x^-14*(a+b*x^2)^7)
@test integrate(x^-22*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-1//9*b^6*x^-9+-1//21*a^6*x^-21+-15//13*a^2*b^4*x^-13+-15//17*a^4*b^2*x^-17+-6//11*a*b^5*x^-11+-6//19*b*a^5*x^-19+-4//3*a^3*b^3*x^-15)
@test integrate(x^11*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(1//8*b^-2*x^8+(1/2)*a^5*b^-6*(a+b*x^2)^-1+-2*a^3*b^-5*x^2+-1//3*a*b^-3*x^6+3//4*a^2*b^-4*x^4+5//2*a^4*b^-6*log(a+b*x^2))
@test integrate(x^9*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(1//6*b^-2*x^6+-2*a^3*b^-5*log(a+b*x^2)+-1//2*a*b^-3*x^4+-1//2*a^4*b^-5*(a+b*x^2)^-1+3//2*a^2*b^-4*x^2)
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(1//4*b^-2*x^4+(1/2)*a^3*b^-4*(a+b*x^2)^-1+-1*a*b^-3*x^2+3//2*a^2*b^-4*log(a+b*x^2))
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :((1/2)*b^-2*x^2+-1*a*b^-3*log(a+b*x^2)+-1//2*a^2*b^-3*(a+b*x^2)^-1)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :((1/2)*b^-2*log(a+b*x^2)+(1/2)*a*b^-2*(a+b*x^2)^-1)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-1//2*b^-1*(a+b*x^2)^-1)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(a^-2*log(x)+(1/2)*a^-1*(a+b*x^2)^-1+-1//2*a^-2*log(a+b*x^2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-1//2*a^-2*x^-2+b*a^-3*log(a+b*x^2)+-2*b*a^-3*log(x)+-1//2*b*a^-2*(a+b*x^2)^-1)
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-1//4*a^-2*x^-4+b*a^-3*x^-2+(1/2)*a^-3*b^2*(a+b*x^2)^-1+3*a^-4*b^2*log(x)+-3//2*a^-4*b^2*log(a+b*x^2))
@test integrate(x^10*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(9//14*b^-2*x^7+-9//2*x*a^3*b^-5+-9//10*a*b^-3*x^5+-1//2*b^-1*x^9*(a+b*x^2)^-1+3//2*a^2*b^-4*x^3+9//2*a^7//2*b^-11//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^8*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(7//10*b^-2*x^5+-7//2*a^5//2*b^-9//2*arctan(x*a^-1//2*b^(1/2))+-7//6*a*b^-3*x^3+-1//2*b^-1*x^7*(a+b*x^2)^-1+7//2*x*a^2*b^-4)
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(5//6*b^-2*x^3+-5//2*a*x*b^-3+-1//2*b^-1*x^5*(a+b*x^2)^-1+5//2*a^3//2*b^-7//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(3//2*x*b^-2+-3//2*a^(1/2)*b^-5//2*arctan(x*a^-1//2*b^(1/2))+-1//2*b^-1*x^3*(a+b*x^2)^-1)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :((1/2)*a^-1//2*b^-3//2*arctan(x*a^-1//2*b^(1/2))+-1//2*x*b^-1*(a+b*x^2)^-1)
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :((1/2)*x*a^-1*(a+b*x^2)^-1+(1/2)*a^-3//2*b^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-3//2*a^-2*x^-1+(1/2)*a^-1*x^-1*(a+b*x^2)^-1+-3//2*a^-5//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-5//6*a^-2*x^-3+(1/2)*a^-1*x^-3*(a+b*x^2)^-1+5//2*b*a^-3*x^-1+5//2*a^-7//2*b^3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-7//10*a^-2*x^-5+(1/2)*a^-1*x^-5*(a+b*x^2)^-1+-7//2*a^-4*b^2*x^-1+-7//2*a^-9//2*b^5//2*arctan(x*a^-1//2*b^(1/2))+7//6*b*a^-3*x^-3)
@test integrate(x^11*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(1//4*b^-4*x^4+-2*a*b^-5*x^2+5*a^2*b^-6*log(a+b*x^2)+5*a^3*b^-6*(a+b*x^2)^-1+-5//4*a^4*b^-6*(a+b*x^2)^-2+1//6*a^5*b^-6*(a+b*x^2)^-3)
@test integrate(x^9*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :((1/2)*b^-4*x^2+a^3*b^-5*(a+b*x^2)^-2+-3*a^2*b^-5*(a+b*x^2)^-1+-2*a*b^-5*log(a+b*x^2)+-1//6*a^4*b^-5*(a+b*x^2)^-3)
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :((1/2)*b^-4*log(a+b*x^2)+-3//4*a^2*b^-4*(a+b*x^2)^-2+1//6*a^3*b^-4*(a+b*x^2)^-3+3//2*a*b^-4*(a+b*x^2)^-1)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(1//6*a^-1*x^6*(a+b*x^2)^-3)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//4*b^-2*(a+b*x^2)^-2+1//6*a*b^-2*(a+b*x^2)^-3)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//6*b^-1*(a+b*x^2)^-3)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(a^-4*log(x)+(1/2)*a^-3*(a+b*x^2)^-1+-1//2*a^-4*log(a+b*x^2)+1//4*a^-2*(a+b*x^2)^-2+1//6*a^-1*(a+b*x^2)^-3)
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//2*a^-4*x^-2+-4*b*a^-5*log(x)+2*b*a^-5*log(a+b*x^2)+-3//2*b*a^-4*(a+b*x^2)^-1+-1//2*b*a^-3*(a+b*x^2)^-2+-1//6*b*a^-2*(a+b*x^2)^-3)
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//4*a^-4*x^-4+-5*a^-6*b^2*log(a+b*x^2)+2*b*a^-5*x^-2+3*a^-5*b^2*(a+b*x^2)^-1+10*a^-6*b^2*log(x)+1//6*a^-3*b^2*(a+b*x^2)^-3+3//4*a^-4*b^2*(a+b*x^2)^-2)
@test integrate(x^12*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(231//80*b^-4*x^5+-231//16*a^5//2*b^-13//2*arctan(x*a^-1//2*b^(1/2))+-77//16*a*b^-5*x^3+-33//16*b^-3*x^7*(a+b*x^2)^-1+-11//24*b^-2*x^9*(a+b*x^2)^-2+-1//6*b^-1*x^11*(a+b*x^2)^-3+231//16*x*a^2*b^-6)
@test integrate(x^10*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(35//16*b^-4*x^3+-105//16*a*x*b^-5+-21//16*b^-3*x^5*(a+b*x^2)^-1+-3//8*b^-2*x^7*(a+b*x^2)^-2+-1//6*b^-1*x^9*(a+b*x^2)^-3+105//16*a^3//2*b^-11//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^8*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(35//16*x*b^-4+-35//16*a^(1/2)*b^-9//2*arctan(x*a^-1//2*b^(1/2))+-35//48*b^-3*x^3*(a+b*x^2)^-1+-7//24*b^-2*x^5*(a+b*x^2)^-2+-1//6*b^-1*x^7*(a+b*x^2)^-3)
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-5//16*x*b^-3*(a+b*x^2)^-1+-5//24*b^-2*x^3*(a+b*x^2)^-2+-1//6*b^-1*x^5*(a+b*x^2)^-3+5//16*a^-1//2*b^-7//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//6*b^-1*x^3*(a+b*x^2)^-3+-1//8*x*b^-2*(a+b*x^2)^-2+1//16*a^-3//2*b^-5//2*arctan(x*a^-1//2*b^(1/2))+1//16*x*a^-1*b^-2*(a+b*x^2)^-1)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//6*x*b^-1*(a+b*x^2)^-3+1//16*a^-5//2*b^-3//2*arctan(x*a^-1//2*b^(1/2))+1//16*x*a^-2*b^-1*(a+b*x^2)^-1+1//24*x*a^-1*b^-1*(a+b*x^2)^-2)
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(1//6*x*a^-1*(a+b*x^2)^-3+5//16*x*a^-3*(a+b*x^2)^-1+5//16*a^-7//2*b^-1//2*arctan(x*a^-1//2*b^(1/2))+5//24*x*a^-2*(a+b*x^2)^-2)
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-35//16*a^-4*x^-1+-35//16*a^-9//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2))+1//6*a^-1*x^-1*(a+b*x^2)^-3+7//24*a^-2*x^-1*(a+b*x^2)^-2+35//48*a^-3*x^-1*(a+b*x^2)^-1)
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-35//16*a^-4*x^-3+1//6*a^-1*x^-3*(a+b*x^2)^-3+3//8*a^-2*x^-3*(a+b*x^2)^-2+21//16*a^-3*x^-3*(a+b*x^2)^-1+105//16*b*a^-5*x^-1+105//16*a^-11//2*b^3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-231//80*a^-4*x^-5+-231//16*a^-6*b^2*x^-1+-231//16*a^-13//2*b^5//2*arctan(x*a^-1//2*b^(1/2))+1//6*a^-1*x^-5*(a+b*x^2)^-3+11//24*a^-2*x^-5*(a+b*x^2)^-2+33//16*a^-3*x^-5*(a+b*x^2)^-1+77//16*b*a^-5*x^-3)
@test integrate(x^15*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1//4*b^-6*x^4+-3*a*b^-7*x^2+-35//4*a^4*b^-8*(a+b*x^2)^-2+-7//8*a^6*b^-8*(a+b*x^2)^-4+1//10*a^7*b^-8*(a+b*x^2)^-5+7//2*a^5*b^-8*(a+b*x^2)^-3+21//2*a^2*b^-8*log(a+b*x^2)+35//2*a^3*b^-8*(a+b*x^2)^-1)
@test integrate(x^13*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :((1/2)*b^-6*x^2+-3*a*b^-7*log(a+b*x^2)+5*a^3*b^-7*(a+b*x^2)^-2+-15//2*a^2*b^-7*(a+b*x^2)^-1+-5//2*a^4*b^-7*(a+b*x^2)^-3+-1//10*a^6*b^-7*(a+b*x^2)^-5+3//4*a^5*b^-7*(a+b*x^2)^-4)
@test integrate(x^11*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :((1/2)*b^-6*log(a+b*x^2)+-5//2*a^2*b^-6*(a+b*x^2)^-2+-5//8*a^4*b^-6*(a+b*x^2)^-4+1//10*a^5*b^-6*(a+b*x^2)^-5+5//2*a*b^-6*(a+b*x^2)^-1+5//3*a^3*b^-6*(a+b*x^2)^-3)
@test integrate(x^9*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1//10*a^-1*x^10*(a+b*x^2)^-5)
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1//10*a^-1*x^8*(a+b*x^2)^-5+1//40*a^-2*x^8*(a+b*x^2)^-4)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//6*b^-3*(a+b*x^2)^-3+-1//10*a^2*b^-3*(a+b*x^2)^-5+1//4*a*b^-3*(a+b*x^2)^-4)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//8*b^-2*(a+b*x^2)^-4+1//10*a*b^-2*(a+b*x^2)^-5)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//10*b^-1*(a+b*x^2)^-5)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(a^-6*log(x)+(1/2)*a^-5*(a+b*x^2)^-1+-1//2*a^-6*log(a+b*x^2)+1//4*a^-4*(a+b*x^2)^-2+1//6*a^-3*(a+b*x^2)^-3+1//8*a^-2*(a+b*x^2)^-4+1//10*a^-1*(a+b*x^2)^-5)
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//2*a^-6*x^-2+-1*b*a^-5*(a+b*x^2)^-2+-6*b*a^-7*log(x)+3*b*a^-7*log(a+b*x^2)+-5//2*b*a^-6*(a+b*x^2)^-1+-1//2*b*a^-4*(a+b*x^2)^-3+-1//4*b*a^-3*(a+b*x^2)^-4+-1//10*b*a^-2*(a+b*x^2)^-5)
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//4*a^-6*x^-4+a^-5*b^2*(a+b*x^2)^-3+3*b*a^-7*x^-2+21*a^-8*b^2*log(x)+-21//2*a^-8*b^2*log(a+b*x^2)+1//10*a^-3*b^2*(a+b*x^2)^-5+3//8*a^-4*b^2*(a+b*x^2)^-4+5//2*a^-6*b^2*(a+b*x^2)^-2+15//2*a^-7*b^2*(a+b*x^2)^-1)
@test integrate(x^16*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(9009//1280*b^-6*x^5+-9009//256*a^5//2*b^-17//2*arctan(x*a^-1//2*b^(1/2))+-3003//256*a*b^-7*x^3+-1287//256*b^-5*x^7*(a+b*x^2)^-1+-143//128*b^-4*x^9*(a+b*x^2)^-2+-13//32*b^-3*x^11*(a+b*x^2)^-3+-3//16*b^-2*x^13*(a+b*x^2)^-4+-1//10*b^-1*x^15*(a+b*x^2)^-5+9009//256*x*a^2*b^-8)
@test integrate(x^14*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1001//256*b^-6*x^3+-3003//256*a*x*b^-7+-3003//1280*b^-5*x^5*(a+b*x^2)^-1+-429//640*b^-4*x^7*(a+b*x^2)^-2+-143//480*b^-3*x^9*(a+b*x^2)^-3+-13//80*b^-2*x^11*(a+b*x^2)^-4+-1//10*b^-1*x^13*(a+b*x^2)^-5+3003//256*a^3//2*b^-15//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^12*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(693//256*x*b^-6+-693//256*a^(1/2)*b^-13//2*arctan(x*a^-1//2*b^(1/2))+-231//256*b^-5*x^3*(a+b*x^2)^-1+-231//640*b^-4*x^5*(a+b*x^2)^-2+-33//160*b^-3*x^7*(a+b*x^2)^-3+-11//80*b^-2*x^9*(a+b*x^2)^-4+-1//10*b^-1*x^11*(a+b*x^2)^-5)
@test integrate(x^10*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-63//256*x*b^-5*(a+b*x^2)^-1+-21//128*b^-4*x^3*(a+b*x^2)^-2+-21//160*b^-3*x^5*(a+b*x^2)^-3+-9//80*b^-2*x^7*(a+b*x^2)^-4+-1//10*b^-1*x^9*(a+b*x^2)^-5+63//256*a^-1//2*b^-11//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^8*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-7//80*b^-2*x^5*(a+b*x^2)^-4+-7//96*b^-3*x^3*(a+b*x^2)^-3+-7//128*x*b^-4*(a+b*x^2)^-2+-1//10*b^-1*x^7*(a+b*x^2)^-5+7//256*a^-3//2*b^-9//2*arctan(x*a^-1//2*b^(1/2))+7//256*x*a^-1*b^-4*(a+b*x^2)^-1)
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//10*b^-1*x^5*(a+b*x^2)^-5+-1//16*b^-2*x^3*(a+b*x^2)^-4+-1//32*x*b^-3*(a+b*x^2)^-3+3//256*a^-5//2*b^-7//2*arctan(x*a^-1//2*b^(1/2))+1//128*x*a^-1*b^-3*(a+b*x^2)^-2+3//256*x*a^-2*b^-3*(a+b*x^2)^-1)
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-3//80*x*b^-2*(a+b*x^2)^-4+-1//10*b^-1*x^3*(a+b*x^2)^-5+3//256*a^-7//2*b^-5//2*arctan(x*a^-1//2*b^(1/2))+1//128*x*a^-2*b^-2*(a+b*x^2)^-2+1//160*x*a^-1*b^-2*(a+b*x^2)^-3+3//256*x*a^-3*b^-2*(a+b*x^2)^-1)
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//10*x*b^-1*(a+b*x^2)^-5+7//256*a^-9//2*b^-3//2*arctan(x*a^-1//2*b^(1/2))+1//80*x*a^-1*b^-1*(a+b*x^2)^-4+7//256*x*a^-4*b^-1*(a+b*x^2)^-1+7//384*x*a^-3*b^-1*(a+b*x^2)^-2+7//480*x*a^-2*b^-1*(a+b*x^2)^-3)
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1//10*x*a^-1*(a+b*x^2)^-5+9//80*x*a^-2*(a+b*x^2)^-4+21//128*x*a^-4*(a+b*x^2)^-2+21//160*x*a^-3*(a+b*x^2)^-3+63//256*x*a^-5*(a+b*x^2)^-1+63//256*a^-11//2*b^-1//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-693//256*a^-6*x^-1+-693//256*a^-13//2*b^(1/2)*arctan(x*a^-1//2*b^(1/2))+1//10*a^-1*x^-1*(a+b*x^2)^-5+11//80*a^-2*x^-1*(a+b*x^2)^-4+33//160*a^-3*x^-1*(a+b*x^2)^-3+231//256*a^-5*x^-1*(a+b*x^2)^-1+231//640*a^-4*x^-1*(a+b*x^2)^-2)
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1001//256*a^-6*x^-3+1//10*a^-1*x^-3*(a+b*x^2)^-5+13//80*a^-2*x^-3*(a+b*x^2)^-4+143//480*a^-3*x^-3*(a+b*x^2)^-3+429//640*a^-4*x^-3*(a+b*x^2)^-2+3003//256*b*a^-7*x^-1+3003//256*a^-15//2*b^3//2*arctan(x*a^-1//2*b^(1/2))+3003//1280*a^-5*x^-3*(a+b*x^2)^-1)
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-9009//1280*a^-6*x^-5+-9009//256*a^-8*b^2*x^-1+-9009//256*a^-17//2*b^5//2*arctan(x*a^-1//2*b^(1/2))+1//10*a^-1*x^-5*(a+b*x^2)^-5+3//16*a^-2*x^-5*(a+b*x^2)^-4+13//32*a^-3*x^-5*(a+b*x^2)^-3+143//128*a^-4*x^-5*(a+b*x^2)^-2+1287//256*a^-5*x^-5*(a+b*x^2)^-1+3003//256*b*a^-7*x^-3)
@test integrate((1+x^4+2*x^2)^-1, x) == :((1/2)*arctan(x)+x*(2+2*x^2)^-1)
@test integrate(x*(1+x^4+2*x^2)^-1, x) == :(-1*(2+2*x^2)^-1)
@test integrate(x^2*(1+x^4+2*x^2)^-1, x) == :((1/2)*arctan(x)+-1*x*(2+2*x^2)^-1)
@test integrate(x^3*(1+x^4+2*x^2)^-1, x) == :((2+2*x^2)^-1+(1/2)*log(1+x^2))
@test integrate(x*(81+x^4+-18*x^2)^-1, x) == :((18+-2*x^2)^-1)
@test integrate(x^3*(16+x^4+-8*x^2)^-1, x) == :((1/2)*log(4+-1*x^2)+2*(4+-1*x^2)^-1)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*x^6*(6a+6*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*x^8*(8a+8*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(1//6*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^3//2+-1//4*a*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a+b*x^2))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(1//4*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a+b*x^2))
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+b*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(b*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-1//2*a*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//4*a^-1*x^-4*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a+b*x^2))
@test integrate(x^-7*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(1//12*a^-2*x^-6*(a^2+b^2*x^4+2*a*b*x^2)^3//2+-1//4*a^-1*x^-6*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*(a+b*x^2))
@test integrate(x^-9*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//6*b*x^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//8*a*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-11*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//8*b*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//10*a*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*x*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(b*x*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*a*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1*b*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*a*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//3*b*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//5*a*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-8*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//5*b*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//7*a*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-10*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-1//7*b*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//9*a*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^9*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*x^10*(10a+10*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*x^16*(16a+16*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*a^2*x^12*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*x^14*(14a+14*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*x^8*(8a+8*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*x^14*(14a+14*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a*b^2*x^12*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*x^10*(10a+10*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(1//10*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^5//2+-1//8*a*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^3//2*(a+b*x^2))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(1//8*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^3//2*(a+b*x^2))
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+b^3*x^6*(6a+6*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*x^4*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(b^3*x^4*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//2*a^3*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x))
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(b^3*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//4*a^3*x^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-3//2*b*a^2*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-7*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(b^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-1//6*a^3*x^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//2*a*b^2*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//4*b*a^2*x^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-9*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//8*a^-1*x^-8*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-11*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(1//40*a^-2*x^-10*(a^2+b^2*x^4+2*a*b*x^2)^5//2+-1//8*a^-1*x^-10*(a^2+b^2*x^4+2*a*b*x^2)^3//2*(a+b*x^2))
@test integrate(x^-13*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//6*b^3*x^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//12*a^3*x^-12*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//8*a*b^2*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//10*b*a^2*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-15*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//8*b^3*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//14*a^3*x^-14*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//10*a*b^2*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//4*b*a^2*x^-12*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-17*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//10*b^3*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//16*a^3*x^-16*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//14*b*a^2*x^-14*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//4*a*b^2*x^-12*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^8*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*x^15*(15a+15*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*a^2*x^9*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a*b^2*x^9*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(x*a^3*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^3//2+1//7*b^3*x^7*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^3//2+b*a^2*x^3*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^3//2+3//5*a*b^2*x^5*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^3//2)
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(b^3*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*a^3*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a*b^2*x^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*x*a^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(b^3*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*a^3*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3*b*a^2*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*x*b^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(x*b^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//5*a^3*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*b*a^2*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3*a*b^2*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-8*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1*b^3*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//7*a^3*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*a*b^2*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//5*b*a^2*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-10*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//3*b^3*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//9*a^3*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//5*a*b^2*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//7*b*a^2*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-12*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//5*b^3*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//11*a^3*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//7*a*b^2*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*b*a^2*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-14*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//7*b^3*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//13*a^3*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//11*b*a^2*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*a*b^2*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-16*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-1//9*b^3*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//15*a^3*x^-15*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//11*a*b^2*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//13*b*a^2*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^13*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^14*(14a+14*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^24*(24a+24*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a^2*b^3*x^20*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^22*(22a+22*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^16*(16a+16*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^3*b^2*x^18*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^11*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^12*(12a+12*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^22*(22a+22*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a*b^4*x^20*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^14*(14a+14*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^2*b^3*x^18*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^3*b^2*x^16*(8a+8*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^9*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(1//20*b^-5*(a+b*x^2)^9*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2//7*a^3*b^-5*(a+b*x^2)^6*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2//9*a*b^-5*(a+b*x^2)^8*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+1//12*a^4*b^-5*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3//8*a^2*b^-5*(a+b*x^2)^7*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(1//18*b^-4*(a+b*x^2)^8*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-3//16*a*b^-4*(a+b*x^2)^7*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//12*a^3*b^-4*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3//14*a^2*b^-4*(a+b*x^2)^6*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(1//16*b^-3*(a+b*x^2)^7*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//7*a*b^-3*(a+b*x^2)^6*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+1//12*a^2*b^-3*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(1//14*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^7//2+-1//12*a*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^5//2*(a+b*x^2))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(1//12*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^5//2*(a+b*x^2))
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+b^5*x^10*(10a+10*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^8*(8a+8*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^2*b^3*x^6*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^3*b^2*x^4*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^8*(8a+8*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//2*a^5*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^6*(6a+6*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+5*a^2*b^3*x^4*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^3*b^2*x^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^6*(6a+6*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//4*a^5*x^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^4*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a^2*b^3*x^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-5//2*b*a^4*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-7*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^4*(4a+4*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//6*a^5*x^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5*a^3*b^2*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-5//4*b*a^4*x^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-9*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^2*(2a+2*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//8*a^5*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5*a^2*b^3*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-5//2*a^3*b^2*x^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//6*b*a^4*x^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-11*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)*log(x)+-1//10*a^5*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//2*a*b^4*x^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//2*a^2*b^3*x^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//3*a^3*b^2*x^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//8*b*a^4*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-13*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//12*a^-1*x^-12*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-15*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(1//84*a^-2*x^-14*(a^2+b^2*x^4+2*a*b*x^2)^7//2+-1//12*a^-1*x^-14*(a^2+b^2*x^4+2*a*b*x^2)^5//2*(a+b*x^2))
@test integrate(x^-17*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//16*a^-1*x^-16*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//336*a^-3*b^2*x^-12*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+1//56*b*a^-2*x^-14*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-19*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//8*b^5*x^-8*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//18*a^5*x^-18*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//6*a^2*b^3*x^-12*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//7*a^3*b^2*x^-14*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//16*b*a^4*x^-16*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//2*a*b^4*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-21*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//10*b^5*x^-10*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//20*a^5*x^-20*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//7*a^2*b^3*x^-14*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//8*a^3*b^2*x^-16*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//12*a*b^4*x^-12*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//18*b*a^4*x^-18*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-23*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//12*b^5*x^-12*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//22*a^5*x^-22*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//8*a^2*b^3*x^-16*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//9*a^3*b^2*x^-18*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//14*a*b^4*x^-14*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//4*b*a^4*x^-20*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-25*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//14*b^5*x^-14*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//24*a^5*x^-24*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//9*a^2*b^3*x^-18*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//16*a*b^4*x^-16*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//22*b*a^4*x^-22*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//2*a^3*b^2*x^-20*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^12*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^23*(23a+23*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*a^4*x^15*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^21*(21a+21*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*x^19*(19a+19*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*x^17*(17a+17*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^10*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^21*(21a+21*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2*a^3*b^2*x^15*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^19*(19a+19*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*x^17*(17a+17*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^8*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^19*(19a+19*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2*a^2*b^3*x^15*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^17*(17a+17*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^17*(17a+17*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a*b^4*x^15*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^15*(15a+15*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*x^13*(13a+13*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*a^4*x^5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^11*(11a+11*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(x*a^5*(a+b*x^2)^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2+1//11*b^5*x^11*(a+b*x^2)^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2+2*a^3*b^2*x^5*(a+b*x^2)^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2+5//3*b*a^4*x^3*(a+b*x^2)^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2+5//9*a*b^4*x^9*(a+b*x^2)^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2+10//7*a^2*b^3*x^7*(a+b*x^2)^-5*(a^2+b^2*x^4+2*a*b*x^2)^5//2)
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^9*(9a+9*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*a^5*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2*a^2*b^3*x^5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*x*a^4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^7*(7a+7*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*a^5*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+a*b^4*x^5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5*b*a^4*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*x*a^3*b^2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-6*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^5*(5a+5*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//5*a^5*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10*a^3*b^2*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*x*a^2*b^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//3*b*a^4*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-8*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(b^5*x^3*(3a+3*b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//7*a^5*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*b*a^4*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10*a^2*b^3*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*x*b^4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//3*a^3*b^2*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-10*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(x*b^5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//9*a^5*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5*a*b^4*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2*a^3*b^2*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//3*a^2*b^3*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//7*b*a^4*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-12*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1*b^5*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//11*a^5*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2*a^2*b^3*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//7*a^3*b^2*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//3*a*b^4*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//9*b*a^4*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-14*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//3*b^5*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//13*a^5*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1*a*b^4*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//7*a^2*b^3*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//9*a^3*b^2*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//11*b*a^4*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-16*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//5*b^5*x^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//15*a^5*x^-15*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//9*a^2*b^3*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//11*a^3*b^2*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//7*a*b^4*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//13*b*a^4*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-18*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//7*b^5*x^-7*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//17*a^5*x^-17*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//11*a^2*b^3*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//13*a^3*b^2*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//9*a*b^4*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*b*a^4*x^-15*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-20*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//9*b^5*x^-9*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//19*a^5*x^-19*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//13*a^2*b^3*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//11*a*b^4*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//17*b*a^4*x^-17*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2//3*a^3*b^2*x^-15*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-22*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//11*b^5*x^-11*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//21*a^5*x^-21*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//17*a^3*b^2*x^-17*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//13*a*b^4*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//19*b*a^4*x^-19*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2//3*a^2*b^3*x^-15*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^-24*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-1//13*b^5*x^-13*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//23*a^5*x^-23*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//17*a^2*b^3*x^-17*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10//19*a^3*b^2*x^-19*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-5//21*b*a^4*x^-21*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//3*a*b^4*x^-15*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(1//4*b^-1*x^4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+(1/2)*a^2*b^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2)+-1//2*a*b^-2*x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2))
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :((1/2)*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-1//2*a*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :((1/2)*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+-1//2*a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :((1/2)*a^-1*x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-1a+-1*b*x^2)+(1/2)*b*a^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2)+-1*b*a^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(1//3*b^-1*x^3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+a^3//2*b^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2))+-1*a*x*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(x*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1*a^(1/2)*b^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(a^-1//2*b^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(-1*a^-1*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1*a^-3//2*b^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(1//3*a^-1*x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-1a+-1*b*x^2)+b*a^-2*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+a^-5//2*b^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-3//2*a^2*b^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+(1/2)*b^-3*x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+1//4*a^3*b^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3//2*a*b^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(a*b^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+(1/2)*b^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2)+-1//4*a^2*b^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-1//4*b^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :((1/2)*a^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//4*a^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+-1//2*a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-1*b*a^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//2*a^-3*x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1//4*b*a^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3*b*a^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+3//2*b*a^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-3//8*x*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*b^-1*x^3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*a^-1//2*b^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(3a+3*b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-1//4*x*b^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*x*a^-1*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*a^-3//2*b^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(1//4*x*a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*(a+b*x^2)+3//8*x*a^-2*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2+3//8*a^-5//2*b^-1//2*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^-3//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(5//8*a^-2*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*a^-3*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(15a+15*b*x^2)+1//4*a^-1*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-15//8*a^-7//2*b^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(7//8*a^-2*x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//24*a^-3*x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(35a+35*b*x^2)+1//4*a^-1*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+35//8*b*a^-4*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+35//8*a^-9//2*b^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^11*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-5*a^2*b^-6*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+(1/2)*b^-5*x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-5//6*a^4*b^-6*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*a^5*b^-6*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+5//2*a^3*b^-6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-5//2*a*b^-6*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^9*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(2*a*b^-5*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+(1/2)*b^-5*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2)+-3//2*a^2*b^-5*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*a^4*b^-5*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+2//3*a^3*b^-5*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2)
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(1//8*a^-1*x^8*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(1//24*a^-2*x^6*(a^2+b^2*x^4+2*a*b*x^2)^-3//2+1//8*a^-1*x^6*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//2)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1//6*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2+1//8*a*b^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//2)
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1//8*b^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-3//2)
@test integrate(x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :((1/2)*a^-4*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//4*a^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//6*a^-2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*a^-1*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+a^-5*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+-1//2*a^-5*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-2*b*a^-5*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3//4*b*a^-4*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//2*a^-5*x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-1//3*b*a^-3*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*b*a^-2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-5*b*a^-6*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(x)+5//2*b*a^-6*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a+b*x^2))
@test integrate(x^6*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-5//48*b^-2*x^3*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-5//64*x*b^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*b^-1*x^5*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+5//128*x*a^-1*b^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//128*a^-3//2*b^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(5a+5*b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^4*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1//8*b^-1*x^3*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//16*x*b^-2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+3//128*x*a^-2*b^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//64*x*a^-1*b^-2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//128*a^-5//2*b^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(3a+3*b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1//8*x*b^-1*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+5//128*x*a^-3*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//48*x*a^-1*b^-1*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//128*a^-7//2*b^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(5a+5*b*x^2)*arctan(x*a^-1//2*b^(1/2))+5//192*x*a^-2*b^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2)
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(1//8*x*a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-5//2*(a+b*x^2)+7//48*x*a^-2*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2+35//128*x*a^-4*(a+b*x^2)^4*(a^2+b^2*x^4+2*a*b*x^2)^-5//2+35//192*x*a^-3*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^-5//2+35//128*a^-9//2*b^-1//2*(a+b*x^2)^5*(a^2+b^2*x^4+2*a*b*x^2)^-5//2*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(105//128*a^-4*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//128*a^-5*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(315a+315*b*x^2)+1//8*a^-1*x^-1*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+3//16*a^-2*x^-1*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+21//64*a^-3*x^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-315//128*a^-11//2*b^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^-4*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(231//128*a^-4*x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//128*a^-5*x^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(385a+385*b*x^2)+1//8*a^-1*x^-3*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+11//48*a^-2*x^-3*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+33//64*a^-3*x^-3*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1155//128*b*a^-6*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+1155//128*a^-13//2*b^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(x*a^-1//2*b^(1/2)))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-1//3, x) == :(3//5*x*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//3*(a+b*x^2)+3//5*3^3//4*a^2*b^-2*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^2//3*(2+-1*3^(1/2))^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-1//3, x) == :(-1*a*3^3//4*b^-1*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^2//3*(2+-1*3^(1/2))^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//3, x) == :(-1*a^-1*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//3*(a+b*x^2)+1//3*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^2//3*(2+-1*3^(1/2))^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^2*(a^2+b^2*x^4+2*a*b*x^2)^-2//3, x) == :(-3//2*x*b^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(a+b*x^2)+-9//2*a*x*b^-1*(1+b*a^-1*x^2)^4//3*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2//3+-3//2*2^(1/2)*3^3//4*a^2*b^-2*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^4//3*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2))+9//4*3^1//4*a^2*b^-2*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^4//3*(2+3^(1/2))^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate((a^2+b^2*x^4+2*a*b*x^2)^-2//3, x) == :(3//2*x*a^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(a+b*x^2)+3//2*x*(1+b*a^-1*x^2)^4//3*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2//3+(1/2)*a*2^(1/2)*3^3//4*b^-1*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^4//3*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2))+-3//4*a*3^1//4*b^-1*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^4//3*(2+3^(1/2))^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate(x^-2*(a^2+b^2*x^4+2*a*b*x^2)^-2//3, x) == :((1/2)*a^-1*x^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(3a+3*b*x^2)+-5//2*a^-2*x^-1*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^-2//3+-5//2*b*x*a^-1*(1+b*a^-1*x^2)^4//3*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-2//3+-5//6*2^(1/2)*3^3//4*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^4//3*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.F(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2))+5//4*3^1//4*x^-1*((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+(1+b*a^-1*x^2)^1//3+(1+b*a^-1*x^2)^2//3))^(1/2)*(-1*(1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-2*(1+-1*(1+b*a^-1*x^2)^1//3))^-1//2*(1+b*a^-1*x^2)^4//3*(2+3^(1/2))^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-2//3*(1+-1*(1+b*a^-1*x^2)^1//3)*Elliptic.E(arcsin((1+-1*3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)^-1*(1+3^(1/2)+-1*(1+b*a^-1*x^2)^1//3)),-7+4*3^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(2//7*a^2*d^-1*(d*x)^7//2+2//15*b^2*d^-5*(d*x)^15//2+4//11*a*b*d^-3*(d*x)^11//2)
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(2//5*a^2*d^-1*(d*x)^5//2+2//13*b^2*d^-5*(d*x)^13//2+4//9*a*b*d^-3*(d*x)^9//2)
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2), x) == :(2//3*a^2*d^-1*(d*x)^3//2+2//11*b^2*d^-5*(d*x)^11//2+4//7*a*b*d^-3*(d*x)^7//2)
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(2*a^2*d^-1*(d*x)^(1/2)+2//9*b^2*d^-5*(d*x)^9//2+4//5*a*b*d^-3*(d*x)^5//2)
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-2*a^2*d^-1*(d*x)^-1//2+2//7*b^2*d^-5*(d*x)^7//2+4//3*a*b*d^-3*(d*x)^3//2)
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-2//3*a^2*d^-1*(d*x)^-3//2+2//5*b^2*d^-5*(d*x)^5//2+4*a*b*d^-3*(d*x)^(1/2))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2), x) == :(-2//5*a^2*d^-1*(d*x)^-5//2+2//3*b^2*d^-5*(d*x)^3//2+-4*a*b*d^-3*(d*x)^-1//2)
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(2//7*a^4*d^-1*(d*x)^7//2+2//23*b^4*d^-9*(d*x)^23//2+4//5*a^2*b^2*d^-5*(d*x)^15//2+8//11*b*a^3*d^-3*(d*x)^11//2+8//19*a*b^3*d^-7*(d*x)^19//2)
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(2//5*a^4*d^-1*(d*x)^5//2+2//21*b^4*d^-9*(d*x)^21//2+8//9*b*a^3*d^-3*(d*x)^9//2+8//17*a*b^3*d^-7*(d*x)^17//2+12//13*a^2*b^2*d^-5*(d*x)^13//2)
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(2//3*a^4*d^-1*(d*x)^3//2+2//19*b^4*d^-9*(d*x)^19//2+8//7*b*a^3*d^-3*(d*x)^7//2+8//15*a*b^3*d^-7*(d*x)^15//2+12//11*a^2*b^2*d^-5*(d*x)^11//2)
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(2*a^4*d^-1*(d*x)^(1/2)+2//17*b^4*d^-9*(d*x)^17//2+4//3*a^2*b^2*d^-5*(d*x)^9//2+8//5*b*a^3*d^-3*(d*x)^5//2+8//13*a*b^3*d^-7*(d*x)^13//2)
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-2*a^4*d^-1*(d*x)^-1//2+2//15*b^4*d^-9*(d*x)^15//2+8//3*b*a^3*d^-3*(d*x)^3//2+8//11*a*b^3*d^-7*(d*x)^11//2+12//7*a^2*b^2*d^-5*(d*x)^7//2)
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-2//3*a^4*d^-1*(d*x)^-3//2+2//13*b^4*d^-9*(d*x)^13//2+8*b*a^3*d^-3*(d*x)^(1/2)+8//9*a*b^3*d^-7*(d*x)^9//2+12//5*a^2*b^2*d^-5*(d*x)^5//2)
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(-2//5*a^4*d^-1*(d*x)^-5//2+2//11*b^4*d^-9*(d*x)^11//2+-8*b*a^3*d^-3*(d*x)^-1//2+4*a^2*b^2*d^-5*(d*x)^3//2+8//7*a*b^3*d^-7*(d*x)^7//2)
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(2//7*a^6*d^-1*(d*x)^7//2+2//31*b^6*d^-13*(d*x)^31//2+2*a^4*b^2*d^-5*(d*x)^15//2+4//9*a*b^5*d^-11*(d*x)^27//2+12//11*b*a^5*d^-3*(d*x)^11//2+30//23*a^2*b^4*d^-9*(d*x)^23//2+40//19*a^3*b^3*d^-7*(d*x)^19//2)
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(2//5*a^6*d^-1*(d*x)^5//2+2//29*b^6*d^-13*(d*x)^29//2+4//3*b*a^5*d^-3*(d*x)^9//2+10//7*a^2*b^4*d^-9*(d*x)^21//2+12//25*a*b^5*d^-11*(d*x)^25//2+30//13*a^4*b^2*d^-5*(d*x)^13//2+40//17*a^3*b^3*d^-7*(d*x)^17//2)
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(2//3*a^6*d^-1*(d*x)^3//2+2//27*b^6*d^-13*(d*x)^27//2+8//3*a^3*b^3*d^-7*(d*x)^15//2+12//7*b*a^5*d^-3*(d*x)^7//2+12//23*a*b^5*d^-11*(d*x)^23//2+30//11*a^4*b^2*d^-5*(d*x)^11//2+30//19*a^2*b^4*d^-9*(d*x)^19//2)
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(2*a^6*d^-1*(d*x)^(1/2)+2//25*b^6*d^-13*(d*x)^25//2+4//7*a*b^5*d^-11*(d*x)^21//2+10//3*a^4*b^2*d^-5*(d*x)^9//2+12//5*b*a^5*d^-3*(d*x)^5//2+30//17*a^2*b^4*d^-9*(d*x)^17//2+40//13*a^3*b^3*d^-7*(d*x)^13//2)
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-2*a^6*d^-1*(d*x)^-1//2+2//23*b^6*d^-13*(d*x)^23//2+2*a^2*b^4*d^-9*(d*x)^15//2+4*b*a^5*d^-3*(d*x)^3//2+12//19*a*b^5*d^-11*(d*x)^19//2+30//7*a^4*b^2*d^-5*(d*x)^7//2+40//11*a^3*b^3*d^-7*(d*x)^11//2)
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-2//3*a^6*d^-1*(d*x)^-3//2+2//21*b^6*d^-13*(d*x)^21//2+6*a^4*b^2*d^-5*(d*x)^5//2+12*b*a^5*d^-3*(d*x)^(1/2)+12//17*a*b^5*d^-11*(d*x)^17//2+30//13*a^2*b^4*d^-9*(d*x)^13//2+40//9*a^3*b^3*d^-7*(d*x)^9//2)
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(-2//5*a^6*d^-1*(d*x)^-5//2+2//19*b^6*d^-13*(d*x)^19//2+-12*b*a^5*d^-3*(d*x)^-1//2+10*a^4*b^2*d^-5*(d*x)^3//2+4//5*a*b^5*d^-11*(d*x)^15//2+30//11*a^2*b^4*d^-9*(d*x)^11//2+40//7*a^3*b^3*d^-7*(d*x)^7//2)
@test integrate((d*x)^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(9//10*b^-2*d^3*(d*x)^5//2+-9//2*a*b^-3*d^5*(d*x)^(1/2)+-1//2*d*b^-1*(d*x)^9//2*(a+b*x^2)^-1+-9//8*2^(1/2)*a^5//4*b^-13//4*d^11//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-9//16*2^(1/2)*a^5//4*b^-13//4*d^11//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+9//8*2^(1/2)*a^5//4*b^-13//4*d^11//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+9//16*2^(1/2)*a^5//4*b^-13//4*d^11//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(7//6*b^-2*d^3*(d*x)^3//2+-1//2*d*b^-1*(d*x)^7//2*(a+b*x^2)^-1+-7//8*2^(1/2)*a^3//4*b^-11//4*d^9//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-7//16*2^(1/2)*a^3//4*b^-11//4*d^9//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+7//8*2^(1/2)*a^3//4*b^-11//4*d^9//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+7//16*2^(1/2)*a^3//4*b^-11//4*d^9//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(5//2*b^-2*d^3*(d*x)^(1/2)+-1//2*d*b^-1*(d*x)^5//2*(a+b*x^2)^-1+-5//8*2^(1/2)*a^1//4*b^-9//4*d^7//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-5//16*2^(1/2)*a^1//4*b^-9//4*d^7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+5//8*2^(1/2)*a^1//4*b^-9//4*d^7//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+5//16*2^(1/2)*a^1//4*b^-9//4*d^7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-1//2*d*b^-1*(d*x)^3//2*(a+b*x^2)^-1+-3//8*2^(1/2)*a^-1//4*b^-7//4*d^5//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-3//16*2^(1/2)*a^-1//4*b^-7//4*d^5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3//8*2^(1/2)*a^-1//4*b^-7//4*d^5//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+3//16*2^(1/2)*a^-1//4*b^-7//4*d^5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-1//2*d*b^-1*(d*x)^(1/2)*(a+b*x^2)^-1+-1//8*2^(1/2)*a^-3//4*b^-5//4*d^3//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//16*2^(1/2)*a^-3//4*b^-5//4*d^3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//8*2^(1/2)*a^-3//4*b^-5//4*d^3//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+1//16*2^(1/2)*a^-3//4*b^-5//4*d^3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :((1/2)*a^-1*d^-1*(d*x)^3//2*(a+b*x^2)^-1+-1//8*2^(1/2)*a^-5//4*b^-3//4*d^(1/2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//16*2^(1/2)*a^-5//4*b^-3//4*d^(1/2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//8*2^(1/2)*a^-5//4*b^-3//4*d^(1/2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+1//16*2^(1/2)*a^-5//4*b^-3//4*d^(1/2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :((1/2)*a^-1*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1+-3//8*2^(1/2)*a^-7//4*b^-1//4*d^-1//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-3//16*2^(1/2)*a^-7//4*b^-1//4*d^-1//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3//8*2^(1/2)*a^-7//4*b^-1//4*d^-1//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+3//16*2^(1/2)*a^-7//4*b^-1//4*d^-1//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-5//2*a^-2*d^-1*(d*x)^-1//2+(1/2)*a^-1*d^-1*(d*x)^-1//2*(a+b*x^2)^-1+-5//8*2^(1/2)*a^-9//4*b^1//4*d^-3//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-5//16*2^(1/2)*a^-9//4*b^1//4*d^-3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+5//8*2^(1/2)*a^-9//4*b^1//4*d^-3//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+5//16*2^(1/2)*a^-9//4*b^1//4*d^-3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-7//6*a^-2*d^-1*(d*x)^-3//2+(1/2)*a^-1*d^-1*(d*x)^-3//2*(a+b*x^2)^-1+-7//8*2^(1/2)*a^-11//4*b^3//4*d^-5//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-7//16*2^(1/2)*a^-11//4*b^3//4*d^-5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+7//8*2^(1/2)*a^-11//4*b^3//4*d^-5//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+7//16*2^(1/2)*a^-11//4*b^3//4*d^-5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1, x) == :(-9//10*a^-2*d^-1*(d*x)^-5//2+(1/2)*a^-1*d^-1*(d*x)^-5//2*(a+b*x^2)^-1+9//2*b*a^-3*d^-3*(d*x)^-1//2+-9//8*2^(1/2)*a^-13//4*b^5//4*d^-7//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-9//16*2^(1/2)*a^-13//4*b^5//4*d^-7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+9//8*2^(1/2)*a^-13//4*b^5//4*d^-7//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+9//16*2^(1/2)*a^-13//4*b^5//4*d^-7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(663//320*b^-4*d^7*(d*x)^5//2+-663//64*a*b^-5*d^9*(d*x)^(1/2)+-221//192*b^-3*d^5*(d*x)^9//2*(a+b*x^2)^-1+-17//48*b^-2*d^3*(d*x)^13//2*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^17//2*(a+b*x^2)^-3+-663//256*2^(1/2)*a^5//4*b^-21//4*d^19//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-663//512*2^(1/2)*a^5//4*b^-21//4*d^19//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+663//256*2^(1/2)*a^5//4*b^-21//4*d^19//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+663//512*2^(1/2)*a^5//4*b^-21//4*d^19//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(385//192*b^-4*d^7*(d*x)^3//2+-55//64*b^-3*d^5*(d*x)^7//2*(a+b*x^2)^-1+-5//16*b^-2*d^3*(d*x)^11//2*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^15//2*(a+b*x^2)^-3+-385//256*2^(1/2)*a^3//4*b^-19//4*d^17//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-385//512*2^(1/2)*a^3//4*b^-19//4*d^17//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+385//256*2^(1/2)*a^3//4*b^-19//4*d^17//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+385//512*2^(1/2)*a^3//4*b^-19//4*d^17//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(195//64*b^-4*d^7*(d*x)^(1/2)+-39//64*b^-3*d^5*(d*x)^5//2*(a+b*x^2)^-1+-13//48*b^-2*d^3*(d*x)^9//2*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^13//2*(a+b*x^2)^-3+-195//256*2^(1/2)*a^1//4*b^-17//4*d^15//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-195//512*2^(1/2)*a^1//4*b^-17//4*d^15//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+195//256*2^(1/2)*a^1//4*b^-17//4*d^15//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+195//512*2^(1/2)*a^1//4*b^-17//4*d^15//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-77//192*b^-3*d^5*(d*x)^3//2*(a+b*x^2)^-1+-11//48*b^-2*d^3*(d*x)^7//2*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^11//2*(a+b*x^2)^-3+-77//256*2^(1/2)*a^-1//4*b^-15//4*d^13//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//512*2^(1/2)*a^-1//4*b^-15//4*d^13//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//256*2^(1/2)*a^-1//4*b^-15//4*d^13//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//512*2^(1/2)*a^-1//4*b^-15//4*d^13//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-15//64*b^-3*d^5*(d*x)^(1/2)*(a+b*x^2)^-1+-3//16*b^-2*d^3*(d*x)^5//2*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^9//2*(a+b*x^2)^-3+-15//256*2^(1/2)*a^-3//4*b^-13//4*d^11//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-15//512*2^(1/2)*a^-3//4*b^-13//4*d^11//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+15//256*2^(1/2)*a^-3//4*b^-13//4*d^11//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+15//512*2^(1/2)*a^-3//4*b^-13//4*d^11//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-7//48*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^7//2*(a+b*x^2)^-3+-7//256*2^(1/2)*a^-5//4*b^-11//4*d^9//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-7//512*2^(1/2)*a^-5//4*b^-11//4*d^9//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+7//64*a^-1*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-1+7//256*2^(1/2)*a^-5//4*b^-11//4*d^9//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+7//512*2^(1/2)*a^-5//4*b^-11//4*d^9//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-5//48*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-2+-1//6*d*b^-1*(d*x)^5//2*(a+b*x^2)^-3+-5//256*2^(1/2)*a^-7//4*b^-9//4*d^7//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-5//512*2^(1/2)*a^-7//4*b^-9//4*d^7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+5//192*a^-1*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-1+5//256*2^(1/2)*a^-7//4*b^-9//4*d^7//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+5//512*2^(1/2)*a^-7//4*b^-9//4*d^7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//6*d*b^-1*(d*x)^3//2*(a+b*x^2)^-3+-5//256*2^(1/2)*a^-9//4*b^-7//4*d^5//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-5//512*2^(1/2)*a^-9//4*b^-7//4*d^5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//16*d*a^-1*b^-1*(d*x)^3//2*(a+b*x^2)^-2+5//64*d*a^-2*b^-1*(d*x)^3//2*(a+b*x^2)^-1+5//256*2^(1/2)*a^-9//4*b^-7//4*d^5//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+5//512*2^(1/2)*a^-9//4*b^-7//4*d^5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-1//6*d*b^-1*(d*x)^(1/2)*(a+b*x^2)^-3+-7//256*2^(1/2)*a^-11//4*b^-5//4*d^3//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-7//512*2^(1/2)*a^-11//4*b^-5//4*d^3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//48*d*a^-1*b^-1*(d*x)^(1/2)*(a+b*x^2)^-2+7//192*d*a^-2*b^-1*(d*x)^(1/2)*(a+b*x^2)^-1+7//256*2^(1/2)*a^-11//4*b^-5//4*d^3//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+7//512*2^(1/2)*a^-11//4*b^-5//4*d^3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(1//6*a^-1*d^-1*(d*x)^3//2*(a+b*x^2)^-3+3//16*a^-2*d^-1*(d*x)^3//2*(a+b*x^2)^-2+15//64*a^-3*d^-1*(d*x)^3//2*(a+b*x^2)^-1+-15//256*2^(1/2)*a^-13//4*b^-3//4*d^(1/2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-15//512*2^(1/2)*a^-13//4*b^-3//4*d^(1/2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+15//256*2^(1/2)*a^-13//4*b^-3//4*d^(1/2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+15//512*2^(1/2)*a^-13//4*b^-3//4*d^(1/2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(1//6*a^-1*d^-1*(d*x)^(1/2)*(a+b*x^2)^-3+11//48*a^-2*d^-1*(d*x)^(1/2)*(a+b*x^2)^-2+77//192*a^-3*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1+-77//256*2^(1/2)*a^-15//4*b^-1//4*d^-1//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//512*2^(1/2)*a^-15//4*b^-1//4*d^-1//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//256*2^(1/2)*a^-15//4*b^-1//4*d^-1//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//512*2^(1/2)*a^-15//4*b^-1//4*d^-1//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-195//64*a^-4*d^-1*(d*x)^-1//2+1//6*a^-1*d^-1*(d*x)^-1//2*(a+b*x^2)^-3+13//48*a^-2*d^-1*(d*x)^-1//2*(a+b*x^2)^-2+39//64*a^-3*d^-1*(d*x)^-1//2*(a+b*x^2)^-1+-195//256*2^(1/2)*a^-17//4*b^1//4*d^-3//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-195//512*2^(1/2)*a^-17//4*b^1//4*d^-3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+195//256*2^(1/2)*a^-17//4*b^1//4*d^-3//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+195//512*2^(1/2)*a^-17//4*b^1//4*d^-3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-385//192*a^-4*d^-1*(d*x)^-3//2+1//6*a^-1*d^-1*(d*x)^-3//2*(a+b*x^2)^-3+5//16*a^-2*d^-1*(d*x)^-3//2*(a+b*x^2)^-2+55//64*a^-3*d^-1*(d*x)^-3//2*(a+b*x^2)^-1+-385//256*2^(1/2)*a^-19//4*b^3//4*d^-5//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-385//512*2^(1/2)*a^-19//4*b^3//4*d^-5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+385//256*2^(1/2)*a^-19//4*b^3//4*d^-5//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+385//512*2^(1/2)*a^-19//4*b^3//4*d^-5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-2, x) == :(-663//320*a^-4*d^-1*(d*x)^-5//2+1//6*a^-1*d^-1*(d*x)^-5//2*(a+b*x^2)^-3+17//48*a^-2*d^-1*(d*x)^-5//2*(a+b*x^2)^-2+221//192*a^-3*d^-1*(d*x)^-5//2*(a+b*x^2)^-1+663//64*b*a^-5*d^-3*(d*x)^-1//2+-663//256*2^(1/2)*a^-21//4*b^5//4*d^-7//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-663//512*2^(1/2)*a^-21//4*b^5//4*d^-7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+663//256*2^(1/2)*a^-21//4*b^5//4*d^-7//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+663//512*2^(1/2)*a^-21//4*b^5//4*d^-7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^27//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(13923//4096*b^-6*d^11*(d*x)^5//2+-69615//4096*a*b^-7*d^13*(d*x)^(1/2)+-7735//4096*b^-5*d^9*(d*x)^9//2*(a+b*x^2)^-1+-595//1024*b^-4*d^7*(d*x)^13//2*(a+b*x^2)^-2+-35//128*b^-3*d^5*(d*x)^17//2*(a+b*x^2)^-3+-5//32*b^-2*d^3*(d*x)^21//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^25//2*(a+b*x^2)^-5+-69615//16384*2^(1/2)*a^5//4*b^-29//4*d^27//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-69615//32768*2^(1/2)*a^5//4*b^-29//4*d^27//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+69615//16384*2^(1/2)*a^5//4*b^-29//4*d^27//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+69615//32768*2^(1/2)*a^5//4*b^-29//4*d^27//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^25//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(33649//12288*b^-6*d^11*(d*x)^3//2+-4807//4096*b^-5*d^9*(d*x)^7//2*(a+b*x^2)^-1+-437//1024*b^-4*d^7*(d*x)^11//2*(a+b*x^2)^-2+-437//1920*b^-3*d^5*(d*x)^15//2*(a+b*x^2)^-3+-23//160*b^-2*d^3*(d*x)^19//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^23//2*(a+b*x^2)^-5+-33649//16384*2^(1/2)*a^3//4*b^-27//4*d^25//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-33649//32768*2^(1/2)*a^3//4*b^-27//4*d^25//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+33649//16384*2^(1/2)*a^3//4*b^-27//4*d^25//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+33649//32768*2^(1/2)*a^3//4*b^-27//4*d^25//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^23//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(13923//4096*b^-6*d^11*(d*x)^(1/2)+-13923//20480*b^-5*d^9*(d*x)^5//2*(a+b*x^2)^-1+-1547//5120*b^-4*d^7*(d*x)^9//2*(a+b*x^2)^-2+-119//640*b^-3*d^5*(d*x)^13//2*(a+b*x^2)^-3+-21//160*b^-2*d^3*(d*x)^17//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^21//2*(a+b*x^2)^-5+-13923//16384*2^(1/2)*a^1//4*b^-25//4*d^23//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-13923//32768*2^(1/2)*a^1//4*b^-25//4*d^23//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+13923//16384*2^(1/2)*a^1//4*b^-25//4*d^23//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+13923//32768*2^(1/2)*a^1//4*b^-25//4*d^23//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^21//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1463//4096*b^-5*d^9*(d*x)^3//2*(a+b*x^2)^-1+-209//1024*b^-4*d^7*(d*x)^7//2*(a+b*x^2)^-2+-19//128*b^-3*d^5*(d*x)^11//2*(a+b*x^2)^-3+-19//160*b^-2*d^3*(d*x)^15//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^19//2*(a+b*x^2)^-5+-4389//16384*2^(1/2)*a^-1//4*b^-23//4*d^21//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-4389//32768*2^(1/2)*a^-1//4*b^-23//4*d^21//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+4389//16384*2^(1/2)*a^-1//4*b^-23//4*d^21//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+4389//32768*2^(1/2)*a^-1//4*b^-23//4*d^21//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-663//4096*b^-5*d^9*(d*x)^(1/2)*(a+b*x^2)^-1+-663//5120*b^-4*d^7*(d*x)^5//2*(a+b*x^2)^-2+-221//1920*b^-3*d^5*(d*x)^9//2*(a+b*x^2)^-3+-17//160*b^-2*d^3*(d*x)^13//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^17//2*(a+b*x^2)^-5+-663//16384*2^(1/2)*a^-3//4*b^-21//4*d^19//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-663//32768*2^(1/2)*a^-3//4*b^-21//4*d^19//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+663//16384*2^(1/2)*a^-3//4*b^-21//4*d^19//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+663//32768*2^(1/2)*a^-3//4*b^-21//4*d^19//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-77//1024*b^-4*d^7*(d*x)^3//2*(a+b*x^2)^-2+-11//128*b^-3*d^5*(d*x)^7//2*(a+b*x^2)^-3+-3//32*b^-2*d^3*(d*x)^11//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^15//2*(a+b*x^2)^-5+-231//16384*2^(1/2)*a^-5//4*b^-19//4*d^17//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-231//32768*2^(1/2)*a^-5//4*b^-19//4*d^17//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+231//4096*a^-1*b^-4*d^7*(d*x)^3//2*(a+b*x^2)^-1+231//16384*2^(1/2)*a^-5//4*b^-19//4*d^17//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+231//32768*2^(1/2)*a^-5//4*b^-19//4*d^17//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-39//640*b^-3*d^5*(d*x)^5//2*(a+b*x^2)^-3+-39//1024*b^-4*d^7*(d*x)^(1/2)*(a+b*x^2)^-2+-13//160*b^-2*d^3*(d*x)^9//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^13//2*(a+b*x^2)^-5+-117//16384*2^(1/2)*a^-7//4*b^-17//4*d^15//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-117//32768*2^(1/2)*a^-7//4*b^-17//4*d^15//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+39//4096*a^-1*b^-4*d^7*(d*x)^(1/2)*(a+b*x^2)^-1+117//16384*2^(1/2)*a^-7//4*b^-17//4*d^15//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+117//32768*2^(1/2)*a^-7//4*b^-17//4*d^15//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-77//1920*b^-3*d^5*(d*x)^3//2*(a+b*x^2)^-3+-11//160*b^-2*d^3*(d*x)^7//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^11//2*(a+b*x^2)^-5+-77//16384*2^(1/2)*a^-9//4*b^-15//4*d^13//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//32768*2^(1/2)*a^-9//4*b^-15//4*d^13//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//4096*a^-2*b^-3*d^5*(d*x)^3//2*(a+b*x^2)^-1+77//5120*a^-1*b^-3*d^5*(d*x)^3//2*(a+b*x^2)^-2+77//16384*2^(1/2)*a^-9//4*b^-15//4*d^13//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//32768*2^(1/2)*a^-9//4*b^-15//4*d^13//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-9//160*b^-2*d^3*(d*x)^5//2*(a+b*x^2)^-4+-3//128*b^-3*d^5*(d*x)^(1/2)*(a+b*x^2)^-3+-1//10*d*b^-1*(d*x)^9//2*(a+b*x^2)^-5+-63//16384*2^(1/2)*a^-11//4*b^-13//4*d^11//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-63//32768*2^(1/2)*a^-11//4*b^-13//4*d^11//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3//1024*a^-1*b^-3*d^5*(d*x)^(1/2)*(a+b*x^2)^-2+21//4096*a^-2*b^-3*d^5*(d*x)^(1/2)*(a+b*x^2)^-1+63//16384*2^(1/2)*a^-11//4*b^-13//4*d^11//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+63//32768*2^(1/2)*a^-11//4*b^-13//4*d^11//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-7//160*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-4+-1//10*d*b^-1*(d*x)^7//2*(a+b*x^2)^-5+-63//16384*2^(1/2)*a^-13//4*b^-11//4*d^9//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-63//32768*2^(1/2)*a^-13//4*b^-11//4*d^9//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+7//640*a^-1*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-3+63//4096*a^-3*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-1+63//5120*a^-2*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-2+63//16384*2^(1/2)*a^-13//4*b^-11//4*d^9//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+63//32768*2^(1/2)*a^-13//4*b^-11//4*d^9//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//10*d*b^-1*(d*x)^5//2*(a+b*x^2)^-5+-1//32*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-4+-77//16384*2^(1/2)*a^-15//4*b^-9//4*d^7//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//32768*2^(1/2)*a^-15//4*b^-9//4*d^7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//384*a^-1*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-3+11//3072*a^-2*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-2+77//12288*a^-3*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-1+77//16384*2^(1/2)*a^-15//4*b^-9//4*d^7//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//32768*2^(1/2)*a^-15//4*b^-9//4*d^7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//10*d*b^-1*(d*x)^3//2*(a+b*x^2)^-5+-117//16384*2^(1/2)*a^-17//4*b^-7//4*d^5//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-117//32768*2^(1/2)*a^-17//4*b^-7//4*d^5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3//160*d*a^-1*b^-1*(d*x)^3//2*(a+b*x^2)^-4+13//640*d*a^-2*b^-1*(d*x)^3//2*(a+b*x^2)^-3+117//4096*d*a^-4*b^-1*(d*x)^3//2*(a+b*x^2)^-1+117//5120*d*a^-3*b^-1*(d*x)^3//2*(a+b*x^2)^-2+117//16384*2^(1/2)*a^-17//4*b^-7//4*d^5//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+117//32768*2^(1/2)*a^-17//4*b^-7//4*d^5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-1//10*d*b^-1*(d*x)^(1/2)*(a+b*x^2)^-5+-231//16384*2^(1/2)*a^-19//4*b^-5//4*d^3//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-231//32768*2^(1/2)*a^-19//4*b^-5//4*d^3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//128*d*a^-2*b^-1*(d*x)^(1/2)*(a+b*x^2)^-3+1//160*d*a^-1*b^-1*(d*x)^(1/2)*(a+b*x^2)^-4+11//1024*d*a^-3*b^-1*(d*x)^(1/2)*(a+b*x^2)^-2+77//4096*d*a^-4*b^-1*(d*x)^(1/2)*(a+b*x^2)^-1+231//16384*2^(1/2)*a^-19//4*b^-5//4*d^3//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+231//32768*2^(1/2)*a^-19//4*b^-5//4*d^3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1//10*a^-1*d^-1*(d*x)^3//2*(a+b*x^2)^-5+17//160*a^-2*d^-1*(d*x)^3//2*(a+b*x^2)^-4+221//1920*a^-3*d^-1*(d*x)^3//2*(a+b*x^2)^-3+663//4096*a^-5*d^-1*(d*x)^3//2*(a+b*x^2)^-1+663//5120*a^-4*d^-1*(d*x)^3//2*(a+b*x^2)^-2+-663//16384*2^(1/2)*a^-21//4*b^-3//4*d^(1/2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-663//32768*2^(1/2)*a^-21//4*b^-3//4*d^(1/2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+663//16384*2^(1/2)*a^-21//4*b^-3//4*d^(1/2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+663//32768*2^(1/2)*a^-21//4*b^-3//4*d^(1/2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(1//10*a^-1*d^-1*(d*x)^(1/2)*(a+b*x^2)^-5+19//128*a^-3*d^-1*(d*x)^(1/2)*(a+b*x^2)^-3+19//160*a^-2*d^-1*(d*x)^(1/2)*(a+b*x^2)^-4+209//1024*a^-4*d^-1*(d*x)^(1/2)*(a+b*x^2)^-2+1463//4096*a^-5*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1+-4389//16384*2^(1/2)*a^-23//4*b^-1//4*d^-1//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-4389//32768*2^(1/2)*a^-23//4*b^-1//4*d^-1//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+4389//16384*2^(1/2)*a^-23//4*b^-1//4*d^-1//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+4389//32768*2^(1/2)*a^-23//4*b^-1//4*d^-1//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-13923//4096*a^-6*d^-1*(d*x)^-1//2+1//10*a^-1*d^-1*(d*x)^-1//2*(a+b*x^2)^-5+21//160*a^-2*d^-1*(d*x)^-1//2*(a+b*x^2)^-4+119//640*a^-3*d^-1*(d*x)^-1//2*(a+b*x^2)^-3+1547//5120*a^-4*d^-1*(d*x)^-1//2*(a+b*x^2)^-2+13923//20480*a^-5*d^-1*(d*x)^-1//2*(a+b*x^2)^-1+-13923//16384*2^(1/2)*a^-25//4*b^1//4*d^-3//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-13923//32768*2^(1/2)*a^-25//4*b^1//4*d^-3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+13923//16384*2^(1/2)*a^-25//4*b^1//4*d^-3//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+13923//32768*2^(1/2)*a^-25//4*b^1//4*d^-3//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-33649//12288*a^-6*d^-1*(d*x)^-3//2+1//10*a^-1*d^-1*(d*x)^-3//2*(a+b*x^2)^-5+23//160*a^-2*d^-1*(d*x)^-3//2*(a+b*x^2)^-4+437//1024*a^-4*d^-1*(d*x)^-3//2*(a+b*x^2)^-2+437//1920*a^-3*d^-1*(d*x)^-3//2*(a+b*x^2)^-3+4807//4096*a^-5*d^-1*(d*x)^-3//2*(a+b*x^2)^-1+-33649//16384*2^(1/2)*a^-27//4*b^3//4*d^-5//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-33649//32768*2^(1/2)*a^-27//4*b^3//4*d^-5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+33649//16384*2^(1/2)*a^-27//4*b^3//4*d^-5//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+33649//32768*2^(1/2)*a^-27//4*b^3//4*d^-5//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-3, x) == :(-13923//4096*a^-6*d^-1*(d*x)^-5//2+1//10*a^-1*d^-1*(d*x)^-5//2*(a+b*x^2)^-5+5//32*a^-2*d^-1*(d*x)^-5//2*(a+b*x^2)^-4+35//128*a^-3*d^-1*(d*x)^-5//2*(a+b*x^2)^-3+595//1024*a^-4*d^-1*(d*x)^-5//2*(a+b*x^2)^-2+7735//4096*a^-5*d^-1*(d*x)^-5//2*(a+b*x^2)^-1+69615//4096*b*a^-7*d^-3*(d*x)^-1//2+-69615//16384*2^(1/2)*a^-29//4*b^5//4*d^-7//2*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-69615//32768*2^(1/2)*a^-29//4*b^5//4*d^-7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+69615//16384*2^(1/2)*a^-29//4*b^5//4*d^-7//2*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+69615//32768*2^(1/2)*a^-29//4*b^5//4*d^-7//2*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(2//7*a*d^-1*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//11*b*d^-3*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(2//5*a*d^-1*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//9*b*d^-3*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(2//3*a*d^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//7*b*d^-3*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(2*a*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//5*b*d^-3*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-2*a*d^-1*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//3*b*d^-3*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(2*b*d^-3*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2//3*a*d^-1*(d*x)^-3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(-2*b*d^-3*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-2//5*a*d^-1*(d*x)^-5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(2//7*a^3*d^-1*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//19*b^3*d^-7*(d*x)^19//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//5*a*b^2*d^-5*(d*x)^15//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//11*b*a^2*d^-3*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(2//5*a^3*d^-1*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//17*b^3*d^-7*(d*x)^17//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//3*b*a^2*d^-3*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//13*a*b^2*d^-5*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(2//3*a^3*d^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//15*b^3*d^-7*(d*x)^15//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//7*b*a^2*d^-3*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//11*a*b^2*d^-5*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(2*a^3*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//13*b^3*d^-7*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//3*a*b^2*d^-5*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//5*b*a^2*d^-3*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-2*a^3*d^-1*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//11*b^3*d^-7*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2*b*a^2*d^-3*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//7*a*b^2*d^-5*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-2//3*a^3*d^-1*(d*x)^-3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//9*b^3*d^-7*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6*b*a^2*d^-3*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+6//5*a*b^2*d^-5*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(-2//5*a^3*d^-1*(d*x)^-5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//7*b^3*d^-7*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-6*b*a^2*d^-3*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2*a*b^2*d^-5*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(2//7*a^5*d^-1*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//27*b^5*d^-11*(d*x)^27//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+4//3*a^3*b^2*d^-5*(d*x)^15//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//11*b*a^4*d^-3*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//23*a*b^4*d^-9*(d*x)^23//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//19*a^2*b^3*d^-7*(d*x)^19//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(2//5*a^5*d^-1*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//25*b^5*d^-11*(d*x)^25//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//9*b*a^4*d^-3*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//21*a*b^4*d^-9*(d*x)^21//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//13*a^3*b^2*d^-5*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//17*a^2*b^3*d^-7*(d*x)^17//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(2//3*a^5*d^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//23*b^5*d^-11*(d*x)^23//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+4//3*a^2*b^3*d^-7*(d*x)^15//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//7*b*a^4*d^-3*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//19*a*b^4*d^-9*(d*x)^19//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//11*a^3*b^2*d^-5*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(2*a^5*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//21*b^5*d^-11*(d*x)^21//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2*b*a^4*d^-3*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//17*a*b^4*d^-9*(d*x)^17//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//9*a^3*b^2*d^-5*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//13*a^2*b^3*d^-7*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-2*a^5*d^-1*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//19*b^5*d^-11*(d*x)^19//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//3*a*b^4*d^-9*(d*x)^15//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//3*b*a^4*d^-3*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//7*a^3*b^2*d^-5*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//11*a^2*b^3*d^-7*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-2//3*a^5*d^-1*(d*x)^-3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//17*b^5*d^-11*(d*x)^17//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+4*a^3*b^2*d^-5*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*b*a^4*d^-3*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//13*a*b^4*d^-9*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//9*a^2*b^3*d^-7*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(-2//5*a^5*d^-1*(d*x)^-5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+2//15*b^5*d^-11*(d*x)^15//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+-10*b*a^4*d^-3*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10//11*a*b^4*d^-9*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//3*a^3*b^2*d^-5*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+20//7*a^2*b^3*d^-7*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(2//5*d*b^-1*(d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-2*a*b^-2*d^3*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+(1/2)*2^(1/2)*a^5//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^5//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^5//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^5//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(2//3*d*b^-1*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+(1/2)*2^(1/2)*a^3//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^3//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^3//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^3//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(2*d*b^-1*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+(1/2)*2^(1/2)*a^1//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^1//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^1//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^1//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :((1/2)*2^(1/2)*a^-1//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^-1//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^-1//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^-1//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :((1/2)*2^(1/2)*a^-3//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^-3//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^-3//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^-3//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(a^-1*d^-1*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-2a+-2*b*x^2)+(1/2)*2^(1/2)*a^-5//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^-5//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^-5//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^-5//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(1//3*a^-1*d^-1*(d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-2a+-2*b*x^2)+(1/2)*2^(1/2)*a^-7//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^-7//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^-7//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^-7//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2, x) == :(1//5*a^-1*d^-1*(d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(-2a+-2*b*x^2)+2*b*a^-2*d^-3*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+(1/2)*2^(1/2)*a^-9//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//2*2^(1/2)*a^-9//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//4*2^(1/2)*a^-9//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4*2^(1/2)*a^-9//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-13//16*b^-2*d^3*(d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*d*b^-1*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+117//80*b^-3*d^5*(d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-117//16*a*b^-4*d^7*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-117//64*2^(1/2)*a^5//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-117//128*2^(1/2)*a^5//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+117//64*2^(1/2)*a^5//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+117//128*2^(1/2)*a^5//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-11//16*b^-2*d^3*(d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*d*b^-1*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+77//48*b^-3*d^5*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-77//64*2^(1/2)*a^3//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//128*2^(1/2)*a^3//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//64*2^(1/2)*a^3//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//128*2^(1/2)*a^3//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-9//16*b^-2*d^3*(d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*d*b^-1*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+45//16*b^-3*d^5*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-45//64*2^(1/2)*a^1//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-45//128*2^(1/2)*a^1//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+45//64*2^(1/2)*a^1//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+45//128*2^(1/2)*a^1//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-7//16*b^-2*d^3*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*d*b^-1*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-21//64*2^(1/2)*a^-1//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-21//128*2^(1/2)*a^-1//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+21//64*2^(1/2)*a^-1//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+21//128*2^(1/2)*a^-1//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-5//16*b^-2*d^3*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4*d*b^-1*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-5//64*2^(1/2)*a^-3//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-5//128*2^(1/2)*a^-3//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+5//64*2^(1/2)*a^-3//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+5//128*2^(1/2)*a^-3//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-1//4*d*b^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+3//16*d*a^-1*b^-1*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3//64*2^(1/2)*a^-5//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-3//128*2^(1/2)*a^-5//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3//64*2^(1/2)*a^-5//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+3//128*2^(1/2)*a^-5//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(-1//4*d*b^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//16*d*a^-1*b^-1*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3//64*2^(1/2)*a^-7//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-3//128*2^(1/2)*a^-7//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3//64*2^(1/2)*a^-7//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+3//128*2^(1/2)*a^-7//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(5//16*a^-2*d^-1*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//4*a^-1*d^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-5//64*2^(1/2)*a^-9//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-5//128*2^(1/2)*a^-9//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+5//64*2^(1/2)*a^-9//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+5//128*2^(1/2)*a^-9//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(7//16*a^-2*d^-1*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//4*a^-1*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//64*2^(1/2)*a^-11//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(21a+21*b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//128*2^(1/2)*a^-11//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(21a+21*b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//64*2^(1/2)*a^-11//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(21a+21*b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+1//128*2^(1/2)*a^-11//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(21a+21*b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(9//16*a^-2*d^-1*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//16*a^-3*d^-1*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(45a+45*b*x^2)+1//4*a^-1*d^-1*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-45//64*2^(1/2)*a^-13//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-45//128*2^(1/2)*a^-13//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+45//64*2^(1/2)*a^-13//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+45//128*2^(1/2)*a^-13//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(11//16*a^-2*d^-1*(d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//48*a^-3*d^-1*(d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(77a+77*b*x^2)+1//4*a^-1*d^-1*(d*x)^-3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-77//64*2^(1/2)*a^-15//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//128*2^(1/2)*a^-15//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//64*2^(1/2)*a^-15//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//128*2^(1/2)*a^-15//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-3//2, x) == :(13//16*a^-2*d^-1*(d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//80*a^-3*d^-1*(d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(117a+117*b*x^2)+1//4*a^-1*d^-1*(d*x)^-5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+117//16*b*a^-4*d^-3*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-117//64*2^(1/2)*a^-17//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-117//128*2^(1/2)*a^-17//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+117//64*2^(1/2)*a^-17//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+117//128*2^(1/2)*a^-17//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^23//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1547//1024*b^-4*d^7*(d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-119//256*b^-3*d^5*(d*x)^13//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-7//32*b^-2*d^3*(d*x)^17//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^21//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+13923//5120*b^-5*d^9*(d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-13923//1024*a*b^-6*d^11*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-13923//4096*2^(1/2)*a^5//4*b^-25//4*d^23//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-13923//8192*2^(1/2)*a^5//4*b^-25//4*d^23//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+13923//4096*2^(1/2)*a^5//4*b^-25//4*d^23//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+13923//8192*2^(1/2)*a^5//4*b^-25//4*d^23//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^21//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1045//1024*b^-4*d^7*(d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-95//256*b^-3*d^5*(d*x)^11//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-19//96*b^-2*d^3*(d*x)^15//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^19//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+7315//3072*b^-5*d^9*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-7315//4096*2^(1/2)*a^3//4*b^-23//4*d^21//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-7315//8192*2^(1/2)*a^3//4*b^-23//4*d^21//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+7315//4096*2^(1/2)*a^3//4*b^-23//4*d^21//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+7315//8192*2^(1/2)*a^3//4*b^-23//4*d^21//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-663//1024*b^-4*d^7*(d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-221//768*b^-3*d^5*(d*x)^9//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-17//96*b^-2*d^3*(d*x)^13//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^17//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+3315//1024*b^-5*d^9*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-3315//4096*2^(1/2)*a^1//4*b^-21//4*d^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-3315//8192*2^(1/2)*a^1//4*b^-21//4*d^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3315//4096*2^(1/2)*a^1//4*b^-21//4*d^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+3315//8192*2^(1/2)*a^1//4*b^-21//4*d^19//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-385//1024*b^-4*d^7*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-55//256*b^-3*d^5*(d*x)^7//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-5//32*b^-2*d^3*(d*x)^11//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^15//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1155//4096*2^(1/2)*a^-1//4*b^-19//4*d^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1155//8192*2^(1/2)*a^-1//4*b^-19//4*d^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1155//4096*2^(1/2)*a^-1//4*b^-19//4*d^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+1155//8192*2^(1/2)*a^-1//4*b^-19//4*d^17//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-195//1024*b^-4*d^7*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-39//256*b^-3*d^5*(d*x)^5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-13//96*b^-2*d^3*(d*x)^9//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^13//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-195//4096*2^(1/2)*a^-3//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-195//8192*2^(1/2)*a^-3//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+195//4096*2^(1/2)*a^-3//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+195//8192*2^(1/2)*a^-3//4*b^-17//4*d^15//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-77//768*b^-3*d^5*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-11//96*b^-2*d^3*(d*x)^7//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^11//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+77//1024*a^-1*b^-3*d^5*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-77//4096*2^(1/2)*a^-5//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//8192*2^(1/2)*a^-5//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//4096*2^(1/2)*a^-5//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//8192*2^(1/2)*a^-5//4*b^-15//4*d^13//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-15//256*b^-3*d^5*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3//32*b^-2*d^3*(d*x)^5//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^9//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+15//1024*a^-1*b^-3*d^5*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-45//4096*2^(1/2)*a^-7//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-45//8192*2^(1/2)*a^-7//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+45//4096*2^(1/2)*a^-7//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+45//8192*2^(1/2)*a^-7//4*b^-13//4*d^11//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-7//96*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^7//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+35//1024*a^-2*b^-2*d^3*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+7//256*a^-1*b^-2*d^3*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-35//4096*2^(1/2)*a^-9//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-35//8192*2^(1/2)*a^-9//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+35//4096*2^(1/2)*a^-9//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+35//8192*2^(1/2)*a^-9//4*b^-11//4*d^9//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-5//96*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//8*d*b^-1*(d*x)^5//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+35//3072*a^-2*b^-2*d^3*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+5//768*a^-1*b^-2*d^3*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-35//4096*2^(1/2)*a^-11//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-35//8192*2^(1/2)*a^-11//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+35//4096*2^(1/2)*a^-11//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+35//8192*2^(1/2)*a^-11//4*b^-9//4*d^7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1//8*d*b^-1*(d*x)^3//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+45//1024*d*a^-3*b^-1*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//32*d*a^-1*b^-1*(d*x)^3//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+9//256*d*a^-2*b^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-45//4096*2^(1/2)*a^-13//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-45//8192*2^(1/2)*a^-13//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+45//4096*2^(1/2)*a^-13//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+45//8192*2^(1/2)*a^-13//4*b^-7//4*d^5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(-1//8*d*b^-1*(d*x)^(1/2)*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+77//3072*d*a^-3*b^-1*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//96*d*a^-1*b^-1*(d*x)^(1/2)*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+11//768*d*a^-2*b^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-77//4096*2^(1/2)*a^-15//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-77//8192*2^(1/2)*a^-15//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+77//4096*2^(1/2)*a^-15//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+77//8192*2^(1/2)*a^-15//4*b^-5//4*d^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(195//1024*a^-4*d^-1*(d*x)^3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*a^-1*d^-1*(d*x)^3//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+13//96*a^-2*d^-1*(d*x)^3//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+39//256*a^-3*d^-1*(d*x)^3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-195//4096*2^(1/2)*a^-17//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-195//8192*2^(1/2)*a^-17//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+195//4096*2^(1/2)*a^-17//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+195//8192*2^(1/2)*a^-17//4*b^-3//4*d^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(385//1024*a^-4*d^-1*(d*x)^(1/2)*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+1//8*a^-1*d^-1*(d*x)^(1/2)*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+5//32*a^-2*d^-1*(d*x)^(1/2)*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+55//256*a^-3*d^-1*(d*x)^(1/2)*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//4096*2^(1/2)*a^-19//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(1155a+1155*b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-1//8192*2^(1/2)*a^-19//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(1155a+1155*b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+1//4096*2^(1/2)*a^-19//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(1155a+1155*b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+1//8192*2^(1/2)*a^-19//4*b^-1//4*d^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(1155a+1155*b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(663//1024*a^-4*d^-1*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//1024*a^-5*d^-1*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(3315a+3315*b*x^2)+1//8*a^-1*d^-1*(d*x)^-1//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+17//96*a^-2*d^-1*(d*x)^-1//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+221//768*a^-3*d^-1*(d*x)^-1//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-3315//4096*2^(1/2)*a^-21//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-3315//8192*2^(1/2)*a^-21//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+3315//4096*2^(1/2)*a^-21//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+3315//8192*2^(1/2)*a^-21//4*b^1//4*d^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(1045//1024*a^-4*d^-1*(d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//3072*a^-5*d^-1*(d*x)^-3//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(7315a+7315*b*x^2)+1//8*a^-1*d^-1*(d*x)^-3//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+19//96*a^-2*d^-1*(d*x)^-3//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+95//256*a^-3*d^-1*(d*x)^-3//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-7315//4096*2^(1/2)*a^-23//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-7315//8192*2^(1/2)*a^-23//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+7315//4096*2^(1/2)*a^-23//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+7315//8192*2^(1/2)*a^-23//4*b^3//4*d^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-5//2, x) == :(1547//1024*a^-4*d^-1*(d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+-1//5120*a^-5*d^-1*(d*x)^-5//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(13923a+13923*b*x^2)+1//8*a^-1*d^-1*(d*x)^-5//2*(a+b*x^2)^-3*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+7//32*a^-2*d^-1*(d*x)^-5//2*(a+b*x^2)^-2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+119//256*a^-3*d^-1*(d*x)^-5//2*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^-1//2+13923//1024*b*a^-6*d^-3*(d*x)^-1//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)+-13923//4096*2^(1/2)*a^-25//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+-1*2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+-13923//8192*2^(1/2)*a^-25//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2))+13923//4096*2^(1/2)*a^-25//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*arctan(1+2^(1/2)*a^-1//4*b^1//4*d^-1//2*(d*x)^(1/2))+13923//8192*2^(1/2)*a^-25//4*b^5//4*d^-7//2*(a^2+b^2*x^4+2*a*b*x^2)^-1//2*(a+b*x^2)*log(a^(1/2)*d^(1/2)+x*b^(1/2)*d^(1/2)+-1*2^(1/2)*a^1//4*b^1//4*(d*x)^(1/2)))
@test integrate((d*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^3, x) == :(a^6*d^-1*(d*x)^(1+m)*(1+m)^-1+b^6*d^-13*(d*x)^(13+m)*(13+m)^-1+6*a*b^5*d^-11*(d*x)^(11+m)*(11+m)^-1+6*b*a^5*d^-3*(d*x)^(3+m)*(3+m)^-1+15*a^2*b^4*d^-9*(d*x)^(9+m)*(9+m)^-1+15*a^4*b^2*d^-5*(d*x)^(5+m)*(5+m)^-1+20*a^3*b^3*d^-7*(d*x)^(7+m)*(7+m)^-1)
@test integrate((d*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^2, x) == :(a^4*d^-1*(d*x)^(1+m)*(1+m)^-1+b^4*d^-9*(d*x)^(9+m)*(9+m)^-1+4*a*b^3*d^-7*(d*x)^(7+m)*(7+m)^-1+4*b*a^3*d^-3*(d*x)^(3+m)*(3+m)^-1+6*a^2*b^2*d^-5*(d*x)^(5+m)*(5+m)^-1)
@test integrate((d*x)^m*(a^2+b^2*x^4+2*a*b*x^2), x) == :(a^2*d^-1*(d*x)^(1+m)*(1+m)^-1+b^2*d^-5*(d*x)^(5+m)*(5+m)^-1+2*a*b*d^-3*(d*x)^(3+m)*(3+m)^-1)
@test integrate((d*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^5//2, x) == :(a^5*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^5*d^-11*(d*x)^(11+m)*(11+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*a*b^4*d^-9*(d*x)^(9+m)*(9+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+5*b*a^4*d^-3*(d*x)^(3+m)*(3+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^2*b^3*d^-7*(d*x)^(7+m)*(7+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+10*a^3*b^2*d^-5*(d*x)^(5+m)*(5+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^3//2, x) == :(a^3*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b^3*d^-7*(d*x)^(7+m)*(7+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*a*b^2*d^-5*(d*x)^(5+m)*(5+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+3*b*a^2*d^-3*(d*x)^(3+m)*(3+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate((d*x)^m*(a^2+b^2*x^4+2*a*b*x^2)^(1/2), x) == :(a*d^-1*(d*x)^(1+m)*(1+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2)+b*d^-3*(d*x)^(3+m)*(3+m)^-1*(a+b*x^2)^-1*(a^2+b^2*x^4+2*a*b*x^2)^(1/2))
@test integrate(x^7*(a^2+b^2*x^4+2*a*b*x^2)^p, x) == :(1//4*b^-4*(2+p)^-1*(a+b*x^2)^4*(a^2+b^2*x^4+2*a*b*x^2)^p+-3//2*a*b^-4*(3+2p)^-1*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^p+-1//2*a^3*b^-4*(1+2p)^-1*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2)+3//4*a^2*b^-4*(1+p)^-1*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^p)
@test integrate(x^5*(a^2+b^2*x^4+2*a*b*x^2)^p, x) == :((1/2)*b^-3*(3+2p)^-1*(a+b*x^2)^3*(a^2+b^2*x^4+2*a*b*x^2)^p+(1/2)*a^2*b^-3*(1+2p)^-1*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2)+-1//2*a*b^-3*(1+p)^-1*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^p)
@test integrate(x^3*(a^2+b^2*x^4+2*a*b*x^2)^p, x) == :(1//4*b^-2*(1+p)^-1*(a+b*x^2)^2*(a^2+b^2*x^4+2*a*b*x^2)^p+-1//2*a*b^-2*(1+2p)^-1*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2))
@test integrate(x*(a^2+b^2*x^4+2*a*b*x^2)^p, x) == :((1/2)*b^-1*(1+2p)^-1*(a^2+b^2*x^4+2*a*b*x^2)^p*(a+b*x^2))
@test integrate(x^2*(a+b*x^2+c*x^4), x) == :(1//3*a*x^3+1//5*b*x^5+1//7*c*x^7)
@test integrate(x*(a+b*x^2+c*x^4), x) == :((1/2)*a*x^2+1//4*b*x^4+1//6*c*x^6)
@test integrate(a+b*x^2+c*x^4, x) == :(a*x+1//3*b*x^3+1//5*c*x^5)
@test integrate(x^-1*(a+b*x^2+c*x^4), x) == :(a*log(x)+(1/2)*b*x^2+1//4*c*x^4)
@test integrate(x^-2*(a+b*x^2+c*x^4), x) == :(b*x+-1*a*x^-1+1//3*c*x^3)
@test integrate(x^-3*(a+b*x^2+c*x^4), x) == :(b*log(x)+(1/2)*c*x^2+-1//2*a*x^-2)
@test integrate(x^-4*(a+b*x^2+c*x^4), x) == :(c*x+-1*b*x^-1+-1//3*a*x^-3)
@test integrate(x^-5*(a+b*x^2+c*x^4), x) == :(c*log(x)+-1//2*b*x^-2+-1//4*a*x^-4)
@test integrate(x^-6*(a+b*x^2+c*x^4), x) == :(-1*c*x^-1+-1//3*b*x^-3+-1//5*a*x^-5)
@test integrate(x^-7*(a+b*x^2+c*x^4), x) == :(-1//2*c*x^-2+-1//4*b*x^-4+-1//6*a*x^-6)
@test integrate(x^-8*(a+b*x^2+c*x^4), x) == :(-1//3*c*x^-3+-1//5*b*x^-5+-1//7*a*x^-7)
@test integrate(x^2*(a+b*x^2+c*x^4)^2, x) == :(x^7*(1//7*b^2+2//7*a*c)+1//3*a^2*x^3+1//11*c^2*x^11+2//5*a*b*x^5+2//9*b*c*x^9)
@test integrate(x*(a+b*x^2+c*x^4)^2, x) == :(x^6*(1//6*b^2+1//3*a*c)+(1/2)*a^2*x^2+1//10*c^2*x^10+(1/2)*a*b*x^4+1//4*b*c*x^8)
@test integrate((a+b*x^2+c*x^4)^2, x) == :(x*a^2+x^5*(1//5*b^2+2//5*a*c)+1//9*c^2*x^9+2//3*a*b*x^3+2//7*b*c*x^7)
@test integrate(x^-1*(a+b*x^2+c*x^4)^2, x) == :(a^2*log(x)+x^4*(1//4*b^2+(1/2)*a*c)+1//8*c^2*x^8+a*b*x^2+1//3*b*c*x^6)
@test integrate(x^-2*(a+b*x^2+c*x^4)^2, x) == :(x^3*(1//3*b^2+2//3*a*c)+-1*a^2*x^-1+1//7*c^2*x^7+2*a*b*x+2//5*b*c*x^5)
@test integrate(x^-3*(a+b*x^2+c*x^4)^2, x) == :(x^2*((1/2)*b^2+a*c)+-1//2*a^2*x^-2+1//6*c^2*x^6+(1/2)*b*c*x^4+2*a*b*log(x))
@test integrate(x^-4*(a+b*x^2+c*x^4)^2, x) == :(x*(b^2+2*a*c)+-1//3*a^2*x^-3+1//5*c^2*x^5+-2*a*b*x^-1+2//3*b*c*x^3)
@test integrate(x^-5*(a+b*x^2+c*x^4)^2, x) == :((b^2+2*a*c)*log(x)+-1//4*a^2*x^-4+1//4*c^2*x^4+b*c*x^2+-1*a*b*x^-2)
@test integrate(x^-6*(a+b*x^2+c*x^4)^2, x) == :(-1*x^-1*(b^2+2*a*c)+-1//5*a^2*x^-5+1//3*c^2*x^3+2*b*c*x+-2//3*a*b*x^-3)
@test integrate(x^-7*(a+b*x^2+c*x^4)^2, x) == :((1/2)*c^2*x^2+-1//2*x^-2*(b^2+2*a*c)+-1//6*a^2*x^-6+2*b*c*log(x)+-1//2*a*b*x^-4)
@test integrate(x^-8*(a+b*x^2+c*x^4)^2, x) == :(x*c^2+-1//3*x^-3*(b^2+2*a*c)+-1//7*a^2*x^-7+-2*b*c*x^-1+-2//5*a*b*x^-5)
@test integrate(x^-9*(a+b*x^2+c*x^4)^2, x) == :(c^2*log(x)+-1//4*x^-4*(b^2+2*a*c)+-1//8*a^2*x^-8+-1*b*c*x^-2+-1//3*a*b*x^-6)
@test integrate(x^-10*(a+b*x^2+c*x^4)^2, x) == :(-1*c^2*x^-1+-1//5*x^-5*(b^2+2*a*c)+-1//9*a^2*x^-9+-2//3*b*c*x^-3+-2//7*a*b*x^-7)
@test integrate(x^-11*(a+b*x^2+c*x^4)^2, x) == :(-1//2*c^2*x^-2+-1//6*x^-6*(b^2+2*a*c)+-1//10*a^2*x^-10+-1//2*b*c*x^-4+-1//4*a*b*x^-8)
@test integrate(x^-12*(a+b*x^2+c*x^4)^2, x) == :(-1//3*c^2*x^-3+-1//7*x^-7*(b^2+2*a*c)+-1//11*a^2*x^-11+-2//5*b*c*x^-5+-2//9*a*b*x^-9)
@test integrate(x^-13*(a+b*x^2+c*x^4)^2, x) == :(-1//4*c^2*x^-4+-1//8*x^-8*(b^2+2*a*c)+-1//12*a^2*x^-12+-1//3*b*c*x^-6+-1//5*a*b*x^-10)
@test integrate(x^2*(a+b*x^2+c*x^4)^3, x) == :(1//3*a^3*x^3+1//15*c^3*x^15+1//9*b*x^9*(b^2+6*a*c)+3//5*b*a^2*x^5+3//7*a*x^7*(b^2+a*c)+3//11*c*x^11*(b^2+a*c)+3//13*b*c^2*x^13)
@test integrate(x*(a+b*x^2+c*x^4)^3, x) == :((1/2)*a^3*x^2+1//14*c^3*x^14+(1/2)*a*x^6*(b^2+a*c)+1//4*b*c^2*x^12+1//8*b*x^8*(b^2+6*a*c)+3//4*b*a^2*x^4+3//10*c*x^10*(b^2+a*c))
@test integrate((a+b*x^2+c*x^4)^3, x) == :(x*a^3+1//13*c^3*x^13+b*a^2*x^3+1//3*c*x^9*(b^2+a*c)+1//7*b*x^7*(b^2+6*a*c)+3//5*a*x^5*(b^2+a*c)+3//11*b*c^2*x^11)
@test integrate(x^-1*(a+b*x^2+c*x^4)^3, x) == :(a^3*log(x)+1//12*c^3*x^12+1//6*b*x^6*(b^2+6*a*c)+3//2*b*a^2*x^2+3//4*a*x^4*(b^2+a*c)+3//8*c*x^8*(b^2+a*c)+3//10*b*c^2*x^10)
@test integrate(x^-2*(a+b*x^2+c*x^4)^3, x) == :(-1*a^3*x^-1+1//11*c^3*x^11+a*x^3*(b^2+a*c)+3*b*x*a^2+1//3*b*c^2*x^9+1//5*b*x^5*(b^2+6*a*c)+3//7*c*x^7*(b^2+a*c))
@test integrate(x^-3*(a+b*x^2+c*x^4)^3, x) == :(-1//2*a^3*x^-2+1//10*c^3*x^10+(1/2)*c*x^6*(b^2+a*c)+3*b*a^2*log(x)+1//4*b*x^4*(b^2+6*a*c)+3//2*a*x^2*(b^2+a*c)+3//8*b*c^2*x^8)
@test integrate(x^-4*(a+b*x^2+c*x^4)^3, x) == :(-1//3*a^3*x^-3+1//9*c^3*x^9+-3*b*a^2*x^-1+3*a*x*(b^2+a*c)+1//3*b*x^3*(b^2+6*a*c)+3//5*c*x^5*(b^2+a*c)+3//7*b*c^2*x^7)
@test integrate(x^7*(a+b*x^2+c*x^4)^-1, x) == :(1//4*c^-1*x^4+-1//2*b*c^-2*x^2+1//4*c^-3*(b^2+-1*a*c)*log(a+b*x^2+c*x^4)+(1/2)*b*c^-3*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*c^-1*x^2+-1//4*b*c^-2*log(a+b*x^2+c*x^4)+-1//2*c^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^3*(a+b*x^2+c*x^4)^-1, x) == :(1//4*c^-1*log(a+b*x^2+c*x^4)+(1/2)*b*c^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x*(a+b*x^2+c*x^4)^-1, x) == :(-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-1, x) == :(a^-1*log(x)+-1//4*a^-1*log(a+b*x^2+c*x^4)+(1/2)*b*a^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-1, x) == :(-1//2*a^-1*x^-2+-1*b*a^-2*log(x)+1//4*b*a^-2*log(a+b*x^2+c*x^4)+-1//2*a^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-5*(a+b*x^2+c*x^4)^-1, x) == :(-1//4*a^-1*x^-4+a^-3*(b^2+-1*a*c)*log(x)+(1/2)*b*a^-2*x^-2+-1//4*a^-3*(b^2+-1*a*c)*log(a+b*x^2+c*x^4)+(1/2)*b*a^-3*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^6*(a+b*x^2+c*x^4)^-1, x) == :(1//3*c^-1*x^3+-1*b*x*c^-2+(1/2)*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-1*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-1*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-3*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-1, x) == :(x*c^-1+-1//2*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+b*x^2+c*x^4)^-1, x) == :(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+-1*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-1, x) == :(-1*a^-1*x^-1+-1//2*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(1+b*(b^2+-4*a*c)^-1//2)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^-1, x) == :(-1//3*a^-1*x^-3+b*a^-2*x^-1+(1/2)*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^7*(a+b*x^2+c*x^4)^-2, x) == :(1//4*c^-2*log(a+b*x^2+c*x^4)+x^4*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1//2*b*c^-1*x^2*(b^2+-4*a*c)^-1+(1/2)*b*c^-2*(b^2+-4*a*c)^-3//2*(b^2+-6*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(a+b*x^2+c*x^4)^-2, x) == :(2*a*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+x^2*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2))
@test integrate(x^3*(a+b*x^2+c*x^4)^-2, x) == :((2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1*b*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x*(a+b*x^2+c*x^4)^-2, x) == :(-1*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2)+2*c*(b^2+-4*a*c)^-3//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-2, x) == :(a^-2*log(x)+-1//4*a^-2*log(a+b*x^2+c*x^4)+(1/2)*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2)+(1/2)*b*a^-2*(b^2+-4*a*c)^-3//2*(b^2+-6*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-2, x) == :((1/2)*b*a^-3*log(a+b*x^2+c*x^4)+-2*b*a^-3*log(x)+-1*a^-3*(b^2+-4*a*c)^-3//2*(b^4+6*a^2*c^2+-6*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1*a^-2*x^-2*(b^2+-4*a*c)^-1*(b^2+-3*a*c)+(1/2)*a^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2))
@test integrate(x^8*(a+b*x^2+c*x^4)^-2, x) == :(x^5*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+(1/2)*x*c^-2*(b^2+-4*a*c)^-1*(3*b^2+-10*a*c)+-1//2*b*c^-1*x^3*(b^2+-4*a*c)^-1+-1//4*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(3*b^3+(b^2+-4*a*c)^-1//2*(3*b^4+20*a^2*c^2+-19*a*c*b^2)+-13*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//4*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(3*b^3+-1*(b^2+-4*a*c)^-1//2*(3*b^4+20*a^2*c^2+-19*a*c*b^2)+-13*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^6*(a+b*x^2+c*x^4)^-2, x) == :(x^3*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1//2*b*x*c^-1*(b^2+-4*a*c)^-1+1//4*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(b^2+-6*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-8*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(b^2+-6*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-8*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-2, x) == :(x*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+1//4*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+4*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-2, x) == :(-1*x*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2)+(1/2)*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(-1*(b^2+-4*a*c)^(1/2)+2b)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+2b)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+b*x^2+c*x^4)^-2, x) == :((1/2)*x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2)+-1//4*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+-1*b*(b^2+-4*a*c)^(1/2)+-12*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(b^2+b*(b^2+-4*a*c)^(1/2)+-12*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-2, x) == :(-1//2*a^-2*x^-1*(b^2+-4*a*c)^-1*(3*b^2+-10*a*c)+(1/2)*a^-1*x^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2)+-1//4*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(3*b^3+(b^2+-4*a*c)^(1/2)*(3*b^2+-10*a*c)+-16*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+1//4*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-3//2*(3*b^3+-1*(b^2+-4*a*c)^(1/2)*(3*b^2+-10*a*c)+-16*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^11*(a+b*x^2+c*x^4)^-3, x) == :(1//4*c^-3*log(a+b*x^2+c*x^4)+x^8*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+(1/2)*b*c^-3*(b^2+-4*a*c)^-5//2*(b^4+30*a^2*c^2+-10*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*b*c^-2*x^2*(b^2+-4*a*c)^-2*(b^2+-7*a*c)+1//4*c^-1*x^4*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(a*(b^2+-16*a*c)+b*x^2*(b^2+-10*a*c)))
@test integrate(x^9*(a+b*x^2+c*x^4)^-3, x) == :(-6*a^2*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+x^6*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+-3//2*a*x^2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(2a+b*x^2))
@test integrate(x^7*(a+b*x^2+c*x^4)^-3, x) == :(-1*x^6*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b+2*c*x^2)+3*a*b*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+3//4*b*x^2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(2a+b*x^2))
@test integrate(x^5*(a+b*x^2+c*x^4)^-3, x) == :((1/2)*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(b^2+2*a*c)+3*a*b)+-1*(b^2+-4*a*c)^-5//2*(b^2+2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+x^2*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2))
@test integrate(x^3*(a+b*x^2+c*x^4)^-3, x) == :((4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+3*b*c*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-3//4*b*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2))
@test integrate(x*(a+b*x^2+c*x^4)^-3, x) == :(-1*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b+2*c*x^2)+-6*c^2*(b^2+-4*a*c)^-5//2*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+3//2*c*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-3, x) == :(a^-3*log(x)+-1//4*a^-3*log(a+b*x^2+c*x^4)+1//4*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b^2+-2*a*c+b*c*x^2)+1//4*a^-2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(2*b^4+16*a^2*c^2+-15*a*c*b^2+2*b*c*x^2*(b^2+-7*a*c))+(1/2)*b*a^-3*(b^2+-4*a*c)^-5//2*(b^4+30*a^2*c^2+-10*a*c*b^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-3, x) == :(-3*b*a^-4*log(x)+3//4*b*a^-4*log(a+b*x^2+c*x^4)+-1//2*a^-4*(b^2+-4*a*c)^-5//2*(3*b^6+-60*a^3*c^3+-30*a*c*b^4+90*a^2*b^2*c^2)*arctanh((b^2+-4*a*c)^-1//2*(b+2*c*x^2))+-1//2*a^-3*x^-2*(b^2+-4*a*c)^-2*(b^2+-2*a*c)*(3*b^2+-15*a*c)+1//4*a^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b^2+-2*a*c+b*c*x^2)+1//4*a^-2*x^-2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(3*b^4+20*a^2*c^2+-20*a*c*b^2+3*b*c*x^2*(b^2+-6*a*c)))
@test integrate(x^10*(a+b*x^2+c*x^4)^-3, x) == :(x^7*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+1//8*c^-1*x^3*(b^2+-4*a*c)^-2*(b^2+-28*a*c)+1//8*x^5*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(-1*x^2*(b^2+-28*a*c)+12*a*b)+-3//8*b*x*c^-2*(b^2+-4*a*c)^-2*(b^2+-8*a*c)+1//16*2^(1/2)*c^-5//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(3*b^4+3*(b^2+-4*a*c)^-1//2*(b^5+-11*a*c*b^3+44*b*a^2*c^2)+84*a^2*c^2+-27*a*c*b^2)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*c^-5//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(3*b^4+-3*(b^2+-4*a*c)^-1//2*(b^5+-11*a*c*b^3+44*b*a^2*c^2)+84*a^2*c^2+-27*a*c*b^2)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^8*(a+b*x^2+c*x^4)^-3, x) == :(x^5*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+-1//8*x*c^-1*(b^2+-4*a*c)^-2*(b^2+20*a*c)+1//8*x^3*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(b^2+20*a*c)+12*a*b)+1//16*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^3+(b^2+-4*a*c)^-1//2*(b^4+-40*a^2*c^2+-18*a*c*b^2)+-16*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^3+-1*(b^2+-4*a*c)^-1//2*(b^4+-40*a^2*c^2+-18*a*c*b^2)+-16*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^6*(a+b*x^2+c*x^4)^-3, x) == :(x^3*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+3//8*x*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(b^2+4*a*c)+4*a*b)+1//16*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(3*b^2+12*a*c+3*b*(b^2+-4*a*c)^-1//2*(b^2+12*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(3*b^2+12*a*c+-3*b*(b^2+-4*a*c)^-1//2*(b^2+12*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-3, x) == :(x*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+-1//8*x*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(7*b^2+-4*a*c+12*b*c*x^2)+-3//8*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(3*b^2+2*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+3//8*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(3*b^2+-2*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-3, x) == :(-1*x*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b+2*c*x^2)+1//8*x*a^-1*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b*(b^2+8*a*c)+c*x^2*(b^2+20*a*c))+1//16*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^2+20*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-52*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+1//16*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^2+20*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-52*a*c))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+b*x^2+c*x^4)^-3, x) == :(1//4*x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b^2+-2*a*c+b*c*x^2)+1//8*x*a^-2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*((b^2+-7*a*c)*(3*b^2+-4*a*c)+3*b*c*x^2*(b^2+-8*a*c))+3//16*2^(1/2)*a^-2*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*(b^3+-1*(b^2+-4*a*c)^-1//2*(b^4+56*a^2*c^2+-10*a*c*b^2)+-8*a*b*c)*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+3//16*2^(1/2)*a^-2*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-5//2*(b^4+56*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(b^2+-8*a*c)+-10*a*c*b^2)*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-3, x) == :(-1//8*a^-3*x^-1*(b^2+-4*a*c)^-2*(b^2+-5*a*c)*(15*b^2+-36*a*c)+1//4*a^-1*x^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b^2+-2*a*c+b*c*x^2)+1//8*a^-2*x^-1*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(5*b^4+36*a^2*c^2+-35*a*c*b^2+b*c*x^2*(5*b^2+-32*a*c))+-3//16*2^(1/2)*a^-3*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-5*a*c)*(5*b^2+-12*a*c)+-1*(b^2+-4*a*c)^-1//2*(5*b^5+-47*a*c*b^3+124*b*a^2*c^2))*arctan(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-3//16*2^(1/2)*a^-3*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-2*((b^2+-5*a*c)*(5*b^2+-12*a*c)+b*(b^2+-4*a*c)^-1//2*(5*b^4+124*a^2*c^2+-47*a*c*b^2))*arctan(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^5*(a+c*x^4+-1*b*x^2)^-1, x) == :((1/2)*c^-1*x^2+1//4*b*c^-2*log(a+c*x^4+-1*b*x^2)+(1/2)*c^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+-2*c*x^2)))
@test integrate(x^3*(a+c*x^4+-1*b*x^2)^-1, x) == :(1//4*c^-1*log(a+c*x^4+-1*b*x^2)+(1/2)*b*c^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+-2*c*x^2)))
@test integrate(x*(a+c*x^4+-1*b*x^2)^-1, x) == :((b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+-2*c*x^2)))
@test integrate(x^-1*(a+c*x^4+-1*b*x^2)^-1, x) == :(a^-1*log(x)+-1//4*a^-1*log(a+c*x^4+-1*b*x^2)+(1/2)*b*a^-1*(b^2+-4*a*c)^-1//2*arctanh((b^2+-4*a*c)^-1//2*(b+-2*c*x^2)))
@test integrate(x^-3*(a+c*x^4+-1*b*x^2)^-1, x) == :(-1//2*a^-1*x^-2+b*a^-2*log(x)+-1//4*b*a^-2*log(a+c*x^4+-1*b*x^2)+(1/2)*a^-2*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c)*arctanh((b^2+-4*a*c)^-1//2*(b+-2*c*x^2)))
@test integrate(x^4*(a+c*x^4+-1*b*x^2)^-1, x) == :(x*c^-1+-1//2*2^(1/2)*c^-3//2*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-3//2*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^2*(a+c*x^4+-1*b*x^2)^-1, x) == :((1/2)*2^(1/2)*c^-1//2*(b+-1*(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctanh(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+-1//2*2^(1/2)*c^-1//2*(b+(b^2+-4*a*c)^(1/2))^(1/2)*(b^2+-4*a*c)^-1//2*arctanh(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate((a+c*x^4+-1*b*x^2)^-1, x) == :(2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctanh(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2)+-1*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(b^2+-4*a*c)^-1//2*arctanh(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^-2*(a+c*x^4+-1*b*x^2)^-1, x) == :(-1*a^-1*x^-1+(1/2)*2^(1/2)*a^-1*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctanh(x*2^(1/2)*c^(1/2)*(b+(b^2+-4*a*c)^(1/2))^-1//2)+(1/2)*2^(1/2)*a^-1*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2*(1+b*(b^2+-4*a*c)^-1//2)*arctanh(x*2^(1/2)*c^(1/2)*(b+-1*(b^2+-4*a*c)^(1/2))^-1//2))
@test integrate(x^5*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :((1/2)*a^-1*x^2+-1//2*a^-1*log(a+-1b+a*x^4+2*a*x^2)+-1//2*a^-3//2*b^-1//2*(a+b)*arctanh(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^3*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :(1//4*a^-1*log(a+-1b+a*x^4+2*a*x^2)+(1/2)*a^-1//2*b^-1//2*arctanh(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :(-1//2*a^-1//2*b^-1//2*arctanh(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^-1*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :((a+-1b)^-1*log(x)+-1*(-4b+4a)^-1*log(a+-1b+a*x^4+2*a*x^2)+a^(1/2)*b^-1//2*(-2b+2a)^-1*arctanh(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^-3*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :(-1*x^-2*(-2b+2a)^-1+(1/2)*a*(a+-1b)^-2*log(a+-1b+a*x^4+2*a*x^2)+-2*a*(a+-1b)^-2*log(x)+-1//2*a^(1/2)*b^-1//2*(a+-1b)^-2*(a+b)*arctanh(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^4*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :(x*a^-1+(1/2)*a^-5//4*b^-1//2*(a^(1/2)+-1*b^(1/2))^3//2*arctan(x*a^1//4*(a^(1/2)+-1*b^(1/2))^-1//2)+-1//2*a^-5//4*b^-1//2*(a^(1/2)+b^(1/2))^3//2*arctan(x*a^1//4*(a^(1/2)+b^(1/2))^-1//2))
@test integrate(x^2*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :((1/2)*a^-3//4*b^-1//2*(a^(1/2)+b^(1/2))^(1/2)*arctan(x*a^1//4*(a^(1/2)+b^(1/2))^-1//2)+-1//2*a^-3//4*b^-1//2*(a^(1/2)+-1*b^(1/2))^(1/2)*arctan(x*a^1//4*(a^(1/2)+-1*b^(1/2))^-1//2))
@test integrate((a+-1b+a*x^4+2*a*x^2)^-1, x) == :((1/2)*a^-1//4*b^-1//2*(a^(1/2)+-1*b^(1/2))^-1//2*arctan(x*a^1//4*(a^(1/2)+-1*b^(1/2))^-1//2)+-1//2*a^-1//4*b^-1//2*(a^(1/2)+b^(1/2))^-1//2*arctan(x*a^1//4*(a^(1/2)+b^(1/2))^-1//2))
@test integrate(x^-2*(a+-1b+a*x^4+2*a*x^2)^-1, x) == :(-1*x^-1*(a+-1b)^-1+(1/2)*a^1//4*b^-1//2*(a^(1/2)+b^(1/2))^-3//2*arctan(x*a^1//4*(a^(1/2)+b^(1/2))^-1//2)+-1//2*a^1//4*b^-1//2*(a^(1/2)+-1*b^(1/2))^-3//2*arctan(x*a^1//4*(a^(1/2)+-1*b^(1/2))^-1//2))
@test integrate(x^5*(a+b+a*x^4+2*a*x^2)^-1, x) == :((1/2)*a^-1*x^2+-1//2*a^-1*log(a+b+a*x^4+2*a*x^2)+(1/2)*a^-3//2*b^-1//2*(a+-1b)*arctan(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^3*(a+b+a*x^4+2*a*x^2)^-1, x) == :(1//4*a^-1*log(a+b+a*x^4+2*a*x^2)+-1//2*a^-1//2*b^-1//2*arctan(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x*(a+b+a*x^4+2*a*x^2)^-1, x) == :((1/2)*a^-1//2*b^-1//2*arctan(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^-1*(a+b+a*x^4+2*a*x^2)^-1, x) == :((a+b)^-1*log(x)+-1*(4a+4b)^-1*log(a+b+a*x^4+2*a*x^2)+-1//2*a^(1/2)*b^-1//2*(a+b)^-1*arctan(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^-3*(a+b+a*x^4+2*a*x^2)^-1, x) == :(-1*x^-2*(2a+2b)^-1+(1/2)*a*(a+b)^-2*log(a+b+a*x^4+2*a*x^2)+-2*a*(a+b)^-2*log(x)+(1/2)*a^(1/2)*b^-1//2*(a+b)^-2*(a+-1b)*arctan(a^(1/2)*b^-1//2*(1+x^2)))
@test integrate(x^4*(a+b+a*x^4+2*a*x^2)^-1, x) == :(x*a^-1+-1//4*2^(1/2)*a^-5//4*(a+b)^-1//2*(a^(1/2)+(a+b)^(1/2))^-1//2*(a+b+2*a^(1/2)*(a+b)^(1/2))*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+x*2^(1/2)*a^1//4))+-1//8*2^(1/2)*a^-5//4*(a+b)^-1//2*((a+b)^(1/2)+-1*a^(1/2))^-1//2*(a+b+-2*a^(1/2)*(a+b)^(1/2))*log((a+b)^(1/2)+a^(1/2)*x^2+x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2))+1//4*2^(1/2)*a^-5//4*(a+b)^-1//2*(a^(1/2)+(a+b)^(1/2))^-1//2*(a+b+2*a^(1/2)*(a+b)^(1/2))*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+-1*x*2^(1/2)*a^1//4))+1//8*2^(1/2)*a^-5//4*(a+b)^-1//2*((a+b)^(1/2)+-1*a^(1/2))^-1//2*(a+b+-2*a^(1/2)*(a+b)^(1/2))*log((a+b)^(1/2)+a^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2)))
@test integrate(x^2*(a+b+a*x^4+2*a*x^2)^-1, x) == :(-1//4*2^(1/2)*a^-3//4*(a^(1/2)+(a+b)^(1/2))^-1//2*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+-1*x*2^(1/2)*a^1//4))+-1//8*2^(1/2)*a^-3//4*((a+b)^(1/2)+-1*a^(1/2))^-1//2*log((a+b)^(1/2)+a^(1/2)*x^2+x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2))+1//4*2^(1/2)*a^-3//4*(a^(1/2)+(a+b)^(1/2))^-1//2*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+x*2^(1/2)*a^1//4))+1//8*2^(1/2)*a^-3//4*((a+b)^(1/2)+-1*a^(1/2))^-1//2*log((a+b)^(1/2)+a^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2)))
@test integrate((a+b+a*x^4+2*a*x^2)^-1, x) == :(-1//4*2^(1/2)*a^-1//4*(a+b)^-1//2*(a^(1/2)+(a+b)^(1/2))^-1//2*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+-1*x*2^(1/2)*a^1//4))+-1//8*2^(1/2)*a^-1//4*(a+b)^-1//2*((a+b)^(1/2)+-1*a^(1/2))^-1//2*log((a+b)^(1/2)+a^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2))+1//4*2^(1/2)*a^-1//4*(a+b)^-1//2*(a^(1/2)+(a+b)^(1/2))^-1//2*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+x*2^(1/2)*a^1//4))+1//8*2^(1/2)*a^-1//4*(a+b)^-1//2*((a+b)^(1/2)+-1*a^(1/2))^-1//2*log((a+b)^(1/2)+a^(1/2)*x^2+x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2)))
@test integrate(x^-2*(a+b+a*x^4+2*a*x^2)^-1, x) == :(-1*x^-1*(a+b)^-1+-1//4*2^(1/2)*a^1//4*(a+b)^-3//2*(a^(1/2)+(a+b)^(1/2))^-1//2*((a+b)^(1/2)+2*a^(1/2))*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+x*2^(1/2)*a^1//4))+-1//8*2^(1/2)*a^1//4*(a+b)^-3//2*((a+b)^(1/2)+-1*a^(1/2))^-1//2*(-1*(a+b)^(1/2)+2*a^(1/2))*log((a+b)^(1/2)+a^(1/2)*x^2+x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2))+1//4*2^(1/2)*a^1//4*(a+b)^-3//2*(a^(1/2)+(a+b)^(1/2))^-1//2*((a+b)^(1/2)+2*a^(1/2))*arctan((a^(1/2)+(a+b)^(1/2))^-1//2*(((a+b)^(1/2)+-1*a^(1/2))^(1/2)+-1*x*2^(1/2)*a^1//4))+1//8*2^(1/2)*a^1//4*(a+b)^-3//2*((a+b)^(1/2)+-1*a^(1/2))^-1//2*(-1*(a+b)^(1/2)+2*a^(1/2))*log((a+b)^(1/2)+a^(1/2)*x^2+-1*x*2^(1/2)*a^1//4*((a+b)^(1/2)+-1*a^(1/2))^(1/2)))
@test integrate(x*(1+x^2+x^4)^-1, x) == :(1//3*3^(1/2)*arctan(1//3*3^(1/2)*(1+2*x^2)))
@test integrate(x*(10+x^4+2*x^2)^-1, x) == :(1//6*arctan(1//3+1//3*x^2))
@test integrate(x^2*(20+x^4+9*x^2)^-1, x) == :(-2*arctan((1/2)*x)+5^(1/2)*arctan(1//5*x*5^(1/2)))
@test integrate(x^2*(1+x^4+-1*x^2)^-1, x) == :((1/2)*arctan(3^(1/2)+2x)+-1//2*arctan(3^(1/2)+-2x)+-1//12*3^(1/2)*log(1+x^2+x*3^(1/2))+1//12*3^(1/2)*log(1+x^2+-1*x*3^(1/2)))
@test integrate(x^2*(2+x^4+-2*x^2)^-1, x) == :((1/2)*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+2x))+-1//2*(1/2+(1/2)*2^(1/2))^(1/2)*arctan((-2+2*2^(1/2))^-1//2*((2+2*2^(1/2))^(1/2)+-2x))+-1//4*(2+2*2^(1/2))^-1//2*log(2^(1/2)+x^2+x*(2+2*2^(1/2))^(1/2))+1//4*(2+2*2^(1/2))^-1//2*log(2^(1/2)+x^2+-1*x*(2+2*2^(1/2))^(1/2)))
@test integrate(x^7*(a+b*x^2+c*x^4)^(1/2), x) == :(1//10*c^-1*x^4*(a+b*x^2+c*x^4)^3//2+1//480*c^-3*(a+b*x^2+c*x^4)^3//2*(35*b^2+-32*a*c+-42*b*c*x^2)+-1//256*b*c^-4*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)*(7*b^2+-12*a*c)+1//512*b*c^-9//2*(b^2+-4*a*c)*(7*b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(a+b*x^2+c*x^4)^(1/2), x) == :(-5//48*b*c^-2*(a+b*x^2+c*x^4)^3//2+1//8*c^-1*x^2*(a+b*x^2+c*x^4)^3//2+-1//256*c^-7//2*(b^2+-4*a*c)*(5*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//128*c^-3*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)*(5*b^2+-4*a*c))
@test integrate(x^3*(a+b*x^2+c*x^4)^(1/2), x) == :(1//6*c^-1*(a+b*x^2+c*x^4)^3//2+-1//16*b*c^-2*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)+1//32*b*c^-5//2*(b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//16*c^-3//2*(b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+1//8*c^-1*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2))
@test integrate(x^-1*(a+b*x^2+c*x^4)^(1/2), x) == :((1/2)*(a+b*x^2+c*x^4)^(1/2)+-1//2*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//4*b*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^(1/2), x) == :((1/2)*c^(1/2)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//2*x^-2*(a+b*x^2+c*x^4)^(1/2)+-1//4*b*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)))
@test integrate(x^-5*(a+b*x^2+c*x^4)^(1/2), x) == :(1//16*a^-3//2*(b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//8*a^-1*x^-4*(a+b*x^2+c*x^4)^(1/2)*(2a+b*x^2))
@test integrate(x^-7*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//6*a^-1*x^-6*(a+b*x^2+c*x^4)^3//2+-1//32*b*a^-5//2*(b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//16*b*a^-2*x^-4*(a+b*x^2+c*x^4)^(1/2)*(2a+b*x^2))
@test integrate(x^-9*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//8*a^-1*x^-8*(a+b*x^2+c*x^4)^3//2+1//256*a^-7//2*(b^2+-4*a*c)*(5*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+5//48*b*a^-2*x^-6*(a+b*x^2+c*x^4)^3//2+-1//128*a^-3*x^-4*(a+b*x^2+c*x^4)^(1/2)*(2a+b*x^2)*(5*b^2+-4*a*c))
@test integrate(x^-11*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//10*a^-1*x^-10*(a+b*x^2+c*x^4)^3//2+-1//480*a^-3*x^-6*(a+b*x^2+c*x^4)^3//2*(35*b^2+-32*a*c)+7//80*b*a^-2*x^-8*(a+b*x^2+c*x^4)^3//2+-1//512*b*a^-9//2*(b^2+-4*a*c)*(7*b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//256*b*a^-4*x^-4*(a+b*x^2+c*x^4)^(1/2)*(2a+b*x^2)*(7*b^2+-12*a*c))
@test integrate(x^4*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//105*x*c^-2*(a+b*x^2+c*x^4)^(1/2)*(4*b^2+-10*a*c)+1//35*c^-1*x^3*(a+b*x^2+c*x^4)^(1/2)*(b+5*c*x^2)+1//105*b*x*c^-5//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(8*b^2+-29*a*c)+1//210*a^1//4*c^-11//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(8*b^3+-29*a*b*c+2*a^(1/2)*c^(1/2)*(2*b^2+-5*a*c))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-1//105*b*a^1//4*c^-11//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(8*b^2+-29*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^(1/2), x) == :(1//15*x*c^-1*(a+b*x^2+c*x^4)^(1/2)*(b+3*c*x^2)+-1//15*x*c^-3//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(2*b^2+-6*a*c)+-1//30*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2*b^2+-6*a*c+b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+2//15*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-3*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate((a+b*x^2+c*x^4)^(1/2), x) == :(1//3*x*(a+b*x^2+c*x^4)^(1/2)+1//3*b*x*c^-1//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+-1//3*b*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//6*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(b+2*a^(1/2)*c^(1/2))*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^(1/2), x) == :(-1*x^-1*(a+b*x^2+c*x^4)^(1/2)+2*x*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+-2*a^1//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+(1/2)*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(b+2*a^(1/2)*c^(1/2))*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//3*x^-3*(a+b*x^2+c*x^4)^(1/2)+-1//3*b*a^-1*x^-1*(a+b*x^2+c*x^4)^(1/2)+1//3*b*x*a^-1*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+-1//3*b*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//6*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(b+2*a^(1/2)*c^(1/2))*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-6*(a+b*x^2+c*x^4)^(1/2), x) == :(-1//5*x^-5*(a+b*x^2+c*x^4)^(1/2)+-1//15*b*a^-1*x^-3*(a+b*x^2+c*x^4)^(1/2)+1//15*a^-2*x^-1*(a+b*x^2+c*x^4)^(1/2)*(2*b^2+-6*a*c)+-2//15*x*a^-2*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+-3*a*c)+-1//30*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2*b^2+-6*a*c+b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+2//15*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-3*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^7*(a+b*x^2+c*x^4)^3//2, x) == :(1//14*c^-1*x^4*(a+b*x^2+c*x^4)^5//2+1//560*c^-3*(a+b*x^2+c*x^4)^5//2*(21*b^2+-16*a*c+-30*b*c*x^2)+-3//4096*b*c^-11//2*(b^2+-4*a*c)^2*(3*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//256*b*c^-4*(a+b*x^2+c*x^4)^3//2*(b+2*c*x^2)*(3*b^2+-4*a*c)+3//2048*b*c^-5*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)*(b^2+-4*a*c)*(3*b^2+-4*a*c))
@test integrate(x^5*(a+b*x^2+c*x^4)^3//2, x) == :(-7//120*b*c^-2*(a+b*x^2+c*x^4)^5//2+1//12*c^-1*x^2*(a+b*x^2+c*x^4)^5//2+1//384*c^-3*(a+b*x^2+c*x^4)^3//2*(b+2*c*x^2)*(7*b^2+-4*a*c)+1//2048*c^-9//2*(b^2+-4*a*c)^2*(7*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//1024*c^-4*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)*(b^2+-4*a*c)*(7*b^2+-4*a*c))
@test integrate(x^3*(a+b*x^2+c*x^4)^3//2, x) == :(1//10*c^-1*(a+b*x^2+c*x^4)^5//2+-3//512*b*c^-7//2*(b^2+-4*a*c)^2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//32*b*c^-2*(a+b*x^2+c*x^4)^3//2*(b+2*c*x^2)+3//256*b*c^-3*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)*(b^2+-4*a*c))
@test integrate(x*(a+b*x^2+c*x^4)^3//2, x) == :(1//16*c^-1*(a+b*x^2+c*x^4)^3//2*(b+2*c*x^2)+3//256*c^-5//2*(b^2+-4*a*c)^2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//128*c^-2*(a+b*x^2+c*x^4)^(1/2)*(b+2*c*x^2)*(3*b^2+-12*a*c))
@test integrate(x^-1*(a+b*x^2+c*x^4)^3//2, x) == :(1//6*(a+b*x^2+c*x^4)^3//2+-1//2*a^3//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//16*c^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+8*a*c+2*b*c*x^2)+-1//32*b*c^-3//2*(b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^3//2, x) == :((a+b*x^2+c*x^4)^(1/2)*(9//8*b+3//4*c*x^2)+-1//2*x^-2*(a+b*x^2+c*x^4)^3//2+-3//4*b*a^(1/2)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//16*c^-1//2*(3*b^2+12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-5*(a+b*x^2+c*x^4)^3//2, x) == :(-1//4*x^-4*(a+b*x^2+c*x^4)^3//2+-1//8*x^-2*(a+b*x^2+c*x^4)^(1/2)*(3b+-6*c*x^2)+-1//16*a^-1//2*(3*b^2+12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+3//4*b*c^(1/2)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-7*(a+b*x^2+c*x^4)^3//2, x) == :((1/2)*c^3//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+-1//6*x^-6*(a+b*x^2+c*x^4)^3//2+-1//16*a^-1*x^-4*(a+b*x^2+c*x^4)^(1/2)*(x^2*(b^2+8*a*c)+2*a*b)+1//32*b*a^-3//2*(b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)))
@test integrate(x^-9*(a+b*x^2+c*x^4)^3//2, x) == :(-3//256*a^-5//2*(b^2+-4*a*c)^2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+-1//16*a^-1*x^-8*(a+b*x^2+c*x^4)^3//2*(2a+b*x^2)+1//128*a^-2*x^-4*(a+b*x^2+c*x^4)^(1/2)*(2a+b*x^2)*(3*b^2+-12*a*c))
@test integrate(x^-11*(a+b*x^2+c*x^4)^3//2, x) == :(-1//10*a^-1*x^-10*(a+b*x^2+c*x^4)^5//2+3//512*b*a^-7//2*(b^2+-4*a*c)^2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+1//32*b*a^-2*x^-8*(a+b*x^2+c*x^4)^3//2*(2a+b*x^2)+-3//256*b*a^-3*x^-4*(a+b*x^2+c*x^4)^(1/2)*(b^2+-4*a*c)*(2a+b*x^2))
@test integrate(x^-13*(a+b*x^2+c*x^4)^3//2, x) == :(-1//12*a^-1*x^-12*(a+b*x^2+c*x^4)^5//2+-1//2048*a^-9//2*(b^2+-4*a*c)^2*(7*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+7//120*b*a^-2*x^-10*(a+b*x^2+c*x^4)^5//2+-1//384*a^-3*x^-8*(a+b*x^2+c*x^4)^3//2*(2a+b*x^2)*(7*b^2+-4*a*c)+1//1024*a^-4*x^-4*(a+b*x^2+c*x^4)^(1/2)*(b^2+-4*a*c)*(2a+b*x^2)*(7*b^2+-4*a*c))
@test integrate(x^4*(a+b*x^2+c*x^4)^3//2, x) == :(-1//385*c^-2*x^3*(a+b*x^2+c*x^4)^(1/2)*(b*(2*b^2+a*c)+10*c*x^2*(b^2+-3*a*c))+1//33*c^-1*x^3*(a+b*x^2+c*x^4)^3//2*(b+3*c*x^2)+1//1155*x*c^-3*(a+b*x^2+c*x^4)^(1/2)*(8*b^4+60*a^2*c^2+-51*a*c*b^2)+-8//1155*b*x*c^-7//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+-3*a*c)*(2*b^2+-9*a*c)+-1//2310*a^1//4*c^-15//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(a^(1/2)*c^(1/2)*(8*b^4+60*a^2*c^2+-51*a*c*b^2)+8*b*(b^2+-3*a*c)*(2*b^2+-9*a*c))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+8//1155*b*a^1//4*c^-15//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-3*a*c)*(2*b^2+-9*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^3//2, x) == :(-1//315*x*c^-2*(a+b*x^2+c*x^4)^(1/2)*(b*(4*b^2+-9*a*c)+6*c*x^2*(2*b^2+-7*a*c))+1//63*x*c^-1*(a+b*x^2+c*x^4)^3//2*(3b+7*c*x^2)+1//315*x*c^-5//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(8*b^4+84*a^2*c^2+-57*a*c*b^2)+-1//315*a^1//4*c^-11//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(8*b^4+84*a^2*c^2+-57*a*c*b^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//630*a^1//4*c^-11//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(8*b^4+84*a^2*c^2+-57*a*c*b^2+4*b*a^(1/2)*c^(1/2)*(b^2+-6*a*c))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate((a+b*x^2+c*x^4)^3//2, x) == :(1//7*x*(a+b*x^2+c*x^4)^3//2+1//35*x*c^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+10*a*c+3*b*c*x^2)+-2//35*b*x*c^-3//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+-8*a*c)+-1//70*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2*b*(b^2+-8*a*c)+a^(1/2)*c^(1/2)*(b^2+-20*a*c))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+2//35*b*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-8*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^3//2, x) == :(-1*x^-1*(a+b*x^2+c*x^4)^3//2+1//5*x*(a+b*x^2+c*x^4)^(1/2)*(7b+6*c*x^2)+1//5*x*c^-1//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+12*a*c)+-1//5*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+12*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//10*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+12*a*c+8*b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^3//2, x) == :(-1//3*x^-3*(a+b*x^2+c*x^4)^3//2+-1//3*x^-1*(a+b*x^2+c*x^4)^(1/2)*(3b+-2*c*x^2)+8*b*x*c^(1/2)*(3*a^(1/2)+3*c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+-8//3*b*a^1//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//6*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(3*b^2+4*a*c+8*b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-6*(a+b*x^2+c*x^4)^3//2, x) == :(-1//5*x^-5*(a+b*x^2+c*x^4)^3//2+-1//5*x^-3*(a+b*x^2+c*x^4)^(1/2)*(b+-6*c*x^2)+-1//5*a^-1*x^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+12*a*c)+1//5*x*a^-1*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+12*a*c)+-1//5*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+12*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+1//10*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+12*a*c+8*b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-8*(a+b*x^2+c*x^4)^3//2, x) == :(-1//7*x^-7*(a+b*x^2+c*x^4)^3//2+-1//35*x^-5*(a+b*x^2+c*x^4)^(1/2)*(3b+30*c*x^2)+-1//35*a^-1*x^-3*(a+b*x^2+c*x^4)^(1/2)*(b^2+-20*a*c)+2//35*b*a^-2*x^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+-8*a*c)+-2//35*b*x*a^-2*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+-8*a*c)+-1//70*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2*b*(b^2+-8*a*c)+a^(1/2)*c^(1/2)*(b^2+-20*a*c))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+2//35*b*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-8*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate((3+-1*x^4+-2*x^2)^(1/2), x) == :(-2//3*3^(1/2)*Elliptic.E(arcsin(x),-1//3)+1//3*x*(3+-1*x^4+-2*x^2)^(1/2)+4//3*3^(1/2)*Elliptic.F(arcsin(x),-1//3))
@test integrate(x^7*(a+b*x^2+c*x^4)^-1//2, x) == :(1//6*c^-1*x^4*(a+b*x^2+c*x^4)^(1/2)+1//48*c^-3*(a+b*x^2+c*x^4)^(1/2)*(15*b^2+-16*a*c+-10*b*c*x^2)+-1//32*b*c^-7//2*(5*b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^5*(a+b*x^2+c*x^4)^-1//2, x) == :(-3//8*b*c^-2*(a+b*x^2+c*x^4)^(1/2)+1//4*c^-1*x^2*(a+b*x^2+c*x^4)^(1/2)+1//16*c^-5//2*(3*b^2+-4*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^3*(a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*c^-1*(a+b*x^2+c*x^4)^(1/2)+-1//4*b*c^-3//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x*(a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*c^-1//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-1//2, x) == :(-1//2*a^-1//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-1//2, x) == :(-1//2*a^-1*x^-2*(a+b*x^2+c*x^4)^(1/2)+1//4*b*a^-3//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)))
@test integrate(x^-5*(a+b*x^2+c*x^4)^-1//2, x) == :(-1//4*a^-1*x^-4*(a+b*x^2+c*x^4)^(1/2)+-1//16*a^-5//2*(3*b^2+-4*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+3//8*b*a^-2*x^-2*(a+b*x^2+c*x^4)^(1/2))
@test integrate(x^-7*(a+b*x^2+c*x^4)^-1//2, x) == :(-1//6*a^-1*x^-6*(a+b*x^2+c*x^4)^(1/2)+-1//48*a^-3*x^-2*(a+b*x^2+c*x^4)^(1/2)*(15*b^2+-16*a*c)+1//32*b*a^-7//2*(5*b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+5//24*b*a^-2*x^-4*(a+b*x^2+c*x^4)^(1/2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-1//2, x) == :(1//3*x*c^-1*(a+b*x^2+c*x^4)^(1/2)+-2//3*b*x*c^-3//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+-1//6*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2b+a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+2//3*b*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-1//2, x) == :(x*c^-1//2*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-1*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate((a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-1//2, x) == :(-1*a^-1*x^-1*(a+b*x^2+c*x^4)^(1/2)+x*a^-1*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-1*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-4*(a+b*x^2+c*x^4)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^2+c*x^4)^(1/2)+2//3*b*a^-2*x^-1*(a+b*x^2+c*x^4)^(1/2)+-2//3*b*x*a^-2*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(a+b*x^2+c*x^4)^(1/2)+-1//6*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2b+a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+2//3*b*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^7*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1//6*c^-1*x^4*(a+b*x^2+-1*c*x^4)^(1/2)+-1//48*c^-3*(a+b*x^2+-1*c*x^4)^(1/2)*(15*b^2+16*a*c+10*b*c*x^2)+-1//32*b*c^-7//2*(5*b^2+12*a*c)*arctan((1/2)*c^-1//2*(a+b*x^2+-1*c*x^4)^-1//2*(b+-2*c*x^2)))
@test integrate(x^5*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-3//8*b*c^-2*(a+b*x^2+-1*c*x^4)^(1/2)+-1//4*c^-1*x^2*(a+b*x^2+-1*c*x^4)^(1/2)+-1//16*c^-5//2*(3*b^2+4*a*c)*arctan((1/2)*c^-1//2*(a+b*x^2+-1*c*x^4)^-1//2*(b+-2*c*x^2)))
@test integrate(x^3*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1//2*c^-1*(a+b*x^2+-1*c*x^4)^(1/2)+-1//4*b*c^-3//2*arctan((1/2)*c^-1//2*(a+b*x^2+-1*c*x^4)^-1//2*(b+-2*c*x^2)))
@test integrate(x*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1//2*c^-1//2*arctan((1/2)*c^-1//2*(a+b*x^2+-1*c*x^4)^-1//2*(b+-2*c*x^2)))
@test integrate(x^-1*(-1a+b*x^2+c*x^4)^-1//2, x) == :(-1//2*a^-1//2*arctan((1/2)*a^-1//2*(-1a+b*x^2+c*x^4)^-1//2*(2a+-1*b*x^2)))
@test integrate(x^-3*(-1a+b*x^2+c*x^4)^-1//2, x) == :((1/2)*a^-1*x^-2*(-1a+b*x^2+c*x^4)^(1/2)+-1//4*b*a^-3//2*arctan((1/2)*a^-1//2*(-1a+b*x^2+c*x^4)^-1//2*(2a+-1*b*x^2)))
@test integrate(x^-5*(-1a+b*x^2+c*x^4)^-1//2, x) == :(-1//16*a^-5//2*(3*b^2+4*a*c)*arctan((1/2)*a^-1//2*(-1a+b*x^2+c*x^4)^-1//2*(2a+-1*b*x^2))+1//4*a^-1*x^-4*(-1a+b*x^2+c*x^4)^(1/2)+3//8*b*a^-2*x^-2*(-1a+b*x^2+c*x^4)^(1/2))
@test integrate(x^-7*(-1a+b*x^2+c*x^4)^-1//2, x) == :(1//6*a^-1*x^-6*(-1a+b*x^2+c*x^4)^(1/2)+-1//32*b*a^-7//2*(5*b^2+12*a*c)*arctan((1/2)*a^-1//2*(-1a+b*x^2+c*x^4)^-1//2*(2a+-1*b*x^2))+1//48*a^-3*x^-2*(-1a+b*x^2+c*x^4)^(1/2)*(15*b^2+16*a*c)+5//24*b*a^-2*x^-4*(-1a+b*x^2+c*x^4)^(1/2))
@test integrate(x^4*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1//3*x*c^-1*(a+b*x^2+-1*c*x^4)^(1/2)+1//6*2^(1/2)*c^-5//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b^2+a*c+-1*b*(b^2+4*a*c)^(1/2))*Elliptic.F(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2)))+-1//6*b*2^(1/2)*c^-5//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b+-1*(b^2+4*a*c)^(1/2))*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2))))
@test integrate(x^2*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1//4*2^(1/2)*c^-3//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b+-1*(b^2+4*a*c)^(1/2))*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2)))+1//4*2^(1/2)*c^-3//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b+-1*(b^2+4*a*c)^(1/2))*Elliptic.F(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2))))
@test integrate((a+b*x^2+-1*c*x^4)^-1//2, x) == :((1/2)*2^(1/2)*c^-1//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*Elliptic.F(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2))))
@test integrate(x^-2*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1*a^-1*x^-1*(a+b*x^2+-1*c*x^4)^(1/2)+-1//4*2^(1/2)*a^-1*c^-1//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b+-1*(b^2+4*a*c)^(1/2))*Elliptic.F(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2)))+1//4*2^(1/2)*a^-1*c^-1//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b+-1*(b^2+4*a*c)^(1/2))*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2))))
@test integrate(x^-4*(a+b*x^2+-1*c*x^4)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^2+-1*c*x^4)^(1/2)+2//3*b*a^-2*x^-1*(a+b*x^2+-1*c*x^4)^(1/2)+1//6*2^(1/2)*a^-2*c^-1//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b^2+a*c+-1*b*(b^2+4*a*c)^(1/2))*Elliptic.F(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2)))+-1//6*b*2^(1/2)*a^-2*c^-1//2*(1+-2*c*x^2*(b+(b^2+4*a*c)^(1/2))^-1)^(1/2)*(1+-2*c*x^2*(b+-1*(b^2+4*a*c)^(1/2))^-1)^(1/2)*(b+(b^2+4*a*c)^(1/2))^(1/2)*(a+b*x^2+-1*c*x^4)^-1//2*(b+-1*(b^2+4*a*c)^(1/2))*Elliptic.E(arcsin(x*2^(1/2)*c^(1/2)*(b+(b^2+4*a*c)^(1/2))^-1//2),(b+-1*(b^2+4*a*c)^(1/2))^-1*(b+(b^2+4*a*c)^(1/2))))
@test integrate(x^9*(a+b*x^2+c*x^4)^-3//2, x) == :(1//16*c^-7//2*(15*b^2+-12*a*c)*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+x^6*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)+-1//8*c^-3*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(b*(15*b^2+-52*a*c)+-2*c*x^2*(5*b^2+-12*a*c))+-1*b*c^-1*x^4*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2))
@test integrate(x^7*(a+b*x^2+c*x^4)^-3//2, x) == :(-3//4*b*c^-5//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+x^4*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)+(1/2)*c^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(3*b^2+-8*a*c+-2*b*c*x^2))
@test integrate(x^5*(a+b*x^2+c*x^4)^-3//2, x) == :((1/2)*c^-3//2*arctanh((1/2)*c^-1//2*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))+x^2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)+-1*b*c^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2))
@test integrate(x^3*(a+b*x^2+c*x^4)^-3//2, x) == :((b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))
@test integrate(x*(a+b*x^2+c*x^4)^-3//2, x) == :(-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2))
@test integrate(x^-1*(a+b*x^2+c*x^4)^-3//2, x) == :(-1//2*a^-3//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2))
@test integrate(x^-3*(a+b*x^2+c*x^4)^-3//2, x) == :(3//4*b*a^-5//2*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+a^-1*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+-1//2*a^-2*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(3*b^2+-8*a*c))
@test integrate(x^-5*(a+b*x^2+c*x^4)^-3//2, x) == :(-1//16*a^-7//2*(15*b^2+-12*a*c)*arctanh((1/2)*a^-1//2*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2))+a^-1*x^-4*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+-1//4*a^-2*x^-4*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(5*b^2+-12*a*c)+1//8*b*a^-3*x^-2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(15*b^2+-52*a*c))
@test integrate(x^6*(a+b*x^2+c*x^4)^-3//2, x) == :(x^3*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)+-1*b*x*c^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)+x*c^-3//2*(a^(1/2)+c^(1/2)*x^2)^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(2*b^2+-6*a*c)+(1/2)*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2*b^2+-6*a*c+b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-2*a^1//4*c^-7//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-3*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^4*(a+b*x^2+c*x^4)^-3//2, x) == :(x*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(2a+b*x^2)+-1*b*x*c^-1//2*(a^(1/2)+c^(1/2)*x^2)^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)+-1*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(2b+-4*a^(1/2)*c^(1/2))^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+b*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^2*(a+b*x^2+c*x^4)^-3//2, x) == :(-1*x*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b+2*c*x^2)+2*x*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)+(1/2)*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b+-2*a^(1/2)*c^(1/2))^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-2*a^1//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate((a+b*x^2+c*x^4)^-3//2, x) == :(x*a^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+-1*b*x*a^-1*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)+-1//2*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b+-2*a^(1/2)*c^(1/2))^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+b*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^-2*(a+b*x^2+c*x^4)^-3//2, x) == :(a^-1*x^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(b^2+-2*a*c+b*c*x^2)+-1*a^-2*x^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(2*b^2+-6*a*c)+2*x*a^-2*c^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^(1/2)*(b^2+-3*a*c)+(1/2)*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(2*b^2+-6*a*c+b*a^(1/2)*c^(1/2))*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2)+-2*a^-7//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+b*x^2+c*x^4))^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*(b^2+-3*a*c)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2+-1//4*b*a^-1//2*c^-1//2))
@test integrate(x^4*(b*x^2+c*x^4)^-1//2, x) == :(1//3*x*c^-1*(b*x^2+c*x^4)^(1/2)+-2//3*b*c^-2*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate(x^3*(b*x^2+c*x^4)^-1//2, x) == :((1/2)*c^-1*(b*x^2+c*x^4)^(1/2)+-1//2*b*c^-3//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate(x^2*(b*x^2+c*x^4)^-1//2, x) == :(c^-1*x^-1*(b*x^2+c*x^4)^(1/2))
@test integrate(x*(b*x^2+c*x^4)^-1//2, x) == :(c^-1//2*arctanh(c^(1/2)*x^2*(b*x^2+c*x^4)^-1//2))
@test integrate((b*x^2+c*x^4)^-1//2, x) == :(-1*b^-1//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2))
@test integrate(x^-1*(b*x^2+c*x^4)^-1//2, x) == :(-1*b^-1*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-2*(b*x^2+c*x^4)^-1//2, x) == :((1/2)*c*b^-3//2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//2*b^-1*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-3*(b*x^2+c*x^4)^-1//2, x) == :(-1//3*b^-1*x^-4*(b*x^2+c*x^4)^(1/2)+2//3*c*b^-2*x^-2*(b*x^2+c*x^4)^(1/2))
@test integrate(x^-4*(b*x^2+c*x^4)^-1//2, x) == :(-3//8*b^-5//2*c^2*arctanh(x*b^(1/2)*(b*x^2+c*x^4)^-1//2)+-1//4*b^-1*x^-5*(b*x^2+c*x^4)^(1/2)+3//8*c*b^-2*x^-3*(b*x^2+c*x^4)^(1/2))
@test integrate(x^4*(a+c*x^4)^-1//2, x) == :(1//3*x*c^-1*(a+c*x^4)^(1/2)+-1//6*a^3//4*c^-5//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^3*(a+c*x^4)^-1//2, x) == :((1/2)*c^-1*(a+c*x^4)^(1/2))
@test integrate(x^2*(a+c*x^4)^-1//2, x) == :(x*c^-1//2*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+(1/2)*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2)+-1*a^1//4*c^-3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x*(a+c*x^4)^-1//2, x) == :((1/2)*c^-1//2*arctanh(c^(1/2)*x^2*(a+c*x^4)^-1//2))
@test integrate((a+c*x^4)^-1//2, x) == :((1/2)*a^-1//4*c^-1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-1*(a+c*x^4)^-1//2, x) == :(-1//2*a^-1//2*arctanh(a^-1//2*(a+c*x^4)^(1/2)))
@test integrate(x^-2*(a+c*x^4)^-1//2, x) == :(-1*a^-1*x^-1*(a+c*x^4)^(1/2)+x*a^-1*c^(1/2)*(a+c*x^4)^(1/2)*(a^(1/2)+c^(1/2)*x^2)^-1+(1/2)*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2)+-1*a^-3//4*c^1//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.E(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^-3*(a+c*x^4)^-1//2, x) == :(-1//2*a^-1*x^-2*(a+c*x^4)^(1/2))
@test integrate(x^-4*(a+c*x^4)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+c*x^4)^(1/2)+-1//6*a^-5//4*c^3//4*((a^(1/2)+c^(1/2)*x^2)^-2*(a+c*x^4))^(1/2)*(a+c*x^4)^-1//2*(a^(1/2)+c^(1/2)*x^2)*Elliptic.F(2*arctan(x*a^-1//4*c^1//4),1/2))
@test integrate(x^4*(a+b*x^2)^-1//2, x) == :(1//4*b^-1*x^3*(a+b*x^2)^(1/2)+3//8*a^2*b^-5//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2)+-3//8*a*x*b^-2*(a+b*x^2)^(1/2))
@test integrate(x^3*(a+b*x^2)^-1//2, x) == :(1//3*b^-2*(a+b*x^2)^3//2+-1*a*b^-2*(a+b*x^2)^(1/2))
@test integrate(x^2*(a+b*x^2)^-1//2, x) == :((1/2)*x*b^-1*(a+b*x^2)^(1/2)+-1//2*a*b^-3//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x*(a+b*x^2)^-1//2, x) == :(b^-1*(a+b*x^2)^(1/2))
@test integrate((a+b*x^2)^-1//2, x) == :(b^-1//2*arctanh(x*b^(1/2)*(a+b*x^2)^-1//2))
@test integrate(x^-1*(a+b*x^2)^-1//2, x) == :(-1*a^-1//2*arctanh(a^-1//2*(a+b*x^2)^(1/2)))
@test integrate(x^-2*(a+b*x^2)^-1//2, x) == :(-1*a^-1*x^-1*(a+b*x^2)^(1/2))
@test integrate(x^-3*(a+b*x^2)^-1//2, x) == :((1/2)*b*a^-3//2*arctanh(a^-1//2*(a+b*x^2)^(1/2))+-1//2*a^-1*x^-2*(a+b*x^2)^(1/2))
@test integrate(x^-4*(a+b*x^2)^-1//2, x) == :(-1//3*a^-1*x^-3*(a+b*x^2)^(1/2)+2//3*b*a^-2*x^-1*(a+b*x^2)^(1/2))
@test integrate(x^4*(c*x^4)^-1//2, x) == :(1//3*x^5*(c*x^4)^-1//2)
@test integrate(x^3*(c*x^4)^-1//2, x) == :((1/2)*x^4*(c*x^4)^-1//2)
@test integrate(x^2*(c*x^4)^-1//2, x) == :(x^3*(c*x^4)^-1//2)
@test integrate(x*(c*x^4)^-1//2, x) == :(x^2*(c*x^4)^-1//2*log(x))
@test integrate((c*x^4)^-1//2, x) == :(-1*x*(c*x^4)^-1//2)
@test integrate(x^-1*(c*x^4)^-1//2, x) == :(-1//2*(c*x^4)^-1//2)
@test integrate(x^-2*(c*x^4)^-1//2, x) == :(-1//3*x^-1*(c*x^4)^-1//2)
@test integrate(x^-3*(c*x^4)^-1//2, x) == :(-1//4*x^-2*(c*x^4)^-1//2)
@test integrate(x^-4*(c*x^4)^-1//2, x) == :(-1//5*x^-3*(c*x^4)^-1//2)
@test integrate(a^-1//2*x^4, x) == :(1//5*a^-1//2*x^5)
@test integrate(a^-1//2*x^3, x) == :(1//4*a^-1//2*x^4)
@test integrate(a^-1//2*x^2, x) == :(1//3*a^-1//2*x^3)
@test integrate(x*a^-1//2, x) == :((1/2)*a^-1//2*x^2)
@test integrate(a^-1//2, x) == :(x*a^-1//2)
@test integrate(a^-1//2*x^-1, x) == :(a^-1//2*log(x))
@test integrate(a^-1//2*x^-2, x) == :(-1*a^-1//2*x^-1)
@test integrate(a^-1//2*x^-3, x) == :(-1//2*a^-1//2*x^-2)
@test integrate(a^-1//2*x^-4, x) == :(-1//3*a^-1//2*x^-3)
@test integrate((3+-1*x^4+-2*x^2)^-1//2, x) == :(1//3*3^(1/2)*Elliptic.F(arcsin(x),-1//3))
@test integrate((-1+-1*x^4+5*x^2)^-1//2, x) == :(-1//21*21^3//4*Elliptic.F(arccos(x*2^(1/2)*(5+21^(1/2))^-1//2),1/2+5//42*21^(1/2)))
@test integrate(x^5//2*(a+b*x^2+c*x^4), x) == :(2//7*a*x^7//2+2//11*b*x^11//2+2//15*c*x^15//2)
@test integrate(x^3//2*(a+b*x^2+c*x^4), x) == :(2//5*a*x^5//2+2//9*b*x^9//2+2//13*c*x^13//2)
@test integrate(x^(1/2)*(a+b*x^2+c*x^4), x) == :(2//3*a*x^3//2+2//7*b*x^7//2+2//11*c*x^11//2)
@test integrate(x^-1//2*(a+b*x^2+c*x^4), x) == :(2*a*x^(1/2)+2//5*b*x^5//2+2//9*c*x^9//2)
@test integrate(x^-3//2*(a+b*x^2+c*x^4), x) == :(-2*a*x^-1//2+2//3*b*x^3//2+2//7*c*x^7//2)
@test integrate(x^-5//2*(a+b*x^2+c*x^4), x) == :(2*b*x^(1/2)+-2//3*a*x^-3//2+2//5*c*x^5//2)
@test integrate(x^-7//2*(a+b*x^2+c*x^4), x) == :(-2*b*x^-1//2+-2//5*a*x^-5//2+2//3*c*x^3//2)
@test integrate(x^5//2*(a+b*x^2+c*x^4)^2, x) == :(x^15//2*(2//15*b^2+4//15*a*c)+2//7*a^2*x^7//2+2//23*c^2*x^23//2+4//11*a*b*x^11//2+4//19*b*c*x^19//2)
@test integrate(x^3//2*(a+b*x^2+c*x^4)^2, x) == :(x^13//2*(2//13*b^2+4//13*a*c)+2//5*a^2*x^5//2+2//21*c^2*x^21//2+4//9*a*b*x^9//2+4//17*b*c*x^17//2)
@test integrate(x^(1/2)*(a+b*x^2+c*x^4)^2, x) == :(x^11//2*(2//11*b^2+4//11*a*c)+2//3*a^2*x^3//2+2//19*c^2*x^19//2+4//7*a*b*x^7//2+4//15*b*c*x^15//2)
@test integrate(x^-1//2*(a+b*x^2+c*x^4)^2, x) == :(x^9//2*(2//9*b^2+4//9*a*c)+2*a^2*x^(1/2)+2//17*c^2*x^17//2+4//5*a*b*x^5//2+4//13*b*c*x^13//2)
@test integrate(x^-3//2*(a+b*x^2+c*x^4)^2, x) == :(x^7//2*(2//7*b^2+4//7*a*c)+-2*a^2*x^-1//2+2//15*c^2*x^15//2+4//3*a*b*x^3//2+4//11*b*c*x^11//2)
@test integrate(x^-5//2*(a+b*x^2+c*x^4)^2, x) == :(x^5//2*(2//5*b^2+4//5*a*c)+-2//3*a^2*x^-3//2+2//13*c^2*x^13//2+4*a*b*x^(1/2)+4//9*b*c*x^9//2)
@test integrate(x^-7//2*(a+b*x^2+c*x^4)^2, x) == :(x^3//2*(2//3*b^2+4//3*a*c)+-2//5*a^2*x^-5//2+2//11*c^2*x^11//2+-4*a*b*x^-1//2+4//7*b*c*x^7//2)
@test integrate(x^5//2*(a+b*x^2+c*x^4)^3, x) == :(2//7*a^3*x^7//2+2//31*c^3*x^31//2+2//5*a*x^15//2*(b^2+a*c)+2//9*b*c^2*x^27//2+2//19*b*x^19//2*(b^2+6*a*c)+6//11*b*a^2*x^11//2+6//23*c*x^23//2*(b^2+a*c))
@test integrate(x^3//2*(a+b*x^2+c*x^4)^3, x) == :(2//5*a^3*x^5//2+2//29*c^3*x^29//2+2//3*b*a^2*x^9//2+2//7*c*x^21//2*(b^2+a*c)+2//17*b*x^17//2*(b^2+6*a*c)+6//13*a*x^13//2*(b^2+a*c)+6//25*b*c^2*x^25//2)
@test integrate(x^(1/2)*(a+b*x^2+c*x^4)^3, x) == :(2//3*a^3*x^3//2+2//27*c^3*x^27//2+2//15*b*x^15//2*(b^2+6*a*c)+6//7*b*a^2*x^7//2+6//11*a*x^11//2*(b^2+a*c)+6//19*c*x^19//2*(b^2+a*c)+6//23*b*c^2*x^23//2)
@test integrate(x^-1//2*(a+b*x^2+c*x^4)^3, x) == :(2*a^3*x^(1/2)+2//25*c^3*x^25//2+2//3*a*x^9//2*(b^2+a*c)+2//7*b*c^2*x^21//2+2//13*b*x^13//2*(b^2+6*a*c)+6//5*b*a^2*x^5//2+6//17*c*x^17//2*(b^2+a*c))
@test integrate(x^-3//2*(a+b*x^2+c*x^4)^3, x) == :(-2*a^3*x^-1//2+2//23*c^3*x^23//2+2*b*a^2*x^3//2+2//5*c*x^15//2*(b^2+a*c)+2//11*b*x^11//2*(b^2+6*a*c)+6//7*a*x^7//2*(b^2+a*c)+6//19*b*c^2*x^19//2)
@test integrate(x^-5//2*(a+b*x^2+c*x^4)^3, x) == :(-2//3*a^3*x^-3//2+2//21*c^3*x^21//2+6*b*a^2*x^(1/2)+2//9*b*x^9//2*(b^2+6*a*c)+6//5*a*x^5//2*(b^2+a*c)+6//13*c*x^13//2*(b^2+a*c)+6//17*b*c^2*x^17//2)
@test integrate(x^-7//2*(a+b*x^2+c*x^4)^3, x) == :(-2//5*a^3*x^-5//2+2//19*c^3*x^19//2+-6*b*a^2*x^-1//2+2*a*x^3//2*(b^2+a*c)+2//5*b*c^2*x^15//2+2//7*b*x^7//2*(b^2+6*a*c)+6//11*c*x^11//2*(b^2+a*c))
@test integrate(x^9//2*(a+b*x^2+c*x^4)^-1, x) == :(2//3*c^-1*x^3//2+(1/2)*2^1//4*c^-7//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^1//4*c^-7//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^1//4*c^-7//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^1//4*c^-7//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^7//2*(a+b*x^2+c*x^4)^-1, x) == :(2*c^-1*x^(1/2)+(1/2)*2^3//4*c^-5//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^3//4*c^-5//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^3//4*c^-5//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+(1/2)*2^3//4*c^-5//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^5//2*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^3//4*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^3//4*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^3//4*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^1//4*c^-3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^3//4*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^3//2*(a+b*x^2+c*x^4)^-1, x) == :((1/2)*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^1//4*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+(1/2)*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^1//4*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^1//4*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^3//4*c^-1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^1//4*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^(1/2)*(a+b*x^2+c*x^4)^-1, x) == :(2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1*2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1*2^1//4*c^1//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-1//2*(a+b*x^2+c*x^4)^-1, x) == :(2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1*2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1*2^3//4*c^3//4*(b^2+-4*a*c)^-1//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^-3//2*(a+b*x^2+c*x^4)^-1, x) == :(-2*a^-1*x^-1//2+(1/2)*2^1//4*a^-1*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(1+b*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^1//4*a^-1*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^1//4*a^-1*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(1+b*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^1//4*a^-1*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-5//2*(a+b*x^2+c*x^4)^-1, x) == :(-2//3*a^-1*x^-3//2+(1/2)*2^3//4*a^-1*c^3//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(1+b*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^3//4*a^-1*c^3//4*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(1+b*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^3//4*a^-1*c^3//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+(1/2)*2^3//4*a^-1*c^3//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(1+-1*b*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-7//2*(a+b*x^2+c*x^4)^-1, x) == :(-2//5*a^-1*x^-5//2+2*b*a^-2*x^-1//2+(1/2)*2^1//4*a^-2*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+(1/2)*2^1//4*a^-2*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//2*2^1//4*a^-2*c^1//4*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//2*2^1//4*a^-2*c^1//4*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-2*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^13//2*(a+b*x^2+c*x^4)^-2, x) == :(x^7//2*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1//2*b*c^-1*x^3//2*(b^2+-4*a*c)^-1+-1//8*2^1//4*c^-7//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(3*b^3+-1*(b^2+-4*a*c)^(1/2)*(3*b^2+-14*a*c)+-20*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^1//4*c^-7//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(3*b^3+(b^2+-4*a*c)^(1/2)*(3*b^2+-14*a*c)+-20*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//8*2^1//4*c^-7//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(3*b^3+-1*(b^2+-4*a*c)^(1/2)*(3*b^2+-14*a*c)+-20*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//8*2^1//4*c^-7//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(3*b^3+(b^2+-4*a*c)^(1/2)*(3*b^2+-14*a*c)+-20*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^11//2*(a+b*x^2+c*x^4)^-2, x) == :(x^5//2*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1//2*b*c^-1*x^(1/2)*(b^2+-4*a*c)^-1+-1//8*2^3//4*c^-5//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b^2+-10*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-12*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^3//4*c^-5//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b^2+-10*a*c+-1*b*(b^2+-4*a*c)^-1//2*(b^2+-12*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^3//4*c^-5//4*(b^2+-4*a*c)^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b^2+-10*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-12*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//8*2^3//4*c^-5//4*(b^2+-4*a*c)^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b^2+-10*a*c+b*(b^2+-4*a*c)^-1//2*(b^2+-12*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^9//2*(a+b*x^2+c*x^4)^-2, x) == :(x^3//2*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1//8*2^1//4*c^-3//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+12*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^1//4*c^-3//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b^2+b*(b^2+-4*a*c)^(1/2)+12*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//8*2^1//4*c^-3//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+12*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//8*2^1//4*c^-3//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b^2+b*(b^2+-4*a*c)^(1/2)+12*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^7//2*(a+b*x^2+c*x^4)^-2, x) == :(x^(1/2)*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(2a+b*x^2)+-1//8*2^3//4*c^-1//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3*b^2+3*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//8*2^3//4*c^-1//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3*b^2+3*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//8*2^3//4*c^-1//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3*b^2+-3*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//8*2^3//4*c^-1//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3*b^2+-3*b*(b^2+-4*a*c)^(1/2)+4*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^5//2*(a+b*x^2+c*x^4)^-2, x) == :(-1*x^3//2*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2)+-1//4*2^1//4*c^1//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(-1*(b^2+-4*a*c)^(1/2)+4b)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//4*2^1//4*c^1//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*((b^2+-4*a*c)^(1/2)+4b)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^1//4*c^1//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(-1*(b^2+-4*a*c)^(1/2)+4b)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^1//4*c^1//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*((b^2+-4*a*c)^(1/2)+4b)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^3//2*(a+b*x^2+c*x^4)^-2, x) == :(-1*x^(1/2)*(2*b^2+-8*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b+2*c*x^2)+1//4*2^3//4*c^3//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3+-4*b*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^3//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3+-4*b*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//4*2^3//4*c^3//4*(b^2+-4*a*c)^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3+4*b*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//4*2^3//4*c^3//4*(b^2+-4*a*c)^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3+4*b*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^(1/2)*(a+b*x^2+c*x^4)^-2, x) == :((1/2)*a^-1*x^3//2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2)+-1//8*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-20*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-20*a*c))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//8*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-1*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b+(b^2+-4*a*c)^-1//2*(b^2+-20*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//8*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-1*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b+-1*(b^2+-4*a*c)^-1//2*(b^2+-20*a*c))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-1//2*(a+b*x^2+c*x^4)^-2, x) == :((1/2)*a^-1*x^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2)+-1//8*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3*b^2+-28*a*c+3*b*(b^2+-4*a*c)^(1/2))*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3*b^2+-28*a*c+3*b*(b^2+-4*a*c)^(1/2))*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//8*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3*b^2+-28*a*c+-3*b*(b^2+-4*a*c)^(1/2))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//8*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3*b^2+-28*a*c+-3*b*(b^2+-4*a*c)^(1/2))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-3//2*(a+b*x^2+c*x^4)^-2, x) == :(-1//2*a^-2*x^-1//2*(b^2+-4*a*c)^-1*(5*b^2+-18*a*c)+(1/2)*a^-1*x^-1//2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-1*(b^2+-2*a*c+b*c*x^2)+-1//8*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(5*b^3+(b^2+-4*a*c)^(1/2)*(5*b^2+-18*a*c)+-28*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//8*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(5*b^3+-1*(b^2+-4*a*c)^(1/2)*(5*b^2+-18*a*c)+-28*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//8*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-3//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(5*b^3+(b^2+-4*a*c)^(1/2)*(5*b^2+-18*a*c)+-28*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//8*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-3//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(5*b^3+-1*(b^2+-4*a*c)^(1/2)*(5*b^2+-18*a*c)+-28*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^15//2*(a+b*x^2+c*x^4)^-3, x) == :(x^9//2*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+-1//16*c^-1*x^(1/2)*(b^2+-4*a*c)^-2*(3*b^2+36*a*c)+3//16*x^5//2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(b^2+12*a*c)+8*a*b)+-1//64*2^3//4*c^-5//4*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3*b^3+-3*(b^2+-4*a*c)^-1//2*(b^4+-24*a^2*c^2+-30*a*c*b^2)+-84*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//64*2^3//4*c^-5//4*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(3*b^3+-3*(b^2+-4*a*c)^-1//2*(b^4+-24*a^2*c^2+-30*a*c*b^2)+-84*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//64*2^3//4*c^-5//4*(b^2+-4*a*c)^-2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3*b^3+3*(b^2+-4*a*c)^-1//2*(b^4+-24*a^2*c^2+-30*a*c*b^2)+-84*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//64*2^3//4*c^-5//4*(b^2+-4*a*c)^-2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(3*b^3+3*(b^2+-4*a*c)^-1//2*(b^4+-24*a^2*c^2+-30*a*c*b^2)+-84*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^13//2*(a+b*x^2+c*x^4)^-3, x) == :(x^7//2*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+1//16*x^3//2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(5*b^2+28*a*c)+24*a*b)+-1//64*2^1//4*c^-3//4*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(5*b^2+-1*(b^2+-4*a*c)^-1//2*(5*b^3+172*a*b*c)+28*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//64*2^1//4*c^-3//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(5*b^3+(b^2+-4*a*c)^(1/2)*(5*b^2+28*a*c)+172*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//64*2^1//4*c^-3//4*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(5*b^2+-1*(b^2+-4*a*c)^-1//2*(5*b^3+172*a*b*c)+28*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//64*2^1//4*c^-3//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(5*b^3+(b^2+-4*a*c)^(1/2)*(5*b^2+28*a*c)+172*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^11//2*(a+b*x^2+c*x^4)^-3, x) == :(x^5//2*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+1//16*x^(1/2)*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(x^2*(7*b^2+20*a*c)+24*a*b)+-1//64*2^3//4*c^-1//4*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(21*b^2+-3*(b^2+-4*a*c)^-1//2*(7*b^3+36*a*b*c)+60*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//64*2^3//4*c^-1//4*(b^2+-4*a*c)^-2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(21*b^2+-3*(b^2+-4*a*c)^-1//2*(7*b^3+36*a*b*c)+60*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//64*2^3//4*c^-1//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(21*b^3+3*(b^2+-4*a*c)^(1/2)*(7*b^2+20*a*c)+108*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-1//64*2^3//4*c^-1//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(21*b^3+3*(b^2+-4*a*c)^(1/2)*(7*b^2+20*a*c)+108*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^9//2*(a+b*x^2+c*x^4)^-3, x) == :(x^3//2*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+-3//16*x^3//2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(5*b^2+-4*a*c+8*b*c*x^2)+-3//32*2^1//4*c^1//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(11*b^2+-4*b*(b^2+-4*a*c)^(1/2)+20*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-3//32*2^1//4*c^1//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(11*b^2+4*b*(b^2+-4*a*c)^(1/2)+20*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+3//32*2^1//4*c^1//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(11*b^2+-4*b*(b^2+-4*a*c)^(1/2)+20*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+3//32*2^1//4*c^1//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(11*b^2+4*b*(b^2+-4*a*c)^(1/2)+20*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^7//2*(a+b*x^2+c*x^4)^-3, x) == :(x^(1/2)*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(2a+b*x^2)+-1//16*x^(1/2)*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(13*b^2+-4*a*c+24*b*c*x^2)+-1//32*2^3//4*c^3//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(41*b^2+-36*b*(b^2+-4*a*c)^(1/2)+28*a*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//32*2^3//4*c^3//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(41*b^2+-36*b*(b^2+-4*a*c)^(1/2)+28*a*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//32*2^3//4*c^3//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(41*b^2+28*a*c+36*b*(b^2+-4*a*c)^(1/2))*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//32*2^3//4*c^3//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(41*b^2+28*a*c+36*b*(b^2+-4*a*c)^(1/2))*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^5//2*(a+b*x^2+c*x^4)^-3, x) == :(-1*x^3//2*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b+2*c*x^2)+3//16*a^-1*x^3//2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b*(b^2+4*a*c)+c*x^2*(b^2+12*a*c))+-3//64*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b^2+-1*b^3*(b^2+-4*a*c)^-1//2+12*a*c+68*a*b*c*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-3//64*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b^3+(b^2+-4*a*c)^(1/2)*(b^2+12*a*c)+-68*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+3//64*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(b^2+-1*b^3*(b^2+-4*a*c)^-1//2+12*a*c+68*a*b*c*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+3//64*2^1//4*a^-1*c^1//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(b^3+(b^2+-4*a*c)^(1/2)*(b^2+12*a*c)+-68*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^3//2*(a+b*x^2+c*x^4)^-3, x) == :(-1*x^(1/2)*(4*b^2+-16*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b+2*c*x^2)+1//16*a^-1*x^(1/2)*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(b*(b^2+20*a*c)+c*x^2*(b^2+44*a*c))+-3//64*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b^2+-1*b^3*(b^2+-4*a*c)^-1//2+44*a*c+68*a*b*c*(b^2+-4*a*c)^-1//2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-3//64*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(b^2+-1*b^3*(b^2+-4*a*c)^-1//2+44*a*c+68*a*b*c*(b^2+-4*a*c)^-1//2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+-3//64*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b^3+(b^2+-4*a*c)^(1/2)*(b^2+44*a*c)+-68*a*b*c)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-3//64*2^3//4*a^-1*c^3//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(b^3+(b^2+-4*a*c)^(1/2)*(b^2+44*a*c)+-68*a*b*c)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4))
@test integrate(x^(1/2)*(a+b*x^2+c*x^4)^-3, x) == :(1//4*a^-1*x^3//2*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b^2+-2*a*c+b*c*x^2)+1//16*a^-2*x^3//2*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(5*b^4+52*a^2*c^2+-45*a*c*b^2+b*c*x^2*(5*b^2+-44*a*c))+-1//64*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(5*b^4+520*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(5*b^2+-44*a*c)+-54*a*c*b^2)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-1//64*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(5*b^4+520*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(5*b^2+-44*a*c)+-54*a*c*b^2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+1//64*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-1//4*(5*b^4+520*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(5*b^2+-44*a*c)+-54*a*c*b^2)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+1//64*2^1//4*a^-2*c^1//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4*(5*b^4+520*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(5*b^2+-44*a*c)+-54*a*c*b^2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate(x^-1//2*(a+b*x^2+c*x^4)^-3, x) == :(1//4*a^-1*x^(1/2)*(b^2+-4*a*c)^-1*(a+b*x^2+c*x^4)^-2*(b^2+-2*a*c+b*c*x^2)+1//16*a^-2*x^(1/2)*(b^2+-4*a*c)^-2*(a+b*x^2+c*x^4)^-1*(7*b^4+60*a^2*c^2+-55*a*c*b^2+b*c*x^2*(7*b^2+-52*a*c))+-3//64*2^3//4*a^-2*c^3//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(7*b^4+280*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(7*b^2+-52*a*c)+-66*a*c*b^2)*arctan(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+-3//64*2^3//4*a^-2*c^3//4*(b^2+-4*a*c)^-5//2*((b^2+-4*a*c)^(1/2)+-1b)^-3//4*(7*b^4+280*a^2*c^2+b*(b^2+-4*a*c)^(1/2)*(7*b^2+-52*a*c)+-66*a*c*b^2)*arctanh(2^1//4*c^1//4*x^(1/2)*((b^2+-4*a*c)^(1/2)+-1b)^-1//4)+3//64*2^3//4*a^-2*c^3//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(7*b^4+280*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(7*b^2+-52*a*c)+-66*a*c*b^2)*arctan(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4)+3//64*2^3//4*a^-2*c^3//4*(b^2+-4*a*c)^-5//2*(-1b+-1*(b^2+-4*a*c)^(1/2))^-3//4*(7*b^4+280*a^2*c^2+-1*b*(b^2+-4*a*c)^(1/2)*(7*b^2+-52*a*c)+-66*a*c*b^2)*arctanh(2^1//4*c^1//4*x^(1/2)*(-1b+-1*(b^2+-4*a*c)^(1/2))^-1//4))
@test integrate((d*x)^m*(a+b*x^2+c*x^4)^3, x) == :(a^3*d^-1*(d*x)^(1+m)*(1+m)^-1+c^3*d^-13*(d*x)^(13+m)*(13+m)^-1+b*d^-7*(d*x)^(7+m)*(7+m)^-1*(b^2+6*a*c)+3*a*d^-5*(d*x)^(5+m)*(5+m)^-1*(b^2+a*c)+3*b*a^2*d^-3*(d*x)^(3+m)*(3+m)^-1+3*b*c^2*d^-11*(d*x)^(11+m)*(11+m)^-1+3*c*d^-9*(d*x)^(9+m)*(9+m)^-1*(b^2+a*c))
@test integrate((d*x)^m*(a+b*x^2+c*x^4)^2, x) == :(a^2*d^-1*(d*x)^(1+m)*(1+m)^-1+c^2*d^-9*(d*x)^(9+m)*(9+m)^-1+d^-5*(d*x)^(5+m)*(5+m)^-1*(b^2+2*a*c)+2*a*b*d^-3*(d*x)^(3+m)*(3+m)^-1+2*b*c*d^-7*(d*x)^(7+m)*(7+m)^-1)
@test integrate((d*x)^m*(a+b*x^2+c*x^4), x) == :(a*d^-1*(d*x)^(1+m)*(1+m)^-1+b*d^-3*(d*x)^(3+m)*(3+m)^-1+c*d^-5*(d*x)^(5+m)*(5+m)^-1)

max_stars_repo_path: test/1 Algebraic functions/1.2 Trinomial products/1.2.2 Quartic/1.2.2.2 (d x)^m (a+b x^2+c x^4)^p.jl