text:
@testset "1.1.3.4 (e x)^m (a+b x^n)^p (c+d x^n)^q" begin
    (A, B, a, b, c, d, e, m, n, p, q, x, ) = @variables A B a b c d e m n p q x

    #= ::Package:: =#

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^p*(c+d*x^3)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^p*(c+d*x^3)^q=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^p*(c+d*x^3)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^2*(a + b*x^3)*(A + B*x^3), x, 3, (a*A*x^3)/3 + ((A*b + a*B)*x^6)/6 + (b*B*x^9)/9]
    @test_int [x*(a + b*x^3)*(A + B*x^3), x, 2, (a*A*x^2)/2 + ((A*b + a*B)*x^5)/5 + (b*B*x^8)/8]
    @test_int [(a + b*x^3)*(A + B*x^3), x, 2, a*A*x + ((A*b + a*B)*x^4)/4 + (b*B*x^7)/7]
    @test_int [((a + b*x^3)*(A + B*x^3))/x, x, 3, ((A*b + a*B)*x^3)/3 + (b*B*x^6)/6 + a*A*log(x)]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^2, x, 2, -((a*A)/x) + ((A*b + a*B)*x^2)/2 + (b*B*x^5)/5]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^3, x, 2, -(a*A)/(2*x^2) + (A*b + a*B)*x + (b*B*x^4)/4]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^4, x, 3, -(a*A)/(3*x^3) + (b*B*x^3)/3 + (A*b + a*B)*log(x)]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^5, x, 2, -(a*A)/(4*x^4) - (A*b + a*B)/x + (b*B*x^2)/2]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^6, x, 2, -(a*A)/(5*x^5) - (A*b + a*B)/(2*x^2) + b*B*x]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^7, x, 3, -(a*A)/(6*x^6) - (A*b + a*B)/(3*x^3) + b*B*log(x)]

    @test_int [x^2*(a + b*x^3)^2*(A + B*x^3), x, 3, ((A*b - a*B)*(a + b*x^3)^3)/(9*b^2) + (B*(a + b*x^3)^4)/(12*b^2)]
    @test_int [x*(a + b*x^3)^2*(A + B*x^3), x, 2, (a^2*A*x^2)/2 + (a*(2*A*b + a*B)*x^5)/5 + (b*(A*b + 2*a*B)*x^8)/8 + (b^2*B*x^11)/11]
    @test_int [(a + b*x^3)^2*(A + B*x^3), x, 2, a^2*A*x + (a*(2*A*b + a*B)*x^4)/4 + (b*(A*b + 2*a*B)*x^7)/7 + (b^2*B*x^10)/10]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x, x, 4, (2*a*A*b*x^3)/3 + (A*b^2*x^6)/6 + (B*(a + b*x^3)^3)/(9*b) + a^2*A*log(x)]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^2, x, 2, -((a^2*A)/x) + (a*(2*A*b + a*B)*x^2)/2 + (b*(A*b + 2*a*B)*x^5)/5 + (b^2*B*x^8)/8]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^3, x, 2, -(a^2*A)/(2*x^2) + a*(2*A*b + a*B)*x + (b*(A*b + 2*a*B)*x^4)/4 + (b^2*B*x^7)/7]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^4, x, 3, -(a^2*A)/(3*x^3) + (b*(A*b + 2*a*B)*x^3)/3 + (b^2*B*x^6)/6 + a*(2*A*b + a*B)*log(x)]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^5, x, 2, -(a^2*A)/(4*x^4) - (a*(2*A*b + a*B))/x + (b*(A*b + 2*a*B)*x^2)/2 + (b^2*B*x^5)/5]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^6, x, 2, -(a^2*A)/(5*x^5) - (a*(2*A*b + a*B))/(2*x^2) + b*(A*b + 2*a*B)*x + (b^2*B*x^4)/4]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^7, x, 3, -(a^2*A)/(6*x^6) - (a*(2*A*b + a*B))/(3*x^3) + (b^2*B*x^3)/3 + b*(A*b + 2*a*B)*log(x)]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^8, x, 2, -(a^2*A)/(7*x^7) - (a*(2*A*b + a*B))/(4*x^4) - (b*(A*b + 2*a*B))/x + (b^2*B*x^2)/2]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^9, x, 2, -(a^2*A)/(8*x^8) - (a*(2*A*b + a*B))/(5*x^5) - (b*(A*b + 2*a*B))/(2*x^2) + b^2*B*x]

    @test_int [x^9*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^10)/10 + (a^4*(5*A*b + a*B)*x^13)/13 + (5*a^3*b*(2*A*b + a*B)*x^16)/16 + (10*a^2*b^2*(A*b + a*B)*x^19)/19 + (5*a*b^3*(A*b + 2*a*B)*x^22)/22 + (b^4*(A*b + 5*a*B)*x^25)/25 + (b^5*B*x^28)/28]
    @test_int [x^8*(a + b*x^3)^5*(A + B*x^3), x, 3, (a^2*(A*b - a*B)*(a + b*x^3)^6)/(18*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x^3)^7)/(21*b^4) + ((A*b - 3*a*B)*(a + b*x^3)^8)/(24*b^4) + (B*(a + b*x^3)^9)/(27*b^4)]
    @test_int [x^7*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^8)/8 + (a^4*(5*A*b + a*B)*x^11)/11 + (5*a^3*b*(2*A*b + a*B)*x^14)/14 + (10*a^2*b^2*(A*b + a*B)*x^17)/17 + (a*b^3*(A*b + 2*a*B)*x^20)/4 + (b^4*(A*b + 5*a*B)*x^23)/23 + (b^5*B*x^26)/26]
    @test_int [x^6*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^7)/7 + (a^4*(5*A*b + a*B)*x^10)/10 + (5*a^3*b*(2*A*b + a*B)*x^13)/13 + (5*a^2*b^2*(A*b + a*B)*x^16)/8 + (5*a*b^3*(A*b + 2*a*B)*x^19)/19 + (b^4*(A*b + 5*a*B)*x^22)/22 + (b^5*B*x^25)/25]
    @test_int [x^5*(a + b*x^3)^5*(A + B*x^3), x, 3, -(a*(A*b - a*B)*(a + b*x^3)^6)/(18*b^3) + ((A*b - 2*a*B)*(a + b*x^3)^7)/(21*b^3) + (B*(a + b*x^3)^8)/(24*b^3)]
    @test_int [x^4*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^5)/5 + (a^4*(5*A*b + a*B)*x^8)/8 + (5*a^3*b*(2*A*b + a*B)*x^11)/11 + (5*a^2*b^2*(A*b + a*B)*x^14)/7 + (5*a*b^3*(A*b + 2*a*B)*x^17)/17 + (b^4*(A*b + 5*a*B)*x^20)/20 + (b^5*B*x^23)/23]
    @test_int [x^3*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^4)/4 + (a^4*(5*A*b + a*B)*x^7)/7 + (a^3*b*(2*A*b + a*B)*x^10)/2 + (10*a^2*b^2*(A*b + a*B)*x^13)/13 + (5*a*b^3*(A*b + 2*a*B)*x^16)/16 + (b^4*(A*b + 5*a*B)*x^19)/19 + (b^5*B*x^22)/22]
    @test_int [x^2*(a + b*x^3)^5*(A + B*x^3), x, 3, ((A*b - a*B)*(a + b*x^3)^6)/(18*b^2) + (B*(a + b*x^3)^7)/(21*b^2)]
    @test_int [x*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^2)/2 + (a^4*(5*A*b + a*B)*x^5)/5 + (5*a^3*b*(2*A*b + a*B)*x^8)/8 + (10*a^2*b^2*(A*b + a*B)*x^11)/11 + (5*a*b^3*(A*b + 2*a*B)*x^14)/14 + (b^4*(A*b + 5*a*B)*x^17)/17 + (b^5*B*x^20)/20]
    @test_int [(a + b*x^3)^5*(A + B*x^3), x, 2, a^5*A*x + (a^4*(5*A*b + a*B)*x^4)/4 + (5*a^3*b*(2*A*b + a*B)*x^7)/7 + a^2*b^2*(A*b + a*B)*x^10 + (5*a*b^3*(A*b + 2*a*B)*x^13)/13 + (b^4*(A*b + 5*a*B)*x^16)/16 + (b^5*B*x^19)/19]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x, x, 4, (5*a^4*A*b*x^3)/3 + (5*a^3*A*b^2*x^6)/3 + (10*a^2*A*b^3*x^9)/9 + (5*a*A*b^4*x^12)/12 + (A*b^5*x^15)/15 + (B*(a + b*x^3)^6)/(18*b) + a^5*A*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^2, x, 2, -((a^5*A)/x) + (a^4*(5*A*b + a*B)*x^2)/2 + a^3*b*(2*A*b + a*B)*x^5 + (5*a^2*b^2*(A*b + a*B)*x^8)/4 + (5*a*b^3*(A*b + 2*a*B)*x^11)/11 + (b^4*(A*b + 5*a*B)*x^14)/14 + (b^5*B*x^17)/17]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^3, x, 2, -(a^5*A)/(2*x^2) + a^4*(5*A*b + a*B)*x + (5*a^3*b*(2*A*b + a*B)*x^4)/4 + (10*a^2*b^2*(A*b + a*B)*x^7)/7 + (a*b^3*(A*b + 2*a*B)*x^10)/2 + (b^4*(A*b + 5*a*B)*x^13)/13 + (b^5*B*x^16)/16]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^4, x, 3, -(a^5*A)/(3*x^3) + (5*a^3*b*(2*A*b + a*B)*x^3)/3 + (5*a^2*b^2*(A*b + a*B)*x^6)/3 + (5*a*b^3*(A*b + 2*a*B)*x^9)/9 + (b^4*(A*b + 5*a*B)*x^12)/12 + (b^5*B*x^15)/15 + a^4*(5*A*b + a*B)*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^5, x, 2, -(a^5*A)/(4*x^4) - (a^4*(5*A*b + a*B))/x + (5*a^3*b*(2*A*b + a*B)*x^2)/2 + 2*a^2*b^2*(A*b + a*B)*x^5 + (5*a*b^3*(A*b + 2*a*B)*x^8)/8 + (b^4*(A*b + 5*a*B)*x^11)/11 + (b^5*B*x^14)/14]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^6, x, 2, -(a^5*A)/(5*x^5) - (a^4*(5*A*b + a*B))/(2*x^2) + 5*a^3*b*(2*A*b + a*B)*x + (5*a^2*b^2*(A*b + a*B)*x^4)/2 + (5*a*b^3*(A*b + 2*a*B)*x^7)/7 + (b^4*(A*b + 5*a*B)*x^10)/10 + (b^5*B*x^13)/13]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^7, x, 3, -(a^5*A)/(6*x^6) - (a^4*(5*A*b + a*B))/(3*x^3) + (10*a^2*b^2*(A*b + a*B)*x^3)/3 + (5*a*b^3*(A*b + 2*a*B)*x^6)/6 + (b^4*(A*b + 5*a*B)*x^9)/9 + (b^5*B*x^12)/12 + 5*a^3*b*(2*A*b + a*B)*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^8, x, 2, -(a^5*A)/(7*x^7) - (a^4*(5*A*b + a*B))/(4*x^4) - (5*a^3*b*(2*A*b + a*B))/x + 5*a^2*b^2*(A*b + a*B)*x^2 + a*b^3*(A*b + 2*a*B)*x^5 + (b^4*(A*b + 5*a*B)*x^8)/8 + (b^5*B*x^11)/11]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^9, x, 2, -(a^5*A)/(8*x^8) - (a^4*(5*A*b + a*B))/(5*x^5) - (5*a^3*b*(2*A*b + a*B))/(2*x^2) + 10*a^2*b^2*(A*b + a*B)*x + (5*a*b^3*(A*b + 2*a*B)*x^4)/4 + (b^4*(A*b + 5*a*B)*x^7)/7 + (b^5*B*x^10)/10]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^10, x, 3, -(a^5*A)/(9*x^9) - (a^4*(5*A*b + a*B))/(6*x^6) - (5*a^3*b*(2*A*b + a*B))/(3*x^3) + (5*a*b^3*(A*b + 2*a*B)*x^3)/3 + (b^4*(A*b + 5*a*B)*x^6)/6 + (b^5*B*x^9)/9 + 10*a^2*b^2*(A*b + a*B)*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^11, x, 2, -(a^5*A)/(10*x^10) - (a^4*(5*A*b + a*B))/(7*x^7) - (5*a^3*b*(2*A*b + a*B))/(4*x^4) - (10*a^2*b^2*(A*b + a*B))/x + (5*a*b^3*(A*b + 2*a*B)*x^2)/2 + (b^4*(A*b + 5*a*B)*x^5)/5 + (b^5*B*x^8)/8]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^12, x, 2, -(a^5*A)/(11*x^11) - (a^4*(5*A*b + a*B))/(8*x^8) - (a^3*b*(2*A*b + a*B))/x^5 - (5*a^2*b^2*(A*b + a*B))/x^2 + 5*a*b^3*(A*b + 2*a*B)*x + (b^4*(A*b + 5*a*B)*x^4)/4 + (b^5*B*x^7)/7]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^13, x, 3, -(a^5*A)/(12*x^12) - (a^4*(5*A*b + a*B))/(9*x^9) - (5*a^3*b*(2*A*b + a*B))/(6*x^6) - (10*a^2*b^2*(A*b + a*B))/(3*x^3) + (b^4*(A*b + 5*a*B)*x^3)/3 + (b^5*B*x^6)/6 + 5*a*b^3*(A*b + 2*a*B)*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^14, x, 2, -(a^5*A)/(13*x^13) - (a^4*(5*A*b + a*B))/(10*x^10) - (5*a^3*b*(2*A*b + a*B))/(7*x^7) - (5*a^2*b^2*(A*b + a*B))/(2*x^4) - (5*a*b^3*(A*b + 2*a*B))/x + (b^4*(A*b + 5*a*B)*x^2)/2 + (b^5*B*x^5)/5]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^15, x, 2, -(a^5*A)/(14*x^14) - (a^4*(5*A*b + a*B))/(11*x^11) - (5*a^3*b*(2*A*b + a*B))/(8*x^8) - (2*a^2*b^2*(A*b + a*B))/x^5 - (5*a*b^3*(A*b + 2*a*B))/(2*x^2) + b^4*(A*b + 5*a*B)*x + (b^5*B*x^4)/4]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^16, x, 3, -(a^5*A)/(15*x^15) - (a^4*(5*A*b + a*B))/(12*x^12) - (5*a^3*b*(2*A*b + a*B))/(9*x^9) - (5*a^2*b^2*(A*b + a*B))/(3*x^6) - (5*a*b^3*(A*b + 2*a*B))/(3*x^3) + (b^5*B*x^3)/3 + b^4*(A*b + 5*a*B)*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^17, x, 2, -(a^5*A)/(16*x^16) - (a^4*(5*A*b + a*B))/(13*x^13) - (a^3*b*(2*A*b + a*B))/(2*x^10) - (10*a^2*b^2*(A*b + a*B))/(7*x^7) - (5*a*b^3*(A*b + 2*a*B))/(4*x^4) - (b^4*(A*b + 5*a*B))/x + (b^5*B*x^2)/2]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^18, x, 2, -(a^5*A)/(17*x^17) - (a^4*(5*A*b + a*B))/(14*x^14) - (5*a^3*b*(2*A*b + a*B))/(11*x^11) - (5*a^2*b^2*(A*b + a*B))/(4*x^8) - (a*b^3*(A*b + 2*a*B))/x^5 - (b^4*(A*b + 5*a*B))/(2*x^2) + b^5*B*x]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^19, x, 4, -(a^5*B)/(15*x^15) - (5*a^4*b*B)/(12*x^12) - (10*a^3*b^2*B)/(9*x^9) - (5*a^2*b^3*B)/(3*x^6) - (5*a*b^4*B)/(3*x^3) - (A*(a + b*x^3)^6)/(18*a*x^18) + b^5*B*log(x)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^20, x, 2, -(a^5*A)/(19*x^19) - (a^4*(5*A*b + a*B))/(16*x^16) - (5*a^3*b*(2*A*b + a*B))/(13*x^13) - (a^2*b^2*(A*b + a*B))/x^10 - (5*a*b^3*(A*b + 2*a*B))/(7*x^7) - (b^4*(A*b + 5*a*B))/(4*x^4) - (b^5*B)/x]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^21, x, 2, -(a^5*A)/(20*x^20) - (a^4*(5*A*b + a*B))/(17*x^17) - (5*a^3*b*(2*A*b + a*B))/(14*x^14) - (10*a^2*b^2*(A*b + a*B))/(11*x^11) - (5*a*b^3*(A*b + 2*a*B))/(8*x^8) - (b^4*(A*b + 5*a*B))/(5*x^5) - (b^5*B)/(2*x^2)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^22, x, 3, -(A*(a + b*x^3)^6)/(21*a*x^21) + ((A*b - 7*a*B)*(a + b*x^3)^6)/(126*a^2*x^18)]
    @test_int [((a + b*x^3)^5*(A + B*x^3))/x^23, x, 2, -(a^5*A)/(22*x^22) - (a^4*(5*A*b + a*B))/(19*x^19) - (5*a^3*b*(2*A*b + a*B))/(16*x^16) - (10*a^2*b^2*(A*b + a*B))/(13*x^13) - (a*b^3*(A*b + 2*a*B))/(2*x^10) - (b^4*(A*b + 5*a*B))/(7*x^7) - (b^5*B)/(4*x^4)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(x^6*(A + B*x^3))/(a + b*x^3), x, 9, -((a*(A*b - a*B)*x)/b^3) + ((A*b - a*B)*x^4)/(4*b^2) + (B*x^7)/(7*b) - (a^(4/3)*(A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(10/3)) + (a^(4/3)*(A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*b^(10/3)) - (a^(4/3)*(A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(10/3))]
    @test_int [(x^5*(A + B*x^3))/(a + b*x^3), x, 3, ((A*b - a*B)*x^3)/(3*b^2) + (B*x^6)/(6*b) - (a*(A*b - a*B)*log(a + b*x^3))/(3*b^3)]
    @test_int [(x^4*(A + B*x^3))/(a + b*x^3), x, 8, ((A*b - a*B)*x^2)/(2*b^2) + (B*x^5)/(5*b) + (a^(2/3)*(A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(8/3)) + (a^(2/3)*(A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*b^(8/3)) - (a^(2/3)*(A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(8/3))]
    @test_int [(x^3*(A + B*x^3))/(a + b*x^3), x, 8, ((A*b - a*B)*x)/b^2 + (B*x^4)/(4*b) + (a^(1/3)*(A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(7/3)) - (a^(1/3)*(A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*b^(7/3)) + (a^(1/3)*(A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(7/3))]
    @test_int [(x^2*(A + B*x^3))/(a + b*x^3), x, 3, (B*x^3)/(3*b) + ((A*b - a*B)*log(a + b*x^3))/(3*b^2)]
    @test_int [(x*(A + B*x^3))/(a + b*x^3), x, 7, (B*x^2)/(2*b) - ((A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*b^(5/3)) - ((A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(1/3)*b^(5/3)) + ((A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(1/3)*b^(5/3))]
    @test_int [(A + B*x^3)/(a + b*x^3), x, 7, (B*x)/b - ((A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*b^(4/3)) + ((A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*b^(4/3)) - ((A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*b^(4/3))]
    @test_int [(A + B*x^3)/(x*(a + b*x^3)), x, 3, (A*log(x))/a - ((A*b - a*B)*log(a + b*x^3))/(3*a*b)]
    @test_int [(A + B*x^3)/(x^2*(a + b*x^3)), x, 7, -(A/(a*x)) + ((A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*b^(2/3)) + ((A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(4/3)*b^(2/3)) - ((A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3)*b^(2/3))]
    @test_int [(A + B*x^3)/(x^3*(a + b*x^3)), x, 7, -A/(2*a*x^2) + ((A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*b^(1/3)) - ((A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)*b^(1/3)) + ((A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3)*b^(1/3))]
    @test_int [(A + B*x^3)/(x^4*(a + b*x^3)), x, 3, -A/(3*a*x^3) - ((A*b - a*B)*log(x))/a^2 + ((A*b - a*B)*log(a + b*x^3))/(3*a^2)]
    @test_int [(A + B*x^3)/(x^5*(a + b*x^3)), x, 8, -A/(4*a*x^4) + (A*b - a*B)/(a^2*x) - (b^(1/3)*(A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(7/3)) - (b^(1/3)*(A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(7/3)) + (b^(1/3)*(A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(7/3))]
    @test_int [(A + B*x^3)/(x^6*(a + b*x^3)), x, 8, -A/(5*a*x^5) + (A*b - a*B)/(2*a^2*x^2) - (b^(2/3)*(A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(8/3)) + (b^(2/3)*(A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(8/3)) - (b^(2/3)*(A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(8/3))]
    @test_int [(A + B*x^3)/(x^7*(a + b*x^3)), x, 3, -A/(6*a*x^6) + (A*b - a*B)/(3*a^2*x^3) + (b*(A*b - a*B)*log(x))/a^3 - (b*(A*b - a*B)*log(a + b*x^3))/(3*a^3)]
    @test_int [(A + B*x^3)/(x^8*(a + b*x^3)), x, 9, -A/(7*a*x^7) + (A*b - a*B)/(4*a^2*x^4) - (b*(A*b - a*B))/(a^3*x) + (b^(4/3)*(A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(10/3)) + (b^(4/3)*(A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(3*a^(10/3)) - (b^(4/3)*(A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(10/3))]

    @test_int [(x^9*(A + B*x^3))/(a + b*x^3)^2, x, 9, -(a*(7*A*b - 10*a*B)*x)/(3*b^4) + ((7*A*b - 10*a*B)*x^4)/(12*b^3) - ((7*A*b - 10*a*B)*x^7)/(21*a*b^2) + ((A*b - a*B)*x^10)/(3*a*b*(a + b*x^3)) - (a^(4/3)*(7*A*b - 10*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*b^(13/3)) + (a^(4/3)*(7*A*b - 10*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*b^(13/3)) - (a^(4/3)*(7*A*b - 10*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*b^(13/3))]
    @test_int [(x^8*(A + B*x^3))/(a + b*x^3)^2, x, 3, ((A*b - 2*a*B)*x^3)/(3*b^3) + (B*x^6)/(6*b^2) - (a^2*(A*b - a*B))/(3*b^4*(a + b*x^3)) - (a*(2*A*b - 3*a*B)*log(a + b*x^3))/(3*b^4)]
    @test_int [(x^7*(A + B*x^3))/(a + b*x^3)^2, x, 9, ((5*A*b - 8*a*B)*x^2)/(6*b^3) - ((5*A*b - 8*a*B)*x^5)/(15*a*b^2) + ((A*b - a*B)*x^8)/(3*a*b*(a + b*x^3)) + (a^(2/3)*(5*A*b - 8*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*b^(11/3)) + (a^(2/3)*(5*A*b - 8*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*b^(11/3)) - (a^(2/3)*(5*A*b - 8*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*b^(11/3))]
    @test_int [(x^6*(A + B*x^3))/(a + b*x^3)^2, x, 9, ((4*A*b - 7*a*B)*x)/(3*b^3) - ((4*A*b - 7*a*B)*x^4)/(12*a*b^2) + ((A*b - a*B)*x^7)/(3*a*b*(a + b*x^3)) + (a^(1/3)*(4*A*b - 7*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*b^(10/3)) - (a^(1/3)*(4*A*b - 7*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*b^(10/3)) + (a^(1/3)*(4*A*b - 7*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*b^(10/3))]
    @test_int [(x^5*(A + B*x^3))/(a + b*x^3)^2, x, 3, (B*x^3)/(3*b^2) + (a*(A*b - a*B))/(3*b^3*(a + b*x^3)) + ((A*b - 2*a*B)*log(a + b*x^3))/(3*b^3)]
    @test_int [(x^4*(A + B*x^3))/(a + b*x^3)^2, x, 8, -((2*A*b - 5*a*B)*x^2)/(6*a*b^2) + ((A*b - a*B)*x^5)/(3*a*b*(a + b*x^3)) - ((2*A*b - 5*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*b^(8/3)) - ((2*A*b - 5*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(1/3)*b^(8/3)) + ((2*A*b - 5*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(1/3)*b^(8/3))]
    @test_int [(x^3*(A + B*x^3))/(a + b*x^3)^2, x, 8, -((A*b - 4*a*B)*x)/(3*a*b^2) + ((A*b - a*B)*x^4)/(3*a*b*(a + b*x^3)) - ((A*b - 4*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*b^(7/3)) + ((A*b - 4*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(2/3)*b^(7/3)) - ((A*b - 4*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(2/3)*b^(7/3))]
    @test_int [(x^2*(A + B*x^3))/(a + b*x^3)^2, x, 3, -(A*b - a*B)/(3*b^2*(a + b*x^3)) + (B*log(a + b*x^3))/(3*b^2)]
    @test_int [(x*(A + B*x^3))/(a + b*x^3)^2, x, 7, ((A*b - a*B)*x^2)/(3*a*b*(a + b*x^3)) - ((A*b + 2*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*b^(5/3)) - ((A*b + 2*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(4/3)*b^(5/3)) + ((A*b + 2*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(4/3)*b^(5/3))]
    @test_int [(A + B*x^3)/(a + b*x^3)^2, x, 7, ((A*b - a*B)*x)/(3*a*b*(a + b*x^3)) - ((2*A*b + a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*b^(4/3)) + ((2*A*b + a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(5/3)*b^(4/3)) - ((2*A*b + a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(5/3)*b^(4/3))]
    @test_int [(A + B*x^3)/(x*(a + b*x^3)^2), x, 3, (A*b - a*B)/(3*a*b*(a + b*x^3)) + (A*log(x))/a^2 - (A*log(a + b*x^3))/(3*a^2)]
    @test_int [(A + B*x^3)/(x^2*(a + b*x^3)^2), x, 8, -(4*A*b - a*B)/(3*a^2*b*x) + (A*b - a*B)/(3*a*b*x*(a + b*x^3)) + ((4*A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*b^(2/3)) + ((4*A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(7/3)*b^(2/3)) - ((4*A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(7/3)*b^(2/3))]
    @test_int [(A + B*x^3)/(x^3*(a + b*x^3)^2), x, 8, -(5*A*b - 2*a*B)/(6*a^2*b*x^2) + (A*b - a*B)/(3*a*b*x^2*(a + b*x^3)) + ((5*A*b - 2*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(8/3)*b^(1/3)) - ((5*A*b - 2*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(8/3)*b^(1/3)) + ((5*A*b - 2*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(8/3)*b^(1/3))]
    @test_int [(A + B*x^3)/(x^4*(a + b*x^3)^2), x, 3, -A/(3*a^2*x^3) - (A*b - a*B)/(3*a^2*(a + b*x^3)) - ((2*A*b - a*B)*log(x))/a^3 + ((2*A*b - a*B)*log(a + b*x^3))/(3*a^3)]
    @test_int [(A + B*x^3)/(x^5*(a + b*x^3)^2), x, 9, -(7*A*b - 4*a*B)/(12*a^2*b*x^4) + (7*A*b - 4*a*B)/(3*a^3*x) + (A*b - a*B)/(3*a*b*x^4*(a + b*x^3)) - (b^(1/3)*(7*A*b - 4*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(10/3)) - (b^(1/3)*(7*A*b - 4*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(10/3)) + (b^(1/3)*(7*A*b - 4*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(10/3))]
    @test_int [(A + B*x^3)/(x^6*(a + b*x^3)^2), x, 9, -(8*A*b - 5*a*B)/(15*a^2*b*x^5) + (8*A*b - 5*a*B)/(6*a^3*x^2) + (A*b - a*B)/(3*a*b*x^5*(a + b*x^3)) - (b^(2/3)*(8*A*b - 5*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(11/3)) + (b^(2/3)*(8*A*b - 5*a*B)*log(a^(1/3) + b^(1/3)*x))/(9*a^(11/3)) - (b^(2/3)*(8*A*b - 5*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(18*a^(11/3))]
    @test_int [(A + B*x^3)/(x^7*(a + b*x^3)^2), x, 3, -A/(6*a^2*x^6) + (2*A*b - a*B)/(3*a^3*x^3) + (b*(A*b - a*B))/(3*a^3*(a + b*x^3)) + (b*(3*A*b - 2*a*B)*log(x))/a^4 - (b*(3*A*b - 2*a*B)*log(a + b*x^3))/(3*a^4)]

    @test_int [(x^11*(A + B*x^3))/(a + b*x^3)^3, x, 3, ((A*b - 3*a*B)*x^3)/(3*b^4) + (B*x^6)/(6*b^3) + (a^3*(A*b - a*B))/(6*b^5*(a + b*x^3)^2) - (a^2*(3*A*b - 4*a*B))/(3*b^5*(a + b*x^3)) - (a*(A*b - 2*a*B)*log(a + b*x^3))/b^5]
    @test_int [(x^8*(A + B*x^3))/(a + b*x^3)^3, x, 3, (B*x^3)/(3*b^3) - (a^2*(A*b - a*B))/(6*b^4*(a + b*x^3)^2) + (a*(2*A*b - 3*a*B))/(3*b^4*(a + b*x^3)) + ((A*b - 3*a*B)*log(a + b*x^3))/(3*b^4)]
    @test_int [(x^5*(A + B*x^3))/(a + b*x^3)^3, x, 3, (a*(A*b - a*B))/(6*b^3*(a + b*x^3)^2) - (A*b - 2*a*B)/(3*b^3*(a + b*x^3)) + (B*log(a + b*x^3))/(3*b^3)]
    @test_int [(x^2*(A + B*x^3))/(a + b*x^3)^3, x, 2, -(A + B*x^3)^2/(6*(A*b - a*B)*(a + b*x^3)^2)]
    @test_int [(A + B*x^3)/(x*(a + b*x^3)^3), x, 3, (A*b - a*B)/(6*a*b*(a + b*x^3)^2) + A/(3*a^2*(a + b*x^3)) + (A*log(x))/a^3 - (A*log(a + b*x^3))/(3*a^3)]
    @test_int [(A + B*x^3)/(x^4*(a + b*x^3)^3), x, 3, -A/(3*a^3*x^3) - (A*b - a*B)/(6*a^2*(a + b*x^3)^2) - (2*A*b - a*B)/(3*a^3*(a + b*x^3)) - ((3*A*b - a*B)*log(x))/a^4 + ((3*A*b - a*B)*log(a + b*x^3))/(3*a^4)]
    @test_int [(A + B*x^3)/(x^7*(a + b*x^3)^3), x, 3, -A/(6*a^3*x^6) + (3*A*b - a*B)/(3*a^4*x^3) + (b*(A*b - a*B))/(6*a^3*(a + b*x^3)^2) + (b*(3*A*b - 2*a*B))/(3*a^4*(a + b*x^3)) + (3*b*(2*A*b - a*B)*log(x))/a^5 - (b*(2*A*b - a*B)*log(a + b*x^3))/a^5]

    @test_int [(x^10*(A + B*x^3))/(a + b*x^3)^3, x, 10, (2*(5*A*b - 11*a*B)*x^2)/(9*b^4) - (4*(5*A*b - 11*a*B)*x^5)/(45*a*b^3) + ((A*b - a*B)*x^11)/(6*a*b*(a + b*x^3)^2) + ((5*A*b - 11*a*B)*x^8)/(18*a*b^2*(a + b*x^3)) + (4*a^(2/3)*(5*A*b - 11*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*b^(14/3)) + (4*a^(2/3)*(5*A*b - 11*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*b^(14/3)) - (2*a^(2/3)*(5*A*b - 11*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(27*b^(14/3))]
    @test_int [(x^9*(A + B*x^3))/(a + b*x^3)^3, x, 10, (7*(2*A*b - 5*a*B)*x)/(9*b^4) - (7*(2*A*b - 5*a*B)*x^4)/(36*a*b^3) + ((A*b - a*B)*x^10)/(6*a*b*(a + b*x^3)^2) + ((2*A*b - 5*a*B)*x^7)/(9*a*b^2*(a + b*x^3)) + (7*a^(1/3)*(2*A*b - 5*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*b^(13/3)) - (7*a^(1/3)*(2*A*b - 5*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*b^(13/3)) + (7*a^(1/3)*(2*A*b - 5*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*b^(13/3))]
    @test_int [(x^7*(A + B*x^3))/(a + b*x^3)^3, x, 9, (-5*(A*b - 4*a*B)*x^2)/(18*a*b^3) + ((A*b - a*B)*x^8)/(6*a*b*(a + b*x^3)^2) + ((A*b - 4*a*B)*x^5)/(9*a*b^2*(a + b*x^3)) - (5*(A*b - 4*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(1/3)*b^(11/3)) - (5*(A*b - 4*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(1/3)*b^(11/3)) + (5*(A*b - 4*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(1/3)*b^(11/3))]
    @test_int [(x^6*(A + B*x^3))/(a + b*x^3)^3, x, 9, (-2*(A*b - 7*a*B)*x)/(9*a*b^3) + ((A*b - a*B)*x^7)/(6*a*b*(a + b*x^3)^2) + ((A*b - 7*a*B)*x^4)/(18*a*b^2*(a + b*x^3)) - (2*(A*b - 7*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(2/3)*b^(10/3)) + (2*(A*b - 7*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(2/3)*b^(10/3)) - ((A*b - 7*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(27*a^(2/3)*b^(10/3))]
    @test_int [(x^4*(A + B*x^3))/(a + b*x^3)^3, x, 8, ((A*b - a*B)*x^5)/(6*a*b*(a + b*x^3)^2) - ((A*b + 5*a*B)*x^2)/(18*a*b^2*(a + b*x^3)) - ((A*b + 5*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(4/3)*b^(8/3)) - ((A*b + 5*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(4/3)*b^(8/3)) + ((A*b + 5*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(4/3)*b^(8/3))]
    @test_int [(x^3*(A + B*x^3))/(a + b*x^3)^3, x, 8, ((A*b - a*B)*x^4)/(6*a*b*(a + b*x^3)^2) - ((A*b + 2*a*B)*x)/(9*a*b^2*(a + b*x^3)) - ((A*b + 2*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*b^(7/3)) + ((A*b + 2*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(5/3)*b^(7/3)) - ((A*b + 2*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(5/3)*b^(7/3))]
    @test_int [(x*(A + B*x^3))/(a + b*x^3)^3, x, 8, ((A*b - a*B)*x^2)/(6*a*b*(a + b*x^3)^2) + ((2*A*b + a*B)*x^2)/(9*a^2*b*(a + b*x^3)) - ((2*A*b + a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*b^(5/3)) - ((2*A*b + a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(7/3)*b^(5/3)) + ((2*A*b + a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(7/3)*b^(5/3))]
    @test_int [(A + B*x^3)/(a + b*x^3)^3, x, 8, ((A*b - a*B)*x)/(6*a*b*(a + b*x^3)^2) + ((5*A*b + a*B)*x)/(18*a^2*b*(a + b*x^3)) - ((5*A*b + a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*b^(4/3)) + ((5*A*b + a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(8/3)*b^(4/3)) - ((5*A*b + a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(8/3)*b^(4/3))]
    @test_int [(A + B*x^3)/(x^2*(a + b*x^3)^3), x, 9, (-2*(7*A*b - a*B))/(9*a^3*b*x) + (A*b - a*B)/(6*a*b*x*(a + b*x^3)^2) + (7*A*b - a*B)/(18*a^2*b*x*(a + b*x^3)) + (2*(7*A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(10/3)*b^(2/3)) + (2*(7*A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(10/3)*b^(2/3)) - ((7*A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(27*a^(10/3)*b^(2/3))]
    @test_int [(A + B*x^3)/(x^3*(a + b*x^3)^3), x, 9, (-5*(4*A*b - a*B))/(18*a^3*b*x^2) + (A*b - a*B)/(6*a*b*x^2*(a + b*x^3)^2) + (4*A*b - a*B)/(9*a^2*b*x^2*(a + b*x^3)) + (5*(4*A*b - a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(11/3)*b^(1/3)) - (5*(4*A*b - a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(11/3)*b^(1/3)) + (5*(4*A*b - a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(11/3)*b^(1/3))]
    @test_int [(A + B*x^3)/(x^5*(a + b*x^3)^3), x, 10, (-7*(5*A*b - 2*a*B))/(36*a^3*b*x^4) + (7*(5*A*b - 2*a*B))/(9*a^4*x) + (A*b - a*B)/(6*a*b*x^4*(a + b*x^3)^2) + (5*A*b - 2*a*B)/(9*a^2*b*x^4*(a + b*x^3)) - (7*b^(1/3)*(5*A*b - 2*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(13/3)) - (7*b^(1/3)*(5*A*b - 2*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(13/3)) + (7*b^(1/3)*(5*A*b - 2*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(54*a^(13/3))]
    @test_int [(A + B*x^3)/(x^6*(a + b*x^3)^3), x, 10, (-4*(11*A*b - 5*a*B))/(45*a^3*b*x^5) + (2*(11*A*b - 5*a*B))/(9*a^4*x^2) + (A*b - a*B)/(6*a*b*x^5*(a + b*x^3)^2) + (11*A*b - 5*a*B)/(18*a^2*b*x^5*(a + b*x^3)) - (4*b^(2/3)*(11*A*b - 5*a*B)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(14/3)) + (4*b^(2/3)*(11*A*b - 5*a*B)*log(a^(1/3) + b^(1/3)*x))/(27*a^(14/3)) - (2*b^(2/3)*(11*A*b - 5*a*B)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(27*a^(14/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^p / (c+d*x^3)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^8/((a + b*x^3)*(c + d*x^3)), x, 3, x^3/(3*b*d) + (a^2*log(a + b*x^3))/(3*b^2*(b*c - a*d)) - (c^2*log(c + d*x^3))/(3*d^2*(b*c - a*d))]
    @test_int [x^7/((a + b*x^3)*(c + d*x^3)), x, 15, x^2/(2*b*d) - (a^(5/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(5/3)*(b*c - a*d)) + (c^(5/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*d^(5/3)*(b*c - a*d)) - (a^(5/3)*log(a^(1/3) + b^(1/3)*x))/(3*b^(5/3)*(b*c - a*d)) + (c^(5/3)*log(c^(1/3) + d^(1/3)*x))/(3*d^(5/3)*(b*c - a*d)) + (a^(5/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(5/3)*(b*c - a*d)) - (c^(5/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*d^(5/3)*(b*c - a*d))]
    @test_int [x^6/((a + b*x^3)*(c + d*x^3)), x, 14, x/(b*d) - (a^(4/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(4/3)*(b*c - a*d)) + (c^(4/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*d^(4/3)*(b*c - a*d)) + (a^(4/3)*log(a^(1/3) + b^(1/3)*x))/(3*b^(4/3)*(b*c - a*d)) - (c^(4/3)*log(c^(1/3) + d^(1/3)*x))/(3*d^(4/3)*(b*c - a*d)) - (a^(4/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(4/3)*(b*c - a*d)) + (c^(4/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*d^(4/3)*(b*c - a*d))]
    @test_int [x^5/((a + b*x^3)*(c + d*x^3)), x, 3, -((a*log(a + b*x^3))/(3*b*(b*c - a*d))) + (c*log(c + d*x^3))/(3*d*(b*c - a*d))]
    @test_int [x^4/((a + b*x^3)*(c + d*x^3)), x, 13, (a^(2/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(2/3)*(b*c - a*d)) - (c^(2/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*d^(2/3)*(b*c - a*d)) + (a^(2/3)*log(a^(1/3) + b^(1/3)*x))/(3*b^(2/3)*(b*c - a*d)) - (c^(2/3)*log(c^(1/3) + d^(1/3)*x))/(3*d^(2/3)*(b*c - a*d)) - (a^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(2/3)*(b*c - a*d)) + (c^(2/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*d^(2/3)*(b*c - a*d))]
    @test_int [x^3/((a + b*x^3)*(c + d*x^3)), x, 13, (a^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^(1/3)*(b*c - a*d)) - (c^(1/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*d^(1/3)*(b*c - a*d)) - (a^(1/3)*log(a^(1/3) + b^(1/3)*x))/(3*b^(1/3)*(b*c - a*d)) + (c^(1/3)*log(c^(1/3) + d^(1/3)*x))/(3*d^(1/3)*(b*c - a*d)) + (a^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*b^(1/3)*(b*c - a*d)) - (c^(1/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*d^(1/3)*(b*c - a*d))]
    @test_int [x^2/((a + b*x^3)*(c + d*x^3)), x, 4, log(a + b*x^3)/(3*(b*c - a*d)) - log(c + d*x^3)/(3*(b*c - a*d))]
    @test_int [x^1/((a + b*x^3)*(c + d*x^3)), x, 13, -((b^(1/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*(b*c - a*d))) + (d^(1/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(1/3)*(b*c - a*d)) - (b^(1/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(1/3)*(b*c - a*d)) + (d^(1/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(1/3)*(b*c - a*d)) + (b^(1/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(1/3)*(b*c - a*d)) - (d^(1/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(1/3)*(b*c - a*d))]
    @test_int [x^0/((a + b*x^3)*(c + d*x^3)), x, 13, -((b^(2/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*(b*c - a*d))) + (d^(2/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(2/3)*(b*c - a*d)) + (b^(2/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(2/3)*(b*c - a*d)) - (d^(2/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(2/3)*(b*c - a*d)) - (b^(2/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(2/3)*(b*c - a*d)) + (d^(2/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(2/3)*(b*c - a*d))]
    @test_int [1/(x^1*(a + b*x^3)*(c + d*x^3)), x, 3, log(x)/(a*c) - (b*log(a + b*x^3))/(3*a*(b*c - a*d)) + (d*log(c + d*x^3))/(3*c*(b*c - a*d))]
    @test_int [1/(x^2*(a + b*x^3)*(c + d*x^3)), x, 15, -(1/(a*c*x)) + (b^(4/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*(b*c - a*d)) - (d^(4/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(4/3)*(b*c - a*d)) + (b^(4/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(4/3)*(b*c - a*d)) - (d^(4/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(4/3)*(b*c - a*d)) - (b^(4/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(4/3)*(b*c - a*d)) + (d^(4/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(4/3)*(b*c - a*d))]
    @test_int [1/(x^3*(a + b*x^3)*(c + d*x^3)), x, 14, -(1/(2*a*c*x^2)) + (b^(5/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*(b*c - a*d)) - (d^(5/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(5/3)*(b*c - a*d)) - (b^(5/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(5/3)*(b*c - a*d)) + (d^(5/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(5/3)*(b*c - a*d)) + (b^(5/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(5/3)*(b*c - a*d)) - (d^(5/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(5/3)*(b*c - a*d))]
    @test_int [1/(x^4*(a + b*x^3)*(c + d*x^3)), x, 3, -(1/(3*a*c*x^3)) - ((b*c + a*d)*log(x))/(a^2*c^2) + (b^2*log(a + b*x^3))/(3*a^2*(b*c - a*d)) - (d^2*log(c + d*x^3))/(3*c^2*(b*c - a*d))]
    @test_int [1/(x^5*(a + b*x^3)*(c + d*x^3)), x, 16, -(1/(4*a*c*x^4)) + (b*c + a*d)/(a^2*c^2*x) - (b^(7/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(7/3)*(b*c - a*d)) + (d^(7/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(7/3)*(b*c - a*d)) - (b^(7/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(7/3)*(b*c - a*d)) + (d^(7/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(7/3)*(b*c - a*d)) + (b^(7/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(7/3)*(b*c - a*d)) - (d^(7/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(7/3)*(b*c - a*d))]
    @test_int [1/(x^6*(a + b*x^3)*(c + d*x^3)), x, 15, -(1/(5*a*c*x^5)) + (b*c + a*d)/(2*a^2*c^2*x^2) - (b^(8/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(8/3)*(b*c - a*d)) + (d^(8/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(8/3)*(b*c - a*d)) + (b^(8/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(8/3)*(b*c - a*d)) - (d^(8/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(8/3)*(b*c - a*d)) - (b^(8/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(8/3)*(b*c - a*d)) + (d^(8/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(8/3)*(b*c - a*d))]
    @test_int [1/(x^7*(a + b*x^3)*(c + d*x^3)), x, 3, -(1/(6*a*c*x^6)) + (b*c + a*d)/(3*a^2*c^2*x^3) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*log(x))/(a^3*c^3) - (b^3*log(a + b*x^3))/(3*a^3*(b*c - a*d)) + (d^3*log(c + d*x^3))/(3*c^3*(b*c - a*d))]
    @test_int [1/(x^8*(a + b*x^3)*(c + d*x^3)), x, 17, -(1/(7*a*c*x^7)) + (b*c + a*d)/(4*a^2*c^2*x^4) - (b^2*c^2 + a*b*c*d + a^2*d^2)/(a^3*c^3*x) + (b^(10/3)*atan((a^(1/3) - 2*b^(1/3)*x)/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(10/3)*(b*c - a*d)) - (d^(10/3)*atan((c^(1/3) - 2*d^(1/3)*x)/(sqrt(3)*c^(1/3))))/(sqrt(3)*c^(10/3)*(b*c - a*d)) + (b^(10/3)*log(a^(1/3) + b^(1/3)*x))/(3*a^(10/3)*(b*c - a*d)) - (d^(10/3)*log(c^(1/3) + d^(1/3)*x))/(3*c^(10/3)*(b*c - a*d)) - (b^(10/3)*log(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2))/(6*a^(10/3)*(b*c - a*d)) + (d^(10/3)*log(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2))/(6*c^(10/3)*(b*c - a*d))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^p*(c+d*x^3)^q*with*m*symbolic=#

    @test_int [x^m*(a + b*x^3)^5*(A + B*x^3), x, 2, (a^5*A*x^(1 + m))/(1 + m) + (a^4*(5*A*b + a*B)*x^(4 + m))/(4 + m) + (5*a^3*b*(2*A*b + a*B)*x^(7 + m))/(7 + m) + (10*a^2*b^2*(A*b + a*B)*x^(10 + m))/(10 + m) + (5*a*b^3*(A*b + 2*a*B)*x^(13 + m))/(13 + m) + (b^4*(A*b + 5*a*B)*x^(16 + m))/(16 + m) + (b^5*B*x^(19 + m))/(19 + m)]
    @test_int [x^m*(a + b*x^3)^2*(A + B*x^3), x, 2, (a^2*A*x^(1 + m))/(1 + m) + (a*(2*A*b + a*B)*x^(4 + m))/(4 + m) + (b*(A*b + 2*a*B)*x^(7 + m))/(7 + m) + (b^2*B*x^(10 + m))/(10 + m)]
    @test_int [x^m*(a + b*x^3)*(A + B*x^3), x, 2, (a*A*x^(1 + m))/(1 + m) + ((A*b + a*B)*x^(4 + m))/(4 + m) + (b*B*x^(7 + m))/(7 + m)]
    @test_int [(x^m*(A + B*x^3))/(a + b*x^3), x, 2, (B*x^(1 + m))/(b*(1 + m)) + ((A*b - a*B)*x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(a*b*(1 + m))]
    @test_int [(x^m*(A + B*x^3))/(a + b*x^3)^2, x, 2, ((A*b - a*B)*x^(1 + m))/(3*a*b*(a + b*x^3)) + ((A*b*(2 - m) + a*B*(1 + m))*x^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(3*a^2*b*(1 + m))]
    @test_int [(x^m*(A + B*x^3))/(a + b*x^3)^3, x, 2, ((A*b - a*B)*x^(1 + m))/(6*a*b*(a + b*x^3)^2) + ((A*b*(5 - m) + a*B*(1 + m))*x^(1 + m)*HypergeometricFunctions._₂F₁(2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(6*a^3*b*(1 + m))]

    @test_int [(e*x)^m/((a + b*x^3)*(c + d*x^3)), x, 3, (b*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(a*(b*c - a*d)*e*(1 + m)) - (d*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/3, (4 + m)/3, -((d*x^3)/c)))/(c*(b*c - a*d)*e*(1 + m))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x^3)^p*(c+d*x^3)^q=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^3)^p*(c+d*x^3)^1=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(7/2)*(a + b*x^3)*(A + B*x^3), x, 2, (2*a*A*x^(9/2))/9 + (2*(A*b + a*B)*x^(15/2))/15 + (2*b*B*x^(21/2))/21]
    @test_int [x^(5/2)*(a + b*x^3)*(A + B*x^3), x, 2, (2*a*A*x^(7/2))/7 + (2*(A*b + a*B)*x^(13/2))/13 + (2*b*B*x^(19/2))/19]
    @test_int [x^(3/2)*(a + b*x^3)*(A + B*x^3), x, 2, (2*a*A*x^(5/2))/5 + (2*(A*b + a*B)*x^(11/2))/11 + (2*b*B*x^(17/2))/17]
    @test_int [sqrt(x)*(a + b*x^3)*(A + B*x^3), x, 2, (2*a*A*x^(3/2))/3 + (2*(A*b + a*B)*x^(9/2))/9 + (2*b*B*x^(15/2))/15]
    @test_int [((a + b*x^3)*(A + B*x^3))/sqrt(x), x, 2, 2*a*A*sqrt(x) + (2*(A*b + a*B)*x^(7/2))/7 + (2*b*B*x^(13/2))/13]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^(3/2), x, 2, (-2*a*A)/sqrt(x) + (2*(A*b + a*B)*x^(5/2))/5 + (2*b*B*x^(11/2))/11]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^(5/2), x, 2, (-2*a*A)/(3*x^(3/2)) + (2*(A*b + a*B)*x^(3/2))/3 + (2*b*B*x^(9/2))/9]
    @test_int [((a + b*x^3)*(A + B*x^3))/x^(7/2), x, 2, (-2*a*A)/(5*x^(5/2)) + 2*(A*b + a*B)*sqrt(x) + (2*b*B*x^(7/2))/7]

    @test_int [x^(7/2)*(a + b*x^3)^2*(A + B*x^3), x, 2, (2*a^2*A*x^(9/2))/9 + (2*a*(2*A*b + a*B)*x^(15/2))/15 + (2*b*(A*b + 2*a*B)*x^(21/2))/21 + (2*b^2*B*x^(27/2))/27]
    @test_int [x^(5/2)*(a + b*x^3)^2*(A + B*x^3), x, 2, (2*a^2*A*x^(7/2))/7 + (2*a*(2*A*b + a*B)*x^(13/2))/13 + (2*b*(A*b + 2*a*B)*x^(19/2))/19 + (2*b^2*B*x^(25/2))/25]
    @test_int [x^(3/2)*(a + b*x^3)^2*(A + B*x^3), x, 2, (2*a^2*A*x^(5/2))/5 + (2*a*(2*A*b + a*B)*x^(11/2))/11 + (2*b*(A*b + 2*a*B)*x^(17/2))/17 + (2*b^2*B*x^(23/2))/23]
    @test_int [sqrt(x)*(a + b*x^3)^2*(A + B*x^3), x, 2, (2*a^2*A*x^(3/2))/3 + (2*a*(2*A*b + a*B)*x^(9/2))/9 + (2*b*(A*b + 2*a*B)*x^(15/2))/15 + (2*b^2*B*x^(21/2))/21]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/sqrt(x), x, 2, 2*a^2*A*sqrt(x) + (2*a*(2*A*b + a*B)*x^(7/2))/7 + (2*b*(A*b + 2*a*B)*x^(13/2))/13 + (2*b^2*B*x^(19/2))/19]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^(3/2), x, 2, (-2*a^2*A)/sqrt(x) + (2*a*(2*A*b + a*B)*x^(5/2))/5 + (2*b*(A*b + 2*a*B)*x^(11/2))/11 + (2*b^2*B*x^(17/2))/17]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^(5/2), x, 2, (-2*a^2*A)/(3*x^(3/2)) + (2*a*(2*A*b + a*B)*x^(3/2))/3 + (2*b*(A*b + 2*a*B)*x^(9/2))/9 + (2*b^2*B*x^(15/2))/15]
    @test_int [((a + b*x^3)^2*(A + B*x^3))/x^(7/2), x, 2, (-2*a^2*A)/(5*x^(5/2)) + 2*a*(2*A*b + a*B)*sqrt(x) + (2*b*(A*b + 2*a*B)*x^(7/2))/7 + (2*b^2*B*x^(13/2))/13]

    @test_int [x^(7/2)*(a + b*x^3)^3*(A + B*x^3), x, 2, (2*a^3*A*x^(9/2))/9 + (2*a^2*(3*A*b + a*B)*x^(15/2))/15 + (2*a*b*(A*b + a*B)*x^(21/2))/7 + (2*b^2*(A*b + 3*a*B)*x^(27/2))/27 + (2*b^3*B*x^(33/2))/33]
    @test_int [x^(5/2)*(a + b*x^3)^3*(A + B*x^3), x, 2, (2*a^3*A*x^(7/2))/7 + (2*a^2*(3*A*b + a*B)*x^(13/2))/13 + (6*a*b*(A*b + a*B)*x^(19/2))/19 + (2*b^2*(A*b + 3*a*B)*x^(25/2))/25 + (2*b^3*B*x^(31/2))/31]
    @test_int [x^(3/2)*(a + b*x^3)^3*(A + B*x^3), x, 2, (2*a^3*A*x^(5/2))/5 + (2*a^2*(3*A*b + a*B)*x^(11/2))/11 + (6*a*b*(A*b + a*B)*x^(17/2))/17 + (2*b^2*(A*b + 3*a*B)*x^(23/2))/23 + (2*b^3*B*x^(29/2))/29]
    @test_int [sqrt(x)*(a + b*x^3)^3*(A + B*x^3), x, 2, (2*a^3*A*x^(3/2))/3 + (2*a^2*(3*A*b + a*B)*x^(9/2))/9 + (2*a*b*(A*b + a*B)*x^(15/2))/5 + (2*b^2*(A*b + 3*a*B)*x^(21/2))/21 + (2*b^3*B*x^(27/2))/27]
    @test_int [((a + b*x^3)^3*(A + B*x^3))/sqrt(x), x, 2, 2*a^3*A*sqrt(x) + (2*a^2*(3*A*b + a*B)*x^(7/2))/7 + (6*a*b*(A*b + a*B)*x^(13/2))/13 + (2*b^2*(A*b + 3*a*B)*x^(19/2))/19 + (2*b^3*B*x^(25/2))/25]
    @test_int [((a + b*x^3)^3*(A + B*x^3))/x^(3/2), x, 2, (-2*a^3*A)/sqrt(x) + (2*a^2*(3*A*b + a*B)*x^(5/2))/5 + (6*a*b*(A*b + a*B)*x^(11/2))/11 + (2*b^2*(A*b + 3*a*B)*x^(17/2))/17 + (2*b^3*B*x^(23/2))/23]
    @test_int [((a + b*x^3)^3*(A + B*x^3))/x^(5/2), x, 2, (-2*a^3*A)/(3*x^(3/2)) + (2*a^2*(3*A*b + a*B)*x^(3/2))/3 + (2*a*b*(A*b + a*B)*x^(9/2))/3 + (2*b^2*(A*b + 3*a*B)*x^(15/2))/15 + (2*b^3*B*x^(21/2))/21]
    @test_int [((a + b*x^3)^3*(A + B*x^3))/x^(7/2), x, 2, (-2*a^3*A)/(5*x^(5/2)) + 2*a^2*(3*A*b + a*B)*sqrt(x) + (6*a*b*(A*b + a*B)*x^(7/2))/7 + (2*b^2*(A*b + 3*a*B)*x^(13/2))/13 + (2*b^3*B*x^(19/2))/19]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(x^(7/2)*(A + B*x^3))/(a + b*x^3), x, 5, (2*(A*b - a*B)*x^(3/2))/(3*b^2) + (2*B*x^(9/2))/(9*b) - (2*sqrt(a)*(A*b - a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(3*b^(5/2))]
    @test_int [(x^(5/2)*(A + B*x^3))/(a + b*x^3), x, 13, (2*(A*b - a*B)*sqrt(x))/b^2 + (2*B*x^(7/2))/(7*b) + (a^(1/6)*(A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*b^(13/6)) - (a^(1/6)*(A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*b^(13/6)) - (2*a^(1/6)*(A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(3*b^(13/6)) + (a^(1/6)*(A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*b^(13/6)) - (a^(1/6)*(A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*b^(13/6))]
    @test_int [(x^(3/2)*(A + B*x^3))/(a + b*x^3), x, 12, (2*B*x^(5/2))/(5*b) - ((A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(1/6)*b^(11/6)) + ((A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(1/6)*b^(11/6)) + (2*(A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(1/6)*b^(11/6)) + ((A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(1/6)*b^(11/6)) - ((A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(1/6)*b^(11/6))]
    @test_int [(sqrt(x)*(A + B*x^3))/(a + b*x^3), x, 4, (2*B*x^(3/2))/(3*b) + (2*(A*b - a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(3*sqrt(a)*b^(3/2))]
    @test_int [(A + B*x^3)/(sqrt(x)*(a + b*x^3)), x, 12, (2*B*sqrt(x))/b - ((A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(5/6)*b^(7/6)) + ((A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(5/6)*b^(7/6)) + (2*(A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(5/6)*b^(7/6)) - ((A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(5/6)*b^(7/6)) + ((A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(5/6)*b^(7/6))]
    @test_int [(A + B*x^3)/(x^(3/2)*(a + b*x^3)), x, 12, -((2*A)/(a*sqrt(x))) + ((A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(7/6)*b^(5/6)) - ((A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(7/6)*b^(5/6)) - (2*(A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(7/6)*b^(5/6)) - ((A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(7/6)*b^(5/6)) + ((A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(7/6)*b^(5/6))]
    @test_int [(A + B*x^3)/(x^(5/2)*(a + b*x^3)), x, 4, (-2*A)/(3*a*x^(3/2)) - (2*(A*b - a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(3*a^(3/2)*sqrt(b))]
    @test_int [(A + B*x^3)/(x^(7/2)*(a + b*x^3)), x, 12, -((2*A)/(5*a*x^(5/2))) + ((A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(11/6)*b^(1/6)) - ((A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(11/6)*b^(1/6)) - (2*(A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(3*a^(11/6)*b^(1/6)) + ((A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(11/6)*b^(1/6)) - ((A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(2*sqrt(3)*a^(11/6)*b^(1/6))]

    @test_int [(x^(7/2)*(A + B*x^3))/(a + b*x^3)^2, x, 5, -((A*b - 3*a*B)*x^(3/2))/(3*a*b^2) + ((A*b - a*B)*x^(9/2))/(3*a*b*(a + b*x^3)) + ((A*b - 3*a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(3*sqrt(a)*b^(5/2))]
    @test_int [(x^(5/2)*(A + B*x^3))/(a + b*x^3)^2, x, 13, -(((A*b - 7*a*B)*sqrt(x))/(3*a*b^2)) + ((A*b - a*B)*x^(7/2))/(3*a*b*(a + b*x^3)) - ((A*b - 7*a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(5/6)*b^(13/6)) + ((A*b - 7*a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(5/6)*b^(13/6)) + ((A*b - 7*a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(9*a^(5/6)*b^(13/6)) - ((A*b - 7*a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(5/6)*b^(13/6)) + ((A*b - 7*a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(5/6)*b^(13/6))]
    @test_int [(x^(3/2)*(A + B*x^3))/(a + b*x^3)^2, x, 12, ((A*b - a*B)*x^(5/2))/(3*a*b*(a + b*x^3)) - ((A*b + 5*a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(7/6)*b^(11/6)) + ((A*b + 5*a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(7/6)*b^(11/6)) + ((A*b + 5*a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(9*a^(7/6)*b^(11/6)) + ((A*b + 5*a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(7/6)*b^(11/6)) - ((A*b + 5*a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(7/6)*b^(11/6))]
    @test_int [(sqrt(x)*(A + B*x^3))/(a + b*x^3)^2, x, 4, ((A*b - a*B)*x^(3/2))/(3*a*b*(a + b*x^3)) + ((A*b + a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(3*a^(3/2)*b^(3/2))]
    @test_int [(A + B*x^3)/(sqrt(x)*(a + b*x^3)^2), x, 12, ((A*b - a*B)*sqrt(x))/(3*a*b*(a + b*x^3)) - ((5*A*b + a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(11/6)*b^(7/6)) + ((5*A*b + a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(11/6)*b^(7/6)) + ((5*A*b + a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(9*a^(11/6)*b^(7/6)) - ((5*A*b + a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(11/6)*b^(7/6)) + ((5*A*b + a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(11/6)*b^(7/6))]
    @test_int [(A + B*x^3)/(x^(3/2)*(a + b*x^3)^2), x, 13, -((7*A*b - a*B)/(3*a^2*b*sqrt(x))) + (A*b - a*B)/(3*a*b*sqrt(x)*(a + b*x^3)) + ((7*A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(13/6)*b^(5/6)) - ((7*A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(13/6)*b^(5/6)) - ((7*A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(9*a^(13/6)*b^(5/6)) - ((7*A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(13/6)*b^(5/6)) + ((7*A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(13/6)*b^(5/6))]
    @test_int [(A + B*x^3)/(x^(5/2)*(a + b*x^3)^2), x, 5, -(3*A*b - a*B)/(3*a^2*b*x^(3/2)) + (A*b - a*B)/(3*a*b*x^(3/2)*(a + b*x^3)) - ((3*A*b - a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(3*a^(5/2)*sqrt(b))]
    @test_int [(A + B*x^3)/(x^(7/2)*(a + b*x^3)^2), x, 13, -((11*A*b - 5*a*B)/(15*a^2*b*x^(5/2))) + (A*b - a*B)/(3*a*b*x^(5/2)*(a + b*x^3)) + ((11*A*b - 5*a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(17/6)*b^(1/6)) - ((11*A*b - 5*a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(18*a^(17/6)*b^(1/6)) - ((11*A*b - 5*a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(9*a^(17/6)*b^(1/6)) + ((11*A*b - 5*a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(17/6)*b^(1/6)) - ((11*A*b - 5*a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(12*sqrt(3)*a^(17/6)*b^(1/6))]

    @test_int [(x^(7/2)*(A + B*x^3))/(a + b*x^3)^3, x, 5, ((A*b - a*B)*x^(9/2))/(6*a*b*(a + b*x^3)^2) - ((A*b + 3*a*B)*x^(3/2))/(12*a*b^2*(a + b*x^3)) + ((A*b + 3*a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(12*a^(3/2)*b^(5/2))]
    @test_int [(x^(5/2)*(A + B*x^3))/(a + b*x^3)^3, x, 13, ((A*b - a*B)*x^(7/2))/(6*a*b*(a + b*x^3)^2) - ((5*A*b + 7*a*B)*sqrt(x))/(36*a*b^2*(a + b*x^3)) - ((5*A*b + 7*a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(11/6)*b^(13/6)) + ((5*A*b + 7*a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(11/6)*b^(13/6)) + ((5*A*b + 7*a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(108*a^(11/6)*b^(13/6)) - ((5*A*b + 7*a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(11/6)*b^(13/6)) + ((5*A*b + 7*a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(11/6)*b^(13/6))]
    @test_int [(x^(3/2)*(A + B*x^3))/(a + b*x^3)^3, x, 13, ((A*b - a*B)*x^(5/2))/(6*a*b*(a + b*x^3)^2) + ((7*A*b + 5*a*B)*x^(5/2))/(36*a^2*b*(a + b*x^3)) - ((7*A*b + 5*a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(13/6)*b^(11/6)) + ((7*A*b + 5*a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(13/6)*b^(11/6)) + ((7*A*b + 5*a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(108*a^(13/6)*b^(11/6)) + ((7*A*b + 5*a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(13/6)*b^(11/6)) - ((7*A*b + 5*a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(13/6)*b^(11/6))]
    @test_int [(sqrt(x)*(A + B*x^3))/(a + b*x^3)^3, x, 5, ((A*b - a*B)*x^(3/2))/(6*a*b*(a + b*x^3)^2) + ((3*A*b + a*B)*x^(3/2))/(12*a^2*b*(a + b*x^3)) + ((3*A*b + a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(12*a^(5/2)*b^(3/2))]
    @test_int [(A + B*x^3)/(sqrt(x)*(a + b*x^3)^3), x, 13, ((A*b - a*B)*sqrt(x))/(6*a*b*(a + b*x^3)^2) + ((11*A*b + a*B)*sqrt(x))/(36*a^2*b*(a + b*x^3)) - (5*(11*A*b + a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(17/6)*b^(7/6)) + (5*(11*A*b + a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(17/6)*b^(7/6)) + (5*(11*A*b + a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(108*a^(17/6)*b^(7/6)) - (5*(11*A*b + a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(17/6)*b^(7/6)) + (5*(11*A*b + a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(17/6)*b^(7/6))]
    @test_int [(A + B*x^3)/(x^(3/2)*(a + b*x^3)^3), x, 14, -((7*(13*A*b - a*B))/(36*a^3*b*sqrt(x))) + (A*b - a*B)/(6*a*b*sqrt(x)*(a + b*x^3)^2) + (13*A*b - a*B)/(36*a^2*b*sqrt(x)*(a + b*x^3)) + (7*(13*A*b - a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(19/6)*b^(5/6)) - (7*(13*A*b - a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(19/6)*b^(5/6)) - (7*(13*A*b - a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(108*a^(19/6)*b^(5/6)) - (7*(13*A*b - a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(19/6)*b^(5/6)) + (7*(13*A*b - a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(19/6)*b^(5/6))]
    @test_int [(A + B*x^3)/(x^(5/2)*(a + b*x^3)^3), x, 6, -(5*A*b - a*B)/(4*a^3*b*x^(3/2)) + (A*b - a*B)/(6*a*b*x^(3/2)*(a + b*x^3)^2) + (5*A*b - a*B)/(12*a^2*b*x^(3/2)*(a + b*x^3)) - ((5*A*b - a*B)*atan((sqrt(b)*x^(3/2))/sqrt(a)))/(4*a^(7/2)*sqrt(b))]
    @test_int [(A + B*x^3)/(x^(7/2)*(a + b*x^3)^3), x, 14, -((11*(17*A*b - 5*a*B))/(180*a^3*b*x^(5/2))) + (A*b - a*B)/(6*a*b*x^(5/2)*(a + b*x^3)^2) + (17*A*b - 5*a*B)/(36*a^2*b*x^(5/2)*(a + b*x^3)) + (11*(17*A*b - 5*a*B)*atan(sqrt(3) - (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(23/6)*b^(1/6)) - (11*(17*A*b - 5*a*B)*atan(sqrt(3) + (2*b^(1/6)*sqrt(x))/a^(1/6)))/(216*a^(23/6)*b^(1/6)) - (11*(17*A*b - 5*a*B)*atan((b^(1/6)*sqrt(x))/a^(1/6)))/(108*a^(23/6)*b^(1/6)) + (11*(17*A*b - 5*a*B)*log(a^(1/3) - sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(23/6)*b^(1/6)) - (11*(17*A*b - 5*a*B)*log(a^(1/3) + sqrt(3)*a^(1/6)*b^(1/6)*sqrt(x) + b^(1/3)*x))/(144*sqrt(3)*a^(23/6)*b^(1/6))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^p*(c+d*x^3)^(q/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)*(c+d*x^3)^(q/2)=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^8*sqrt(a + b*x^3)*(A + B*x^3), x, 3, (2*a^2*(A*b - a*B)*(a + b*x^3)^(3/2))/(9*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x^3)^(5/2))/(15*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(7/2))/(21*b^4) + (2*B*(a + b*x^3)^(9/2))/(27*b^4)]
    @test_int [x^5*sqrt(a + b*x^3)*(A + B*x^3), x, 3, (-2*a*(A*b - a*B)*(a + b*x^3)^(3/2))/(9*b^3) + (2*(A*b - 2*a*B)*(a + b*x^3)^(5/2))/(15*b^3) + (2*B*(a + b*x^3)^(7/2))/(21*b^3)]
    @test_int [x^2*sqrt(a + b*x^3)*(A + B*x^3), x, 3, (2*(A*b - a*B)*(a + b*x^3)^(3/2))/(9*b^2) + (2*B*(a + b*x^3)^(5/2))/(15*b^2)]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^1, x, 5, (2*A*sqrt(a + b*x^3))/3 + (2*B*(a + b*x^3)^(3/2))/(9*b) - (2*sqrt(a)*A*atanh(sqrt(a + b*x^3)/sqrt(a)))/3]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^4, x, 5, ((A*b + 2*a*B)*sqrt(a + b*x^3))/(3*a) - (A*(a + b*x^3)^(3/2))/(3*a*x^3) - ((A*b + 2*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^7, x, 5, ((A*b - 4*a*B)*sqrt(a + b*x^3))/(12*a*x^3) - (A*(a + b*x^3)^(3/2))/(6*a*x^6) + (b*(A*b - 4*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(12*a^(3/2))]

    @test_int [x^3*sqrt(a + b*x^3)*(A + B*x^3), x, 4, (6*a*(17*A*b - 8*a*B)*x*sqrt(a + b*x^3))/(935*b^2) + (2*(17*A*b - 8*a*B)*x^4*sqrt(a + b*x^3))/(187*b) + (2*B*x^4*(a + b*x^3)^(3/2))/(17*b) - (4*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(17*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(935*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*sqrt(a + b*x^3)*(A + B*x^3), x, 3, (2*(11*A*b - 2*a*B)*x*sqrt(a + b*x^3))/(55*b) + (2*B*x*(a + b*x^3)^(3/2))/(11*b) + (2*3^(3/4)*sqrt(2 + sqrt(3))*a*(11*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(55*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^3, x, 3, ((5*A*b + 4*a*B)*x*sqrt(a + b*x^3))/(10*a) - (A*(a + b*x^3)^(3/2))/(2*a*x^2) + (3^(3/4)*sqrt(2 + sqrt(3))*(5*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(10*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^6, x, 3, ((A*b - 10*a*B)*sqrt(a + b*x^3))/(20*a*x^2) - (A*(a + b*x^3)^(3/2))/(5*a*x^5) - (3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*(A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(20*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^9, x, 4, ((7*A*b - 16*a*B)*sqrt(a + b*x^3))/(80*a*x^5) + (3*b*(7*A*b - 16*a*B)*sqrt(a + b*x^3))/(320*a^2*x^2) - (A*(a + b*x^3)^(3/2))/(8*a*x^8) + (3^(3/4)*sqrt(2 + sqrt(3))*b^(5/3)*(7*A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(320*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^4*sqrt(a + b*x^3)*(A + B*x^3), x, 6, (6*a*(19*A*b - 10*a*B)*x^2*sqrt(a + b*x^3))/(1729*b^2) + (2*(19*A*b - 10*a*B)*x^5*sqrt(a + b*x^3))/(247*b) - (24*a^2*(19*A*b - 10*a*B)*sqrt(a + b*x^3))/(1729*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*B*x^5*(a + b*x^3)^(3/2))/(19*b) + (12*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(19*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (8*sqrt(2)*3^(3/4)*a^(7/3)*(19*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1*sqrt(a + b*x^3)*(A + B*x^3), x, 5, (2*(13*A*b - 4*a*B)*x^2*sqrt(a + b*x^3))/(91*b) + (6*a*(13*A*b - 4*a*B)*sqrt(a + b*x^3))/(91*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*B*x^2*(a + b*x^3)^(3/2))/(13*b) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2)*3^(3/4)*a^(4/3)*(13*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^2, x, 5, ((7*A*b + 2*a*B)*x^2*sqrt(a + b*x^3))/(7*a) + (3*(7*A*b + 2*a*B)*sqrt(a + b*x^3))/(7*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(a*x) - (3*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(14*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (sqrt(2)*3^(3/4)*a^(1/3)*(7*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^5, x, 5, -(((A*b + 8*a*B)*sqrt(a + b*x^3))/(8*a*x)) + (3*b^(1/3)*(A*b + 8*a*B)*sqrt(a + b*x^3))/(8*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(4*a*x^4) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*b^(1/3)*(A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^8, x, 6, ((5*A*b - 14*a*B)*sqrt(a + b*x^3))/(56*a*x^4) + (3*b*(5*A*b - 14*a*B)*sqrt(a + b*x^3))/(112*a^2*x) - (3*b^(4/3)*(5*A*b - 14*a*B)*sqrt(a + b*x^3))/(112*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(7*a*x^7) + (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(5*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*b^(4/3)*(5*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(56*sqrt(2)*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^11, x, 7, ((11*A*b - 20*a*B)*sqrt(a + b*x^3))/(140*a*x^7) + (3*b*(11*A*b - 20*a*B)*sqrt(a + b*x^3))/(1120*a^2*x^4) - (3*b^2*(11*A*b - 20*a*B)*sqrt(a + b*x^3))/(448*a^3*x) + (3*b^(7/3)*(11*A*b - 20*a*B)*sqrt(a + b*x^3))/(448*a^3*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(10*a*x^10) - (3*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(11*A*b - 20*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(896*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (3^(3/4)*b^(7/3)*(11*A*b - 20*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*sqrt(2)*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^8*(a + b*x^3)^(3/2)*(A + B*x^3), x, 3, (2*a^2*(A*b - a*B)*(a + b*x^3)^(5/2))/(15*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x^3)^(7/2))/(21*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(9/2))/(27*b^4) + (2*B*(a + b*x^3)^(11/2))/(33*b^4)]
    @test_int [x^5*(a + b*x^3)^(3/2)*(A + B*x^3), x, 3, (-2*a*(A*b - a*B)*(a + b*x^3)^(5/2))/(15*b^3) + (2*(A*b - 2*a*B)*(a + b*x^3)^(7/2))/(21*b^3) + (2*B*(a + b*x^3)^(9/2))/(27*b^3)]
    @test_int [x^2*(a + b*x^3)^(3/2)*(A + B*x^3), x, 3, (2*(A*b - a*B)*(a + b*x^3)^(5/2))/(15*b^2) + (2*B*(a + b*x^3)^(7/2))/(21*b^2)]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^1, x, 6, (2*a*A*sqrt(a + b*x^3))/3 + (2*A*(a + b*x^3)^(3/2))/9 + (2*B*(a + b*x^3)^(5/2))/(15*b) - (2*a^(3/2)*A*atanh(sqrt(a + b*x^3)/sqrt(a)))/3]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^4, x, 6, ((3*A*b + 2*a*B)*sqrt(a + b*x^3))/3 + ((3*A*b + 2*a*B)*(a + b*x^3)^(3/2))/(9*a) - (A*(a + b*x^3)^(5/2))/(3*a*x^3) - (sqrt(a)*(3*A*b + 2*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/3]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^7, x, 6, (b*(A*b + 4*a*B)*sqrt(a + b*x^3))/(4*a) - ((A*b + 4*a*B)*(a + b*x^3)^(3/2))/(12*a*x^3) - (A*(a + b*x^3)^(5/2))/(6*a*x^6) - (b*(A*b + 4*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*sqrt(a))]

    @test_int [x^3*(a + b*x^3)^(3/2)*(A + B*x^3), x, 5, (54*a^2*(23*A*b - 8*a*B)*x*sqrt(a + b*x^3))/(21505*b^2) + (18*a*(23*A*b - 8*a*B)*x^4*sqrt(a + b*x^3))/(4301*b) + (2*(23*A*b - 8*a*B)*x^4*(a + b*x^3)^(3/2))/(391*b) + (2*B*x^4*(a + b*x^3)^(5/2))/(23*b) - (36*3^(3/4)*sqrt(2 + sqrt(3))*a^3*(23*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21505*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*(a + b*x^3)^(3/2)*(A + B*x^3), x, 4, (18*a*(17*A*b - 2*a*B)*x*sqrt(a + b*x^3))/(935*b) + (2*(17*A*b - 2*a*B)*x*(a + b*x^3)^(3/2))/(187*b) + (2*B*x*(a + b*x^3)^(5/2))/(17*b) + (18*3^(3/4)*sqrt(2 + sqrt(3))*a^2*(17*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(935*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^3, x, 4, (9/110)*(11*A*b + 4*a*B)*x*sqrt(a + b*x^3) + ((11*A*b + 4*a*B)*x*(a + b*x^3)^(3/2))/(22*a) - (A*(a + b*x^3)^(5/2))/(2*a*x^2) + (9*3^(3/4)*sqrt(2 + sqrt(3))*a*(11*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(110*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^6, x, 4, (9*b*(A*b + 2*a*B)*x*sqrt(a + b*x^3))/(20*a) - ((A*b + 2*a*B)*(a + b*x^3)^(3/2))/(4*a*x^2) - (A*(a + b*x^3)^(5/2))/(5*a*x^5) + (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(2/3)*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(20*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^9, x, 4, (9*b*(A*b - 16*a*B)*sqrt(a + b*x^3))/(320*a*x^2) + ((A*b - 16*a*B)*(a + b*x^3)^(3/2))/(80*a*x^5) - (A*(a + b*x^3)^(5/2))/(8*a*x^8) - (9*3^(3/4)*sqrt(2 + sqrt(3))*b^(5/3)*(A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(320*a*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [x^4*(a + b*x^3)^(3/2)*(A + B*x^3), x, 7, (54*a^2*(5*A*b - 2*a*B)*x^2*sqrt(a + b*x^3))/(8645*b^2) + (18*a*(5*A*b - 2*a*B)*x^5*sqrt(a + b*x^3))/(1235*b) - (216*a^3*(5*A*b - 2*a*B)*sqrt(a + b*x^3))/(8645*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*(5*A*b - 2*a*B)*x^5*(a + b*x^3)^(3/2))/(95*b) + (2*B*x^5*(a + b*x^3)^(5/2))/(25*b) + (108*3^(1/4)*sqrt(2 - sqrt(3))*a^(10/3)*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(8645*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (72*sqrt(2)*3^(3/4)*a^(10/3)*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(8645*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^1*(a + b*x^3)^(3/2)*(A + B*x^3), x, 6, (18*a*(19*A*b - 4*a*B)*x^2*sqrt(a + b*x^3))/(1729*b) + (54*a^2*(19*A*b - 4*a*B)*sqrt(a + b*x^3))/(1729*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (2*(19*A*b - 4*a*B)*x^2*(a + b*x^3)^(3/2))/(247*b) + (2*B*x^2*(a + b*x^3)^(5/2))/(19*b) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(7/3)*(19*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (18*sqrt(2)*3^(3/4)*a^(7/3)*(19*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^2, x, 6, (9/91)*(13*A*b + 2*a*B)*x^2*sqrt(a + b*x^3) + (27*a*(13*A*b + 2*a*B)*sqrt(a + b*x^3))/(91*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + ((13*A*b + 2*a*B)*x^2*(a + b*x^3)^(3/2))/(13*a) - (A*(a + b*x^3)^(5/2))/(a*x) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(182*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*sqrt(2)*3^(3/4)*a^(4/3)*(13*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^5, x, 6, (9*b*(7*A*b + 8*a*B)*x^2*sqrt(a + b*x^3))/(56*a) + (27*b^(1/3)*(7*A*b + 8*a*B)*sqrt(a + b*x^3))/(56*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - ((7*A*b + 8*a*B)*(a + b*x^3)^(3/2))/(8*a*x) - (A*(a + b*x^3)^(5/2))/(4*a*x^4) - (27*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*b^(1/3)*(7*A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(112*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*a^(1/3)*b^(1/3)*(7*A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(28*sqrt(2)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^8, x, 6, -((9*b*(A*b + 14*a*B)*sqrt(a + b*x^3))/(112*a*x)) + (27*b^(4/3)*(A*b + 14*a*B)*sqrt(a + b*x^3))/(112*a*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - ((A*b + 14*a*B)*(a + b*x^3)^(3/2))/(56*a*x^4) - (A*(a + b*x^3)^(5/2))/(7*a*x^7) - (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(A*b + 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (9*3^(3/4)*b^(4/3)*(A*b + 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(56*sqrt(2)*a^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/x^11, x, 7, (9*b*(A*b - 4*a*B)*sqrt(a + b*x^3))/(224*a*x^4) + (27*b^2*(A*b - 4*a*B)*sqrt(a + b*x^3))/(448*a^2*x) - (27*b^(7/3)*(A*b - 4*a*B)*sqrt(a + b*x^3))/(448*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + ((A*b - 4*a*B)*(a + b*x^3)^(3/2))/(28*a*x^7) - (A*(a + b*x^3)^(5/2))/(10*a*x^10) + (27*3^(1/4)*sqrt(2 - sqrt(3))*b^(7/3)*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(896*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (9*3^(3/4)*b^(7/3)*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*sqrt(2)*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [(x^8*(A + B*x^3))/sqrt(a + b*x^3), x, 3, (2*a^2*(A*b - a*B)*sqrt(a + b*x^3))/(3*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x^3)^(3/2))/(9*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(5/2))/(15*b^4) + (2*B*(a + b*x^3)^(7/2))/(21*b^4)]
    @test_int [(x^5*(A + B*x^3))/sqrt(a + b*x^3), x, 3, (-2*a*(A*b - a*B)*sqrt(a + b*x^3))/(3*b^3) + (2*(A*b - 2*a*B)*(a + b*x^3)^(3/2))/(9*b^3) + (2*B*(a + b*x^3)^(5/2))/(15*b^3)]
    @test_int [(x^2*(A + B*x^3))/sqrt(a + b*x^3), x, 3, (2*(A*b - a*B)*sqrt(a + b*x^3))/(3*b^2) + (2*B*(a + b*x^3)^(3/2))/(9*b^2)]
    @test_int [(A + B*x^3)/(x^1*sqrt(a + b*x^3)), x, 4, (2*B*sqrt(a + b*x^3))/(3*b) - (2*A*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*sqrt(a))]
    @test_int [(A + B*x^3)/(x^4*sqrt(a + b*x^3)), x, 4, -(A*sqrt(a + b*x^3))/(3*a*x^3) + ((A*b - 2*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(3/2))]
    @test_int [(A + B*x^3)/(x^7*sqrt(a + b*x^3)), x, 5, -(A*sqrt(a + b*x^3))/(6*a*x^6) + ((3*A*b - 4*a*B)*sqrt(a + b*x^3))/(12*a^2*x^3) - (b*(3*A*b - 4*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(12*a^(5/2))]

    @test_int [(x^3*(A + B*x^3))/sqrt(a + b*x^3), x, 3, (2*(11*A*b - 8*a*B)*x*sqrt(a + b*x^3))/(55*b^2) + (2*B*x^4*sqrt(a + b*x^3))/(11*b) - (4*sqrt(2 + sqrt(3))*a*(11*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(55*3^(1/4)*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*(A + B*x^3)/sqrt(a + b*x^3), x, 2, (2*B*x*sqrt(a + b*x^3))/(5*b) + (2*sqrt(2 + sqrt(3))*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(5*3^(1/4)*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^3*sqrt(a + b*x^3)), x, 2, -((A*sqrt(a + b*x^3))/(2*a*x^2)) - (sqrt(2 + sqrt(3))*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*3^(1/4)*a*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^6*sqrt(a + b*x^3)), x, 3, -((A*sqrt(a + b*x^3))/(5*a*x^5)) + ((7*A*b - 10*a*B)*sqrt(a + b*x^3))/(20*a^2*x^2) + (sqrt(2 + sqrt(3))*b^(2/3)*(7*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(20*3^(1/4)*a^2*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(x^4*(A + B*x^3))/sqrt(a + b*x^3), x, 5, (2*(13*A*b - 10*a*B)*x^2*sqrt(a + b*x^3))/(91*b^2) + (2*B*x^5*sqrt(a + b*x^3))/(13*b) - (8*a*(13*A*b - 10*a*B)*sqrt(a + b*x^3))/(91*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(4/3)*(13*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (8*sqrt(2)*a^(4/3)*(13*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(91*3^(1/4)*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(x^1*(A + B*x^3))/sqrt(a + b*x^3), x, 4, (2*B*x^2*sqrt(a + b*x^3))/(7*b) + (2*(7*A*b - 4*a*B)*sqrt(a + b*x^3))/(7*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2)*a^(1/3)*(7*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^2*sqrt(a + b*x^3)), x, 4, -((A*sqrt(a + b*x^3))/(a*x)) + ((A*b + 2*a*B)*sqrt(a + b*x^3))/(a*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(2*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (sqrt(2)*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*a^(2/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^5*sqrt(a + b*x^3)), x, 5, -((A*sqrt(a + b*x^3))/(4*a*x^4)) + ((5*A*b - 8*a*B)*sqrt(a + b*x^3))/(8*a^2*x) - (b^(1/3)*(5*A*b - 8*a*B)*sqrt(a + b*x^3))/(8*a^2*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(5*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(16*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (b^(1/3)*(5*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*a^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^8*sqrt(a + b*x^3)), x, 6, -((A*sqrt(a + b*x^3))/(7*a*x^7)) + ((11*A*b - 14*a*B)*sqrt(a + b*x^3))/(56*a^2*x^4) - (5*b*(11*A*b - 14*a*B)*sqrt(a + b*x^3))/(112*a^3*x) + (5*b^(4/3)*(11*A*b - 14*a*B)*sqrt(a + b*x^3))/(112*a^3*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(11*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(224*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (5*b^(4/3)*(11*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(56*sqrt(2)*3^(1/4)*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(x^8*(A + B*x^3))/(a + b*x^3)^(3/2), x, 3, -((2*a^2*(A*b - a*B))/(3*b^4*sqrt(a + b*x^3))) - (2*a*(2*A*b - 3*a*B)*sqrt(a + b*x^3))/(3*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(3/2))/(9*b^4) + (2*B*(a + b*x^3)^(5/2))/(15*b^4)]
    @test_int [(x^5*(A + B*x^3))/(a + b*x^3)^(3/2), x, 3, (2*a*(A*b - a*B))/(3*b^3*sqrt(a + b*x^3)) + (2*(A*b - 2*a*B)*sqrt(a + b*x^3))/(3*b^3) + (2*B*(a + b*x^3)^(3/2))/(9*b^3)]
    @test_int [(x^2*(A + B*x^3))/(a + b*x^3)^(3/2), x, 3, (-2*(A*b - a*B))/(3*b^2*sqrt(a + b*x^3)) + (2*B*sqrt(a + b*x^3))/(3*b^2)]
    @test_int [(A + B*x^3)/(x^1*(a + b*x^3)^(3/2)), x, 4, (2*(A*b - a*B))/(3*a*b*sqrt(a + b*x^3)) - (2*A*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(3/2))]
    @test_int [(A + B*x^3)/(x^4*(a + b*x^3)^(3/2)), x, 5, -(3*A*b - 2*a*B)/(3*a^2*sqrt(a + b*x^3)) - A/(3*a*x^3*sqrt(a + b*x^3)) + ((3*A*b - 2*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(5/2))]
    @test_int [(A + B*x^3)/(x^7*(a + b*x^3)^(3/2)), x, 6, (b*(5*A*b - 4*a*B))/(4*a^3*sqrt(a + b*x^3)) - A/(6*a*x^6*sqrt(a + b*x^3)) + (5*A*b - 4*a*B)/(12*a^2*x^3*sqrt(a + b*x^3)) - (b*(5*A*b - 4*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(4*a^(7/2))]

    @test_int [(x^6*(A + B*x^3))/(a + b*x^3)^(3/2), x, 4, -((2*(11*A*b - 14*a*B)*x^4)/(33*b^2*sqrt(a + b*x^3))) + (2*B*x^7)/(11*b*sqrt(a + b*x^3)) + (16*(11*A*b - 14*a*B)*x*sqrt(a + b*x^3))/(165*b^3) - (32*sqrt(2 + sqrt(3))*a*(11*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(165*3^(1/4)*b^(10/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(x^3*(A + B*x^3))/(a + b*x^3)^(3/2), x, 3, -((2*(5*A*b - 8*a*B)*x)/(15*b^2*sqrt(a + b*x^3))) + (2*B*x^4)/(5*b*sqrt(a + b*x^3)) + (4*sqrt(2 + sqrt(3))*(5*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(15*3^(1/4)*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x^0*(A + B*x^3)/(a + b*x^3)^(3/2), x, 2, (2*(A*b - a*B)*x)/(3*a*b*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^3*(a + b*x^3)^(3/2)), x, 3, -(A/(2*a*x^2*sqrt(a + b*x^3))) - ((7*A*b - 4*a*B)*x)/(6*a^2*sqrt(a + b*x^3)) - (sqrt(2 + sqrt(3))*(7*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(6*3^(1/4)*a^2*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^6*(a + b*x^3)^(3/2)), x, 4, -(A/(5*a*x^5*sqrt(a + b*x^3))) - (13*A*b - 10*a*B)/(15*a^2*x^2*sqrt(a + b*x^3)) + (7*(13*A*b - 10*a*B)*sqrt(a + b*x^3))/(60*a^3*x^2) + (7*sqrt(2 + sqrt(3))*b^(2/3)*(13*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(60*3^(1/4)*a^3*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(x^4*(A + B*x^3))/(a + b*x^3)^(3/2), x, 5, -((2*(7*A*b - 10*a*B)*x^2)/(21*b^2*sqrt(a + b*x^3))) + (2*B*x^5)/(7*b*sqrt(a + b*x^3)) + (8*(7*A*b - 10*a*B)*sqrt(a + b*x^3))/(21*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (4*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (8*sqrt(2)*a^(1/3)*(7*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(21*3^(1/4)*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(x^1*(A + B*x^3))/(a + b*x^3)^(3/2), x, 4, (2*(A*b - a*B)*x^2)/(3*a*b*sqrt(a + b*x^3)) - (2*(A*b - 4*a*B)*sqrt(a + b*x^3))/(3*a*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*sqrt(2 - sqrt(3))*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*a^(2/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (2*sqrt(2)*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(2/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^2*(a + b*x^3)^(3/2)), x, 5, -(A/(a*x*sqrt(a + b*x^3))) - ((5*A*b - 2*a*B)*x^2)/(3*a^2*sqrt(a + b*x^3)) + ((5*A*b - 2*a*B)*sqrt(a + b*x^3))/(3*a^2*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*sqrt(2 - sqrt(3))*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(6*a^(5/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (sqrt(2)*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*a^(5/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^5*(a + b*x^3)^(3/2)), x, 6, -(A/(4*a*x^4*sqrt(a + b*x^3))) - (11*A*b - 8*a*B)/(12*a^2*x*sqrt(a + b*x^3)) + (5*(11*A*b - 8*a*B)*sqrt(a + b*x^3))/(24*a^3*x) - (5*b^(1/3)*(11*A*b - 8*a*B)*sqrt(a + b*x^3))/(24*a^3*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (5*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(11*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(48*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (5*b^(1/3)*(11*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(12*sqrt(2)*3^(1/4)*a^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^8*(a + b*x^3)^(3/2)), x, 7, -(A/(7*a*x^7*sqrt(a + b*x^3))) - (17*A*b - 14*a*B)/(21*a^2*x^4*sqrt(a + b*x^3)) + (11*(17*A*b - 14*a*B)*sqrt(a + b*x^3))/(168*a^3*x^4) - (55*b*(17*A*b - 14*a*B)*sqrt(a + b*x^3))/(336*a^4*x) + (55*b^(4/3)*(17*A*b - 14*a*B)*sqrt(a + b*x^3))/(336*a^4*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (55*3^(1/4)*sqrt(2 - sqrt(3))*b^(4/3)*(17*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(672*a^(11/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (55*b^(4/3)*(17*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(168*sqrt(2)*3^(1/4)*a^(11/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(x^8*(A + B*x^3))/(a + b*x^3)^(5/2), x, 3, -((2*a^2*(A*b - a*B))/(9*b^4*(a + b*x^3)^(3/2))) + (2*a*(2*A*b - 3*a*B))/(3*b^4*sqrt(a + b*x^3)) + (2*(A*b - 3*a*B)*sqrt(a + b*x^3))/(3*b^4) + (2*B*(a + b*x^3)^(3/2))/(9*b^4)]
    @test_int [(x^5*(A + B*x^3))/(a + b*x^3)^(5/2), x, 3, (2*a*(A*b - a*B))/(9*b^3*(a + b*x^3)^(3/2)) - (2*(A*b - 2*a*B))/(3*b^3*sqrt(a + b*x^3)) + (2*B*sqrt(a + b*x^3))/(3*b^3)]
    @test_int [(x^2*(A + B*x^3))/(a + b*x^3)^(5/2), x, 3, (-2*(A*b - a*B))/(9*b^2*(a + b*x^3)^(3/2)) - (2*B)/(3*b^2*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x*(a + b*x^3)^(5/2)), x, 5, (2*(A*b - a*B))/(9*a*b*(a + b*x^3)^(3/2)) + (2*A)/(3*a^2*sqrt(a + b*x^3)) - (2*A*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(5/2))]
    @test_int [(A + B*x^3)/(x^4*(a + b*x^3)^(5/2)), x, 6, -(5*A*b - 2*a*B)/(9*a^2*(a + b*x^3)^(3/2)) - A/(3*a*x^3*(a + b*x^3)^(3/2)) - (5*A*b - 2*a*B)/(3*a^3*sqrt(a + b*x^3)) + ((5*A*b - 2*a*B)*atanh(sqrt(a + b*x^3)/sqrt(a)))/(3*a^(7/2))]

    @test_int [(x^6*(A + B*x^3))/(a + b*x^3)^(5/2), x, 4, -((2*(5*A*b - 14*a*B)*x^4)/(45*b^2*(a + b*x^3)^(3/2))) + (2*B*x^7)/(5*b*(a + b*x^3)^(3/2)) - (16*(5*A*b - 14*a*B)*x)/(135*b^3*sqrt(a + b*x^3)) + (32*sqrt(2 + sqrt(3))*(5*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(135*3^(1/4)*b^(10/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(x^3*(A + B*x^3))/(a + b*x^3)^(5/2), x, 3, (2*(A*b - a*B)*x^4)/(9*a*b*(a + b*x^3)^(3/2)) - (2*(A*b + 8*a*B)*x)/(27*a*b^2*sqrt(a + b*x^3)) + (4*sqrt(2 + sqrt(3))*(A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a*b^(7/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(a + b*x^3)^(5/2), x, 3, (2*(A*b - a*B)*x)/(9*a*b*(a + b*x^3)^(3/2)) + (2*(7*A*b + 2*a*B)*x)/(27*a^2*b*sqrt(a + b*x^3)) + (2*sqrt(2 + sqrt(3))*(7*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a^2*b^(4/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^3*(a + b*x^3)^(5/2)), x, 4, -(A/(2*a*x^2*(a + b*x^3)^(3/2))) - ((13*A*b - 4*a*B)*x)/(18*a^2*(a + b*x^3)^(3/2)) - (7*(13*A*b - 4*a*B)*x)/(54*a^3*sqrt(a + b*x^3)) - (7*sqrt(2 + sqrt(3))*(13*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(54*3^(1/4)*a^3*b^(1/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^6*(a + b*x^3)^(5/2)), x, 5, -(A/(5*a*x^5*(a + b*x^3)^(3/2))) - (19*A*b - 10*a*B)/(45*a^2*x^2*(a + b*x^3)^(3/2)) - (13*(19*A*b - 10*a*B))/(135*a^3*x^2*sqrt(a + b*x^3)) + (91*(19*A*b - 10*a*B)*sqrt(a + b*x^3))/(540*a^4*x^2) + (91*sqrt(2 + sqrt(3))*b^(2/3)*(19*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(540*3^(1/4)*a^4*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(x^7*(A + B*x^3))/(a + b*x^3)^(5/2), x, 6, -((2*(7*A*b - 16*a*B)*x^5)/(63*b^2*(a + b*x^3)^(3/2))) + (2*B*x^8)/(7*b*(a + b*x^3)^(3/2)) - (20*(7*A*b - 16*a*B)*x^2)/(189*b^3*sqrt(a + b*x^3)) + (80*(7*A*b - 16*a*B)*sqrt(a + b*x^3))/(189*b^(11/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (40*3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(7*A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(189*b^(11/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (80*sqrt(2)*a^(1/3)*(7*A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(189*3^(1/4)*b^(11/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(x^4*(A + B*x^3))/(a + b*x^3)^(5/2), x, 5, (2*(A*b - a*B)*x^5)/(9*a*b*(a + b*x^3)^(3/2)) + (2*(A*b - 10*a*B)*x^2)/(27*a*b^2*sqrt(a + b*x^3)) - (8*(A*b - 10*a*B)*sqrt(a + b*x^3))/(27*a*b^(8/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*sqrt(2 - sqrt(3))*(A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*a^(2/3)*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (8*sqrt(2)*(A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a^(2/3)*b^(8/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(x*(A + B*x^3))/(a + b*x^3)^(5/2), x, 5, (2*(A*b - a*B)*x^2)/(9*a*b*(a + b*x^3)^(3/2)) + (2*(5*A*b + 4*a*B)*x^2)/(27*a^2*b*sqrt(a + b*x^3)) - (2*(5*A*b + 4*a*B)*sqrt(a + b*x^3))/(27*a^2*b^(5/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*sqrt(2 - sqrt(3))*(5*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*a^(5/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (2*sqrt(2)*(5*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a^(5/3)*b^(5/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^2*(a + b*x^3)^(5/2)), x, 6, -(A/(a*x*(a + b*x^3)^(3/2))) - ((11*A*b - 2*a*B)*x^2)/(9*a^2*(a + b*x^3)^(3/2)) - (5*(11*A*b - 2*a*B)*x^2)/(27*a^3*sqrt(a + b*x^3)) + (5*(11*A*b - 2*a*B)*sqrt(a + b*x^3))/(27*a^3*b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (5*3^(1/4)*sqrt(2 - sqrt(3))*(11*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(54*a^(8/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (5*sqrt(2)*(11*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*a^(8/3)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(x^5*(a + b*x^3)^(5/2)), x, 7, -(A/(4*a*x^4*(a + b*x^3)^(3/2))) - (17*A*b - 8*a*B)/(36*a^2*x*(a + b*x^3)^(3/2)) - (11*(17*A*b - 8*a*B))/(108*a^3*x*sqrt(a + b*x^3)) + (55*(17*A*b - 8*a*B)*sqrt(a + b*x^3))/(216*a^4*x) - (55*b^(1/3)*(17*A*b - 8*a*B)*sqrt(a + b*x^3))/(216*a^4*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (55*3^(1/4)*sqrt(2 - sqrt(3))*b^(1/3)*(17*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(432*a^(11/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (55*b^(1/3)*(17*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(108*sqrt(2)*3^(1/4)*a^(11/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^3)^(q/2) / (a+b*x^3)=#

    #= ::Subsubsection::Closed:: =#
    #=q>0*when*4*b*c-a*d=0=#

    @test_int [x^8*sqrt(c + d*x^3)/(4*c + d*x^3), x, 6, (32*c^2*sqrt(c + d*x^3))/(3*d^3) - (10*c*(c + d*x^3)^(3/2))/(9*d^3) + (2*(c + d*x^3)^(5/2))/(15*d^3) - (32*c^(5/2)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(sqrt(3)*d^3)]
    @test_int [x^5*sqrt(c + d*x^3)/(4*c + d*x^3), x, 5, -((8*c*sqrt(c + d*x^3))/(3*d^2)) + (2*(c + d*x^3)^(3/2))/(9*d^2) + (8*c^(3/2)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(sqrt(3)*d^2)]
    @test_int [x^2*sqrt(c + d*x^3)/(4*c + d*x^3), x, 4, (2*sqrt(c + d*x^3))/(3*d) - (2*sqrt(c)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(sqrt(3)*d)]
    @test_int [sqrt(c + d*x^3)/(x^1*(4*c + d*x^3)), x, 6, atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c)))/(2*sqrt(3)*sqrt(c)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(6*sqrt(c))]
    @test_int [sqrt(c + d*x^3)/(x^4*(4*c + d*x^3)), x, 7, -(sqrt(c + d*x^3)/(12*c*x^3)) - (d*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(8*sqrt(3)*c^(3/2)) - (d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(24*c^(3/2))]

    @test_int [x^4*sqrt(c + d*x^3)/(4*c + d*x^3), x, 7, (2*x^2*sqrt(c + d*x^3))/(7*d) - (50*c*sqrt(c + d*x^3))/(7*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (2*2^(1/3)*c^(7/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(sqrt(3)*d^(5/3)) + (2*2^(1/3)*c^(7/6)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(sqrt(3)*d^(5/3)) - (2*2^(1/3)*c^(7/6)*atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/d^(5/3) + (2*2^(1/3)*c^(7/6)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*d^(5/3)) + (25*3^(1/4)*sqrt(2 - sqrt(3))*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (50*sqrt(2)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^1*sqrt(c + d*x^3)/(4*c + d*x^3), x, 5, (2*sqrt(c + d*x^3))/(d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(2^(2/3)*sqrt(3)*d^(2/3)) - (c^(1/6)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(2^(2/3)*sqrt(3)*d^(2/3)) + (c^(1/6)*atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(2^(2/3)*d^(2/3)) - (c^(1/6)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*2^(2/3)*d^(2/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (2*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^2*(4*c + d*x^3)), x, 7, -(sqrt(c + d*x^3)/(4*c*x)) + (d^(1/3)*sqrt(c + d*x^3))/(4*c*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(4*2^(2/3)*sqrt(3)*c^(5/6)) + (d^(1/3)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(4*2^(2/3)*sqrt(3)*c^(5/6)) - (d^(1/3)*atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(4*2^(2/3)*c^(5/6)) + (d^(1/3)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(12*2^(2/3)*c^(5/6)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(8*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(2*sqrt(2)*3^(1/4)*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [x^3*sqrt(c + d*x^3)/(4*c + d*x^3), x, 2, (x^4*sqrt(c + d*x^3)*AppellF1(4/3, 1, -(1/2), 7/3, -((d*x^3)/(4*c)), -((d*x^3)/c)))/(16*c*sqrt(1 + (d*x^3)/c))]
    @test_int [x^0*sqrt(c + d*x^3)/(4*c + d*x^3), x, 2, (x*sqrt(c + d*x^3)*AppellF1(1/3, 1, -(1/2), 4/3, -((d*x^3)/(4*c)), -((d*x^3)/c)))/(4*c*sqrt(1 + (d*x^3)/c))]
    @test_int [sqrt(c + d*x^3)/(x^3*(4*c + d*x^3)), x, 2, -((sqrt(c + d*x^3)*AppellF1(-(2/3), 1, -(1/2), 1/3, -((d*x^3)/(4*c)), -((d*x^3)/c)))/(8*c*x^2*sqrt(1 + (d*x^3)/c)))]

    #= ::Subsubsection::Closed:: =#
    #=q<0*when*4*b*c-a*d=0=#
    #==#

    @test_int [x^8/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 5, -((10*c*sqrt(c + d*x^3))/(3*d^3)) + (2*(c + d*x^3)^(3/2))/(9*d^3) + (32*c^(3/2)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(3*sqrt(3)*d^3)]
    @test_int [x^5/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 4, (2*sqrt(c + d*x^3))/(3*d^2) - (8*sqrt(c)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(3*sqrt(3)*d^2)]
    @test_int [x^2/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 3, (2*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(3*sqrt(3)*sqrt(c)*d)]
    @test_int [1/(x^1*(4*c + d*x^3)*sqrt(c + d*x^3)), x, 6, -(atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c)))/(6*sqrt(3)*c^(3/2))) - atanh(sqrt(c + d*x^3)/sqrt(c))/(6*c^(3/2))]
    @test_int [1/(x^4*(4*c + d*x^3)*sqrt(c + d*x^3)), x, 7, -(sqrt(c + d*x^3)/(12*c^2*x^3)) + (d*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(24*sqrt(3)*c^(5/2)) + (d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(8*c^(5/2))]

    @test_int [x^4/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 5, (2*sqrt(c + d*x^3))/(d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (2*2^(1/3)*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(3*sqrt(3)*d^(5/3)) - (2*2^(1/3)*c^(1/6)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(3*sqrt(3)*d^(5/3)) + (2*2^(1/3)*c^(1/6)*atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(3*d^(5/3)) - (2*2^(1/3)*c^(1/6)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(9*d^(5/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (2*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^1/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 1, -(atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3))/(3*2^(2/3)*sqrt(3)*c^(5/6)*d^(2/3))) + atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c)))/(3*2^(2/3)*sqrt(3)*c^(5/6)*d^(2/3)) - atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3))/(3*2^(2/3)*c^(5/6)*d^(2/3)) + atanh(sqrt(c + d*x^3)/sqrt(c))/(9*2^(2/3)*c^(5/6)*d^(2/3))]
    @test_int [1/(x^2*(4*c + d*x^3)*sqrt(c + d*x^3)), x, 7, -(sqrt(c + d*x^3)/(4*c^2*x)) + (d^(1/3)*sqrt(c + d*x^3))/(4*c^2*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(12*2^(2/3)*sqrt(3)*c^(11/6)) - (d^(1/3)*atan(sqrt(c + d*x^3)/(sqrt(3)*sqrt(c))))/(12*2^(2/3)*sqrt(3)*c^(11/6)) + (d^(1/3)*atanh((c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/sqrt(c + d*x^3)))/(12*2^(2/3)*c^(11/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(36*2^(2/3)*c^(11/6)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(8*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(2*sqrt(2)*3^(1/4)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [x^3/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 1, 1/2, 7/3, -((d*x^3)/(4*c)), -((d*x^3)/c)))/(16*c*sqrt(c + d*x^3))]
    @test_int [x^0/((4*c + d*x^3)*sqrt(c + d*x^3)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 1, 1/2, 4/3, -((d*x^3)/(4*c)), -((d*x^3)/c)))/(4*c*sqrt(c + d*x^3))]
    @test_int [1/(x^3*(4*c + d*x^3)*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 1, 1/2, 1/3, -((d*x^3)/(4*c)), -((d*x^3)/c)))/(8*c*x^2*sqrt(c + d*x^3)))]

    @test_int [x/(sqrt(1 - x^3)*(4 - x^3)), x, 1, -(atan((sqrt(3)*(1 - 2^(1/3)*x))/sqrt(1 - x^3))/(3*2^(2/3)*sqrt(3))) + atan(sqrt(1 - x^3)/sqrt(3))/(3*2^(2/3)*sqrt(3)) - atanh((1 + 2^(1/3)*x)/sqrt(1 - x^3))/(3*2^(2/3)) + atanh(sqrt(1 - x^3))/(9*2^(2/3))]

    #= ::Subsubsection::Closed:: =#
    #=q>0*when*8*b*c+a*d=0=#

    @test_int [(x^11*sqrt(c + d*x^3))/(8*c - d*x^3), x, 6, (-1024*c^3*sqrt(c + d*x^3))/(3*d^4) - (38*c^2*(c + d*x^3)^(3/2))/(3*d^4) - (4*c*(c + d*x^3)^(5/2))/(5*d^4) - (2*(c + d*x^3)^(7/2))/(21*d^4) + (1024*c^(7/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^4]
    @test_int [(x^8*sqrt(c + d*x^3))/(8*c - d*x^3), x, 6, (-128*c^2*sqrt(c + d*x^3))/(3*d^3) - (14*c*(c + d*x^3)^(3/2))/(9*d^3) - (2*(c + d*x^3)^(5/2))/(15*d^3) + (128*c^(5/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^3]
    @test_int [(x^5*sqrt(c + d*x^3))/(8*c - d*x^3), x, 5, (-16*c*sqrt(c + d*x^3))/(3*d^2) - (2*(c + d*x^3)^(3/2))/(9*d^2) + (16*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^2]
    @test_int [(x^2*sqrt(c + d*x^3))/(8*c - d*x^3), x, 4, (-2*sqrt(c + d*x^3))/(3*d) + (2*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d]
    @test_int [sqrt(c + d*x^3)/(x^1*(8*c - d*x^3)), x, 6, atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(4*sqrt(c)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(12*sqrt(c))]
    @test_int [sqrt(c + d*x^3)/(x^4*(8*c - d*x^3)), x, 7, -sqrt(c + d*x^3)/(24*c*x^3) + (d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(32*c^(3/2)) - (5*d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(96*c^(3/2))]
    @test_int [sqrt(c + d*x^3)/(x^7*(8*c - d*x^3)), x, 8, -sqrt(c + d*x^3)/(48*c*x^6) - (d*sqrt(c + d*x^3))/(64*c^2*x^3) + (d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(256*c^(5/2)) + (d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(256*c^(5/2))]

    @test_int [(x^7*sqrt(c + d*x^3))/(8*c - d*x^3), x, 15, -((214*c*x^2*sqrt(c + d*x^3))/(91*d^2)) - (2*x^5*sqrt(c + d*x^3))/(13*d) - (12248*c^2*sqrt(c + d*x^3))/(91*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (32*sqrt(3)*c^(13/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/d^(8/3) + (32*c^(13/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/d^(8/3) - (32*c^(13/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^(8/3) + (6124*3^(1/4)*sqrt(2 - sqrt(3))*c^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(91*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (12248*sqrt(2)*c^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(91*3^(1/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^4*sqrt(c + d*x^3))/(8*c - d*x^3), x, 14, -((2*x^2*sqrt(c + d*x^3))/(7*d)) - (118*c*sqrt(c + d*x^3))/(7*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (4*sqrt(3)*c^(7/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/d^(5/3) + (4*c^(7/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/d^(5/3) - (4*c^(7/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^(5/3) + (59*3^(1/4)*sqrt(2 - sqrt(3))*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (118*sqrt(2)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^1*sqrt(c + d*x^3))/(8*c - d*x^3), x, 12, -((2*sqrt(c + d*x^3))/(d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x))) - (sqrt(3)*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(2*d^(2/3)) + (c^(1/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(2*d^(2/3)) - (c^(1/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(2*d^(2/3)) + (3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (2*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^2*(8*c - d*x^3)), x, 14, -(sqrt(c + d*x^3)/(8*c*x)) + (d^(1/3)*sqrt(c + d*x^3))/(8*c*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (sqrt(3)*d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(16*c^(5/6)) + (d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(16*c^(5/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(16*c^(5/6)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(16*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^5*(8*c - d*x^3)), x, 15, -(sqrt(c + d*x^3)/(32*c*x^4)) - (d*sqrt(c + d*x^3))/(16*c^2*x) + (d^(4/3)*sqrt(c + d*x^3))/(16*c^2*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (sqrt(3)*d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(128*c^(11/6)) + (d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(128*c^(11/6)) - (d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(128*c^(11/6)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(32*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(8*sqrt(2)*3^(1/4)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^8*(8*c - d*x^3)), x, 16, -(sqrt(c + d*x^3)/(56*c*x^7)) - (19*d*sqrt(c + d*x^3))/(1792*c^2*x^4) + (d^2*sqrt(c + d*x^3))/(112*c^3*x) - (d^(7/3)*sqrt(c + d*x^3))/(112*c^3*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (sqrt(3)*d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(1024*c^(17/6)) + (d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(1024*c^(17/6)) - (d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1024*c^(17/6)) + (3^(1/4)*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(224*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(56*sqrt(2)*3^(1/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [(x^11*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 7, (-3072*c^4*sqrt(c + d*x^3))/d^4 - (1024*c^3*(c + d*x^3)^(3/2))/(9*d^4) - (38*c^2*(c + d*x^3)^(5/2))/(5*d^4) - (4*c*(c + d*x^3)^(7/2))/(7*d^4) - (2*(c + d*x^3)^(9/2))/(27*d^4) + (9216*c^(9/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^4]
    @test_int [(x^8*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 7, (-384*c^3*sqrt(c + d*x^3))/d^3 - (128*c^2*(c + d*x^3)^(3/2))/(9*d^3) - (14*c*(c + d*x^3)^(5/2))/(15*d^3) - (2*(c + d*x^3)^(7/2))/(21*d^3) + (1152*c^(7/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^3]
    @test_int [(x^5*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 6, (-48*c^2*sqrt(c + d*x^3))/d^2 - (16*c*(c + d*x^3)^(3/2))/(9*d^2) - (2*(c + d*x^3)^(5/2))/(15*d^2) + (144*c^(5/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^2]
    @test_int [(x^2*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 5, (-6*c*sqrt(c + d*x^3))/d - (2*(c + d*x^3)^(3/2))/(9*d) + (18*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d]
    @test_int [(c + d*x^3)^(3/2)/(x^1*(8*c - d*x^3)), x, 7, (-2*sqrt(c + d*x^3))/3 + (9*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/4 - (sqrt(c)*atanh(sqrt(c + d*x^3)/sqrt(c)))/12]
    @test_int [(c + d*x^3)^(3/2)/(x^4*(8*c - d*x^3)), x, 7, -sqrt(c + d*x^3)/(24*x^3) + (9*d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(32*sqrt(c)) - (13*d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(96*sqrt(c))]
    @test_int [(c + d*x^3)^(3/2)/(x^7*(8*c - d*x^3)), x, 8, -sqrt(c + d*x^3)/(48*x^6) - (11*d*sqrt(c + d*x^3))/(192*c*x^3) + (9*d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(256*c^(3/2)) - (37*d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(768*c^(3/2))]

    @test_int [(x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 16, -((36534*c^2*x^2*sqrt(c + d*x^3))/(1729*d^2)) - (348*c*x^5*sqrt(c + d*x^3))/(247*d) - (2/19)*x^8*sqrt(c + d*x^3) - (2094648*c^3*sqrt(c + d*x^3))/(1729*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (288*sqrt(3)*c^(19/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/d^(8/3) + (288*c^(19/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/d^(8/3) - (288*c^(19/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^(8/3) + (1047324*3^(1/4)*sqrt(2 - sqrt(3))*c^(10/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (698216*sqrt(2)*3^(3/4)*c^(10/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(1729*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 15, -((240*c*x^2*sqrt(c + d*x^3))/(91*d)) - (2/13)*x^5*sqrt(c + d*x^3) - (13782*c^2*sqrt(c + d*x^3))/(91*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (36*sqrt(3)*c^(13/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/d^(5/3) + (36*c^(13/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/d^(5/3) - (36*c^(13/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^(5/3) + (6891*3^(1/4)*sqrt(2 - sqrt(3))*c^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(91*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (4594*sqrt(2)*3^(3/4)*c^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(91*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^1*(c + d*x^3)^(3/2))/(8*c - d*x^3), x, 14, (-(2/7))*x^2*sqrt(c + d*x^3) - (132*c*sqrt(c + d*x^3))/(7*d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (9*sqrt(3)*c^(7/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(2*d^(2/3)) + (9*c^(7/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(2*d^(2/3)) - (9*c^(7/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(2*d^(2/3)) + (66*3^(1/4)*sqrt(2 - sqrt(3))*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (44*sqrt(2)*3^(3/4)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)), x, 14, -(sqrt(c + d*x^3)/(8*x)) - (15*d^(1/3)*sqrt(c + d*x^3))/(8*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (9/16)*sqrt(3)*c^(1/6)*d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)) + (9/16)*c^(1/6)*d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))) - (9/16)*c^(1/6)*d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))) + (15*3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(16*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (5*3^(3/4)*c^(1/3)*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)), x, 15, -(sqrt(c + d*x^3)/(32*x^4)) - (3*d*sqrt(c + d*x^3))/(16*c*x) + (3*d^(4/3)*sqrt(c + d*x^3))/(16*c*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (9*sqrt(3)*d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(128*c^(5/6)) + (9*d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(128*c^(5/6)) - (9*d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(128*c^(5/6)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(32*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (3^(3/4)*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(8*sqrt(2)*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)), x, 16, -(sqrt(c + d*x^3)/(56*x^7)) - (75*d*sqrt(c + d*x^3))/(1792*c*x^4) - (3*d^2*sqrt(c + d*x^3))/(56*c^2*x) + (3*d^(7/3)*sqrt(c + d*x^3))/(56*c^2*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (9*sqrt(3)*d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(1024*c^(11/6)) + (9*d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(1024*c^(11/6)) - (9*d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1024*c^(11/6)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(112*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (3^(3/4)*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(28*sqrt(2)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    #= ::Subsubsection::Closed:: =#
    #=q<0*when*8*b*c+a*d=0=#
    #==#

    @test_int [x^11/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 5, (-38*c^2*sqrt(c + d*x^3))/d^4 - (4*c*(c + d*x^3)^(3/2))/(3*d^4) - (2*(c + d*x^3)^(5/2))/(15*d^4) + (1024*c^(5/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^4)]
    @test_int [x^8/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 5, (-14*c*sqrt(c + d*x^3))/(3*d^3) - (2*(c + d*x^3)^(3/2))/(9*d^3) + (128*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^3)]
    @test_int [x^5/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 4, (-2*sqrt(c + d*x^3))/(3*d^2) + (16*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^2)]
    @test_int [x^2/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 3, (2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*sqrt(c)*d)]
    @test_int [1/(x^1*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 6, atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(36*c^(3/2)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(12*c^(3/2))]
    @test_int [1/(x^4*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 7, -sqrt(c + d*x^3)/(24*c^2*x^3) + (d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(288*c^(5/2)) + (d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(32*c^(5/2))]
    @test_int [1/(x^7*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 8, -sqrt(c + d*x^3)/(48*c^2*x^6) + (5*d*sqrt(c + d*x^3))/(192*c^3*x^3) + (d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(2304*c^(7/2)) - (7*d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(256*c^(7/2))]

    @test_int [x^7/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 14, -((2*x^2*sqrt(c + d*x^3))/(7*d^2)) - (104*c*sqrt(c + d*x^3))/(7*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (32*c^(7/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3*sqrt(3)*d^(8/3)) + (32*c^(7/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(9*d^(8/3)) - (32*c^(7/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^(8/3)) + (52*3^(1/4)*sqrt(2 - sqrt(3))*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (104*sqrt(2)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^4/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 12, -((2*sqrt(c + d*x^3))/(d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x))) - (4*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3*sqrt(3)*d^(5/3)) + (4*c^(1/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(9*d^(5/3)) - (4*c^(1/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^(5/3)) + (3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (2*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^1/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 8, -(atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3))/(6*sqrt(3)*c^(5/6)*d^(2/3))) + atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3)))/(18*c^(5/6)*d^(2/3)) - atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(18*c^(5/6)*d^(2/3))]
    @test_int [1/(x^2*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 14, -(sqrt(c + d*x^3)/(8*c^2*x)) + (d^(1/3)*sqrt(c + d*x^3))/(8*c^2*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(48*sqrt(3)*c^(11/6)) + (d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(144*c^(11/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(144*c^(11/6)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(16*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^5*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 15, -(sqrt(c + d*x^3)/(32*c^2*x^4)) + (d*sqrt(c + d*x^3))/(16*c^3*x) - (d^(4/3)*sqrt(c + d*x^3))/(16*c^3*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(384*sqrt(3)*c^(17/6)) + (d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(1152*c^(17/6)) - (d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1152*c^(17/6)) + (3^(1/4)*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(32*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(8*sqrt(2)*3^(1/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^8*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 16, -(sqrt(c + d*x^3)/(56*c^2*x^7)) + (37*d*sqrt(c + d*x^3))/(1792*c^3*x^4) - (3*d^2*sqrt(c + d*x^3))/(56*c^4*x) + (3*d^(7/3)*sqrt(c + d*x^3))/(56*c^4*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3072*sqrt(3)*c^(23/6)) + (d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(9216*c^(23/6)) - (d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9216*c^(23/6)) - (3*3^(1/4)*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(112*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (3^(3/4)*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(28*sqrt(2)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [x^3/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 1, 1/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(32*c*sqrt(c + d*x^3))]
    @test_int [x^0/((8*c - d*x^3)*sqrt(c + d*x^3)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 1, 1/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(8*c*sqrt(c + d*x^3))]
    @test_int [1/(x^3*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 1, 1/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(16*c*x^2*sqrt(c + d*x^3)))]
    @test_int [1/(x^6*(8*c - d*x^3)*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(5/3), 1, 1/2, -(2/3), (d*x^3)/(8*c), -((d*x^3)/c)))/(40*c*x^5*sqrt(c + d*x^3)))]

    @test_int [x^11/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 7, (2*c^2)/(27*d^4*sqrt(c + d*x^3)) - (4*c*sqrt(c + d*x^3))/d^4 - (2*(c + d*x^3)^(3/2))/(9*d^4) + (1024*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*d^4)]
    @test_int [x^8/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 5, (-2*c)/(27*d^3*sqrt(c + d*x^3)) - (2*sqrt(c + d*x^3))/(3*d^3) + (128*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*d^3)]
    @test_int [x^5/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 4, 2/(27*d^2*sqrt(c + d*x^3)) + (16*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*sqrt(c)*d^2)]
    @test_int [x^2/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 4, -2/(27*c*d*sqrt(c + d*x^3)) + (2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*c^(3/2)*d)]
    @test_int [1/(x^1*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 7, 2/(27*c^2*sqrt(c + d*x^3)) + atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(324*c^(5/2)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(12*c^(5/2))]
    @test_int [1/(x^4*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 8, (-25*d)/(216*c^3*sqrt(c + d*x^3)) - 1/(24*c^2*x^3*sqrt(c + d*x^3)) + (d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(2592*c^(7/2)) + (11*d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(96*c^(7/2))]
    @test_int [1/(x^7*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 9, (245*d^2)/(1728*c^4*sqrt(c + d*x^3)) - 1/(48*c^2*x^6*sqrt(c + d*x^3)) + (3*d)/(64*c^3*x^3*sqrt(c + d*x^3)) + (d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(20736*c^(9/2)) - (109*d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(768*c^(9/2))]

    @test_int [x^7/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 14, (2*x^2)/(27*d^2*sqrt(c + d*x^3)) - (56*sqrt(c + d*x^3))/(27*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (32*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(27*sqrt(3)*d^(8/3)) + (32*c^(1/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(81*d^(8/3)) - (32*c^(1/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*d^(8/3)) + (28*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(9*3^(3/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (56*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^4/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 14, -((2*x^2)/(27*c*d*sqrt(c + d*x^3))) + (2*sqrt(c + d*x^3))/(27*c*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (4*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(27*sqrt(3)*c^(5/6)*d^(5/3)) + (4*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(81*c^(5/6)*d^(5/3)) - (4*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*c^(5/6)*d^(5/3)) - (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(9*3^(3/4)*c^(2/3)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (2*sqrt(2)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*c^(2/3)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^1/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 14, (2*x^2)/(27*c^2*sqrt(c + d*x^3)) - (2*sqrt(c + d*x^3))/(27*c^2*d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3))/(54*sqrt(3)*c^(11/6)*d^(2/3)) + atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3)))/(162*c^(11/6)*d^(2/3)) - atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(162*c^(11/6)*d^(2/3)) + (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(9*3^(3/4)*c^(5/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (2*sqrt(2)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*c^(5/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 15, 2/(27*c^2*x*sqrt(c + d*x^3)) - (43*sqrt(c + d*x^3))/(216*c^3*x) + (43*d^(1/3)*sqrt(c + d*x^3))/(216*c^3*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(432*sqrt(3)*c^(17/6)) + (d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(1296*c^(17/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1296*c^(17/6)) - (43*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(144*3^(3/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (43*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(108*sqrt(2)*3^(1/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^5*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 16, 2/(27*c^2*x^4*sqrt(c + d*x^3)) - (91*sqrt(c + d*x^3))/(864*c^3*x^4) + (113*d*sqrt(c + d*x^3))/(432*c^4*x) - (113*d^(4/3)*sqrt(c + d*x^3))/(432*c^4*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3456*sqrt(3)*c^(23/6)) + (d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(10368*c^(23/6)) - (d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(10368*c^(23/6)) + (113*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(288*3^(3/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (113*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(216*sqrt(2)*3^(1/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^8*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 17, 2/(27*c^2*x^7*sqrt(c + d*x^3)) - (139*sqrt(c + d*x^3))/(1512*c^3*x^7) + (6095*d*sqrt(c + d*x^3))/(48384*c^4*x^4) - (953*d^2*sqrt(c + d*x^3))/(3024*c^5*x) + (953*d^(7/3)*sqrt(c + d*x^3))/(3024*c^5*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(27648*sqrt(3)*c^(29/6)) + (d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(82944*c^(29/6)) - (d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(82944*c^(29/6)) - (953*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(2016*3^(3/4)*c^(14/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (953*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(1512*sqrt(2)*3^(1/4)*c^(14/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [x^3/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 1, 3/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(32*c^2*sqrt(c + d*x^3))]
    @test_int [x^0/((8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 1, 3/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(8*c^2*sqrt(c + d*x^3))]
    @test_int [1/(x^3*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 1, 3/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(16*c^2*x^2*sqrt(c + d*x^3)))]
    @test_int [1/(x^6*(8*c - d*x^3)*(c + d*x^3)^(3/2)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(5/3), 1, 3/2, -(2/3), (d*x^3)/(8*c), -((d*x^3)/c)))/(40*c^2*x^5*sqrt(c + d*x^3)))]

    #= ::Subsubsection::Closed:: =#
    #=q>0*when*b^2*c^2-20*a*b*c*d-8*a^2*d^2=0=#

    @test_int [x*(sqrt(a + b*x^3)/(2*(5 + 3*sqrt(3))*a + b*x^3)), x, 5, (2*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) + (3^(3/4)*a^(1/6)*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(2*sqrt(2)*b^(2/3)) + (a^(1/6)*atan(((1 - sqrt(3))*sqrt(a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(sqrt(2)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(2*sqrt(2)*b^(2/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x*(sqrt(a - b*x^3)/(2*(5 + 3*sqrt(3))*a - b*x^3)), x, 5, (2*sqrt(a - b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)) + (3^(3/4)*a^(1/6)*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(2*sqrt(2)*b^(2/3)) + (a^(1/6)*atan(((1 - sqrt(3))*sqrt(a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(2*sqrt(2)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(sqrt(2)*b^(2/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [x*(sqrt(-a + b*x^3)/(-2*(5 + 3*sqrt(3))*a + b*x^3)), x, 5, -((2*sqrt(-a + b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) - b^(1/3)*x))) + (3^(1/4)*a^(1/6)*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(2*sqrt(2)*b^(2/3)) + (3^(1/4)*a^(1/6)*atan((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(sqrt(2)*b^(2/3)) + (3^(3/4)*a^(1/6)*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(2*sqrt(2)*b^(2/3)) - (a^(1/6)*atanh(((1 - sqrt(3))*sqrt(-a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3)) - (2*sqrt(2)*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [x*(sqrt(-a - b*x^3)/(-2*(5 + 3*sqrt(3))*a - b*x^3)), x, 5, -((2*sqrt(-a - b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) + b^(1/3)*x))) + (3^(1/4)*a^(1/6)*atan((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(sqrt(2)*b^(2/3)) + (3^(1/4)*a^(1/6)*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(2*sqrt(2)*b^(2/3)) + (3^(3/4)*a^(1/6)*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(2*sqrt(2)*b^(2/3)) - (a^(1/6)*atanh(((1 - sqrt(3))*sqrt(-a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) + (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3)) - (2*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    @test_int [x*(sqrt(a + b*x^3)/(2*(5 - 3*sqrt(3))*a + b*x^3)), x, 5, (2*sqrt(a + b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*a^(1/6)*atan((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(sqrt(2)*b^(2/3)) - (3^(1/4)*a^(1/6)*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(2*sqrt(2)*b^(2/3)) + (3^(3/4)*a^(1/6)*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(2*sqrt(2)*b^(2/3)) + (a^(1/6)*atanh(((1 + sqrt(3))*sqrt(a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [x*(sqrt(a - b*x^3)/(2*(5 - 3*sqrt(3))*a - b*x^3)), x, 5, (2*sqrt(a - b*x^3))/(b^(2/3)*((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*a^(1/6)*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(2*sqrt(2)*b^(2/3)) - (3^(1/4)*a^(1/6)*atan((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(sqrt(2)*b^(2/3)) + (3^(3/4)*a^(1/6)*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(2*sqrt(2)*b^(2/3)) + (a^(1/6)*atanh(((1 + sqrt(3))*sqrt(a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) - (3^(1/4)*sqrt(2 - sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 - 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*sqrt(a - b*x^3))]
    @test_int [x*(sqrt(-a + b*x^3)/(2*(5 - 3*sqrt(3))*a - b*x^3)), x, 5, (2*sqrt(-a + b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)) - (3^(3/4)*a^(1/6)*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(2*sqrt(2)*b^(2/3)) + (a^(1/6)*atan(((1 + sqrt(3))*sqrt(-a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(2*sqrt(2)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(sqrt(2)*b^(2/3)) - (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) - b^(1/3)*x)*sqrt((a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) - b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) - b^(1/3)*x)^2))*sqrt(-a + b*x^3))]
    @test_int [x*(sqrt(-a - b*x^3)/(2*(5 - 3*sqrt(3))*a + b*x^3)), x, 5, (2*sqrt(-a - b*x^3))/(b^(2/3)*((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)) - (3^(3/4)*a^(1/6)*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(2*sqrt(2)*b^(2/3)) + (a^(1/6)*atan(((1 + sqrt(3))*sqrt(-a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(sqrt(2)*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(sqrt(2)*b^(2/3)) + (3^(1/4)*a^(1/6)*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(2*sqrt(2)*b^(2/3)) - (3^(1/4)*sqrt(2 + sqrt(3))*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.E(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3)) + (2*sqrt(2)*a^(1/3)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2)*Elliptic.F(asin(((1 + sqrt(3))*a^(1/3) + b^(1/3)*x)/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)), -7 + 4*sqrt(3)))/(3^(1/4)*b^(2/3)*sqrt(-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - sqrt(3))*a^(1/3) + b^(1/3)*x)^2))*sqrt(-a - b*x^3))]

    #= ::Subsubsection::Closed:: =#
    #=q<0*when*b^2*c^2-20*a*b*c*d-8*a^2*d^2=0=#
    #==#

    @test_int [x/(sqrt(a + b*x^3)*(2*(5 + 3*sqrt(3))*a + b*x^3)), x, 1, -(((2 - sqrt(3))*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3))) - ((2 - sqrt(3))*atan(((1 - sqrt(3))*sqrt(a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - sqrt(3))*atanh((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 - sqrt(3))*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3))]
    @test_int [x/(sqrt(a - b*x^3)*(2*(5 + 3*sqrt(3))*a - b*x^3)), x, 1, -(((2 - sqrt(3))*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3))) - ((2 - sqrt(3))*atan(((1 - sqrt(3))*sqrt(a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - sqrt(3))*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 - sqrt(3))*atanh((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3))]
    @test_int [x/(sqrt(-a + b*x^3)*(-2*(5 + 3*sqrt(3))*a + b*x^3)), x, 1, ((2 - sqrt(3))*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - sqrt(3))*atan((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - sqrt(3))*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - sqrt(3))*atanh(((1 - sqrt(3))*sqrt(-a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3))]
    @test_int [x/(sqrt(-a - b*x^3)*(-2*(5 + 3*sqrt(3))*a - b*x^3)), x, 1, ((2 - sqrt(3))*atan((3^(1/4)*a^(1/6)*((1 + sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - sqrt(3))*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - sqrt(3))*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - sqrt(3))*atanh(((1 - sqrt(3))*sqrt(-a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3))]

    @test_int [x/(sqrt(a + b*x^3)*(2*(5 - 3*sqrt(3))*a + b*x^3)), x, 1, -(((2 + sqrt(3))*atan((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3))) - ((2 + sqrt(3))*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 + sqrt(3))*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(a + b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) + ((2 + sqrt(3))*atanh(((1 + sqrt(3))*sqrt(a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3))]
    @test_int [x/(sqrt(a - b*x^3)*(2*(5 - 3*sqrt(3))*a - b*x^3)), x, 1, -(((2 + sqrt(3))*atan((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3))) - ((2 + sqrt(3))*atan((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 + sqrt(3))*atanh((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(a - b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) + ((2 + sqrt(3))*atanh(((1 + sqrt(3))*sqrt(a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3))]
    @test_int [x/(sqrt(-a + b*x^3)*(2*(5 - 3*sqrt(3))*a - b*x^3)), x, 1, ((2 + sqrt(3))*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + sqrt(3))*atan(((1 + sqrt(3))*sqrt(-a + b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + sqrt(3))*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 + sqrt(3))*atanh((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) + 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a + b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3))]
    @test_int [x/(sqrt(-a - b*x^3)*(2*(5 - 3*sqrt(3))*a + b*x^3)), x, 1, ((2 + sqrt(3))*atan((3^(1/4)*(1 - sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(2*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + sqrt(3))*atan(((1 + sqrt(3))*sqrt(-a - b*x^3))/(sqrt(2)*3^(3/4)*sqrt(a))))/(3*sqrt(2)*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + sqrt(3))*atanh((3^(1/4)*a^(1/6)*((1 - sqrt(3))*a^(1/3) - 2*b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(3*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 + sqrt(3))*atanh((3^(1/4)*(1 + sqrt(3))*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(sqrt(2)*sqrt(-a - b*x^3))))/(6*sqrt(2)*3^(1/4)*a^(5/6)*b^(2/3))]

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^8*sqrt(c + d*x^3)/(a + b*x^3), x, 6, (2*a^2*sqrt(c + d*x^3))/(3*b^3) - (2*(b*c + a*d)*(c + d*x^3)^(3/2))/(9*b^2*d^2) + (2*(c + d*x^3)^(5/2))/(15*b*d^2) - (2*a^2*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(7/2))]
    @test_int [x^5*sqrt(c + d*x^3)/(a + b*x^3), x, 5, -((2*a*sqrt(c + d*x^3))/(3*b^2)) + (2*(c + d*x^3)^(3/2))/(9*b*d) + (2*a*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(5/2))]
    @test_int [x^2*sqrt(c + d*x^3)/(a + b*x^3), x, 4, (2*sqrt(c + d*x^3))/(3*b) - (2*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(3/2))]
    @test_int [sqrt(c + d*x^3)/(x^1*(a + b*x^3)), x, 6, -((2*sqrt(c)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a)) + (2*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a*sqrt(b))]
    @test_int [sqrt(c + d*x^3)/(x^4*(a + b*x^3)), x, 7, -(sqrt(c + d*x^3)/(3*a*x^3)) + ((2*b*c - a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2*sqrt(c)) - (2*sqrt(b)*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2)]

    @test_int [x^3*sqrt(c + d*x^3)/(a + b*x^3), x, 2, (x^4*sqrt(c + d*x^3)*AppellF1(4/3, 1, -(1/2), 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a*sqrt(1 + (d*x^3)/c))]
    @test_int [x^1*sqrt(c + d*x^3)/(a + b*x^3), x, 2, (x^2*sqrt(c + d*x^3)*AppellF1(2/3, 1, -(1/2), 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*sqrt(1 + (d*x^3)/c))]
    @test_int [x^0*sqrt(c + d*x^3)/(a + b*x^3), x, 2, (x*sqrt(c + d*x^3)*AppellF1(1/3, 1, -(1/2), 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*sqrt(1 + (d*x^3)/c))]
    @test_int [sqrt(c + d*x^3)/(x^2*(a + b*x^3)), x, 2, -((sqrt(c + d*x^3)*AppellF1(-(1/3), 1, -(1/2), 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*x*sqrt(1 + (d*x^3)/c)))]
    @test_int [sqrt(c + d*x^3)/(x^3*(a + b*x^3)), x, 2, -((sqrt(c + d*x^3)*AppellF1(-(2/3), 1, -(1/2), 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*x^2*sqrt(1 + (d*x^3)/c)))]

    @test_int [x^8*(c + d*x^3)^(3/2)/(a + b*x^3), x, 7, (2*a^2*(b*c - a*d)*sqrt(c + d*x^3))/(3*b^4) + (2*a^2*(c + d*x^3)^(3/2))/(9*b^3) - (2*(b*c + a*d)*(c + d*x^3)^(5/2))/(15*b^2*d^2) + (2*(c + d*x^3)^(7/2))/(21*b*d^2) - (2*a^2*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(9/2))]
    @test_int [x^5*(c + d*x^3)^(3/2)/(a + b*x^3), x, 6, (-2*a*(b*c - a*d)*sqrt(c + d*x^3))/(3*b^3) - (2*a*(c + d*x^3)^(3/2))/(9*b^2) + (2*(c + d*x^3)^(5/2))/(15*b*d) + (2*a*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(7/2))]
    @test_int [x^2*(c + d*x^3)^(3/2)/(a + b*x^3), x, 5, (2*(b*c - a*d)*sqrt(c + d*x^3))/(3*b^2) + (2*(c + d*x^3)^(3/2))/(9*b) - (2*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(5/2))]
    @test_int [(c + d*x^3)^(3/2)/(x^1*(a + b*x^3)), x, 7, (2*d*sqrt(c + d*x^3))/(3*b) - (2*c^(3/2)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a) + (2*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a*b^(3/2))]
    @test_int [(c + d*x^3)^(3/2)/(x^4*(a + b*x^3)), x, 7, -(c*sqrt(c + d*x^3))/(3*a*x^3) + (sqrt(c)*(2*b*c - 3*a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2) - (2*(b*c - a*d)^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*sqrt(b))]

    @test_int [x^3*(c + d*x^3)^(3/2)/(a + b*x^3), x, 2, (c*x^4*sqrt(c + d*x^3)*AppellF1(4/3, 1, -3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a*sqrt(1 + (d*x^3)/c))]
    @test_int [x^1*(c + d*x^3)^(3/2)/(a + b*x^3), x, 2, (c*x^2*sqrt(c + d*x^3)*AppellF1(2/3, 1, -3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*sqrt(1 + (d*x^3)/c))]
    @test_int [x^0*(c + d*x^3)^(3/2)/(a + b*x^3), x, 2, (c*x*sqrt(c + d*x^3)*AppellF1(1/3, 1, -(3/2), 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*sqrt(1 + (d*x^3)/c))]
    @test_int [(c + d*x^3)^(3/2)/(x^2*(a + b*x^3)), x, 2, -((c*sqrt(c + d*x^3)*AppellF1(-1/3, 1, -3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*x*sqrt(1 + (d*x^3)/c)))]
    @test_int [(c + d*x^3)^(3/2)/(x^3*(a + b*x^3)), x, 2, -(c*sqrt(c + d*x^3)*AppellF1(-2/3, 1, -3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*x^2*sqrt(1 + (d*x^3)/c))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x^8/((a + b*x^3)*sqrt(c + d*x^3)), x, 5, -((2*(b*c + a*d)*sqrt(c + d*x^3))/(3*b^2*d^2)) + (2*(c + d*x^3)^(3/2))/(9*b*d^2) - (2*a^2*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(5/2)*sqrt(b*c - a*d))]
    @test_int [x^5/((a + b*x^3)*sqrt(c + d*x^3)), x, 4, (2*sqrt(c + d*x^3))/(3*b*d) + (2*a*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(3/2)*sqrt(b*c - a*d))]
    @test_int [x^2/((a + b*x^3)*sqrt(c + d*x^3)), x, 3, -((2*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*sqrt(b)*sqrt(b*c - a*d)))]
    @test_int [1/(x^1*(a + b*x^3)*sqrt(c + d*x^3)), x, 6, -((2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a*sqrt(c))) + (2*sqrt(b)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a*sqrt(b*c - a*d))]
    @test_int [1/(x^4*(a + b*x^3)*sqrt(c + d*x^3)), x, 7, -(sqrt(c + d*x^3)/(3*a*c*x^3)) + ((2*b*c + a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2*c^(3/2)) - (2*b^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*sqrt(b*c - a*d))]

    @test_int [x^3/((a + b*x^3)*sqrt(c + d*x^3)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 1, 1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a*sqrt(c + d*x^3))]
    @test_int [x^1/((a + b*x^3)*sqrt(c + d*x^3)), x, 2, (x^2*sqrt(1 + (d*x^3)/c)*AppellF1(2/3, 1, 1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*sqrt(c + d*x^3))]
    @test_int [x^0/((a + b*x^3)*sqrt(c + d*x^3)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 1, 1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(a + b*x^3)*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(1/3), 1, 1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*x*sqrt(c + d*x^3)))]
    @test_int [1/(x^3*(a + b*x^3)*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 1, 1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*x^2*sqrt(c + d*x^3)))]

    @test_int [x^8/((a + b*x^3)*(c + d*x^3)^(3/2)), x, 5, (2*c^2)/(3*d^2*(b*c - a*d)*sqrt(c + d*x^3)) + (2*sqrt(c + d*x^3))/(3*b*d^2) - (2*a^2*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [x^5/((a + b*x^3)*(c + d*x^3)^(3/2)), x, 4, (-2*c)/(3*d*(b*c - a*d)*sqrt(c + d*x^3)) + (2*a*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*sqrt(b)*(b*c - a*d)^(3/2))]
    @test_int [x^2/((a + b*x^3)*(c + d*x^3)^(3/2)), x, 4, 2/(3*(b*c - a*d)*sqrt(c + d*x^3)) - (2*sqrt(b)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*(b*c - a*d)^(3/2))]
    @test_int [1/(x^1*(a + b*x^3)*(c + d*x^3)^(3/2)), x, 7, (-2*d)/(3*c*(b*c - a*d)*sqrt(c + d*x^3)) - (2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a*c^(3/2)) + (2*b^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a*(b*c - a*d)^(3/2))]
    @test_int [1/(x^4*(a + b*x^3)*(c + d*x^3)^(3/2)), x, 8, -(d*(b*c - 3*a*d))/(3*a*c^2*(b*c - a*d)*sqrt(c + d*x^3)) - 1/(3*a*c*x^3*sqrt(c + d*x^3)) + ((2*b*c + 3*a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2*c^(5/2)) - (2*b^(5/2)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*(b*c - a*d)^(3/2))]

    @test_int [x^3/((a + b*x^3)*(c + d*x^3)^(3/2)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 1, 3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a*c*sqrt(c + d*x^3))]
    @test_int [x^1/((a + b*x^3)*(c + d*x^3)^(3/2)), x, 2, (x^2*sqrt(1 + (d*x^3)/c)*AppellF1(2/3, 1, 3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*c*sqrt(c + d*x^3))]
    @test_int [x^0/((a + b*x^3)*(c + d*x^3)^(3/2)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 1, 3/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*c*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(a + b*x^3)*(c + d*x^3)^(3/2)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-1/3, 1, 3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*c*x*sqrt(c + d*x^3)))]
    @test_int [1/(x^3*(a + b*x^3)*(c + d*x^3)^(3/2)), x, 2, -(sqrt(1 + (d*x^3)/c)*AppellF1(-2/3, 1, 3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*c*x^2*sqrt(c + d*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(c+d*x^3)^(q/2) / (a+b*x^3)^2=#

    #= ::Subsubsection::Closed:: =#
    #=q>0*when*8*b*c+a*d=0=#

    @test_int [(x^11*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 6, (7*x^6*sqrt(c + d*x^3))/(15*d^2) + (x^9*sqrt(c + d*x^3))/(3*d*(8*c - d*x^3)) + (2*c*sqrt(c + d*x^3)*(1146*c + 47*d*x^3))/(15*d^4) - (3968*c^(5/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^4)]
    @test_int [(x^8*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 6, (352*c*sqrt(c + d*x^3))/(27*d^3) + (2*(c + d*x^3)^(3/2))/(9*d^3) + (64*c*(c + d*x^3)^(3/2))/(27*d^3*(8*c - d*x^3)) - (352*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^3)]
    @test_int [(x^5*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 5, (26*sqrt(c + d*x^3))/(27*d^2) + (8*(c + d*x^3)^(3/2))/(27*d^2*(8*c - d*x^3)) - (26*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^2)]
    @test_int [(x^2*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 4, sqrt(c + d*x^3)/(3*d*(8*c - d*x^3)) - atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(9*sqrt(c)*d)]
    @test_int [sqrt(c + d*x^3)/(x^1*(8*c - d*x^3)^2), x, 7, sqrt(c + d*x^3)/(24*c*(8*c - d*x^3)) + (5*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(288*c^(3/2)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(96*c^(3/2))]
    @test_int [sqrt(c + d*x^3)/(x^4*(8*c - d*x^3)^2), x, 8, (d*sqrt(c + d*x^3))/(96*c^2*(8*c - d*x^3)) - sqrt(c + d*x^3)/(24*c*x^3*(8*c - d*x^3)) + (7*d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1152*c^(5/2)) - (d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(128*c^(5/2))]
    @test_int [sqrt(c + d*x^3)/(x^7*(8*c - d*x^3)^2), x, 9, (5*d^2*sqrt(c + d*x^3))/(1536*c^3*(8*c - d*x^3)) - sqrt(c + d*x^3)/(48*c*x^6*(8*c - d*x^3)) - (7*d*sqrt(c + d*x^3))/(384*c^2*x^3*(8*c - d*x^3)) + (23*d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(18432*c^(7/2)) - (d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(2048*c^(7/2))]

    @test_int [(x^7*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 15, (13*x^2*sqrt(c + d*x^3))/(21*d^2) + (746*c*sqrt(c + d*x^3))/(21*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^5*sqrt(c + d*x^3))/(3*d*(8*c - d*x^3)) + (76*c^(7/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3*sqrt(3)*d^(8/3)) - (76*c^(7/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(9*d^(8/3)) + (76*c^(7/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^(8/3)) - (373*sqrt(2 - sqrt(3))*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(3/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (746*sqrt(2)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(21*3^(1/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^4*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 14, (7*sqrt(c + d*x^3))/(3*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^2*sqrt(c + d*x^3))/(3*d*(8*c - d*x^3)) + (5*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3*sqrt(3)*d^(5/3)) - (5*c^(1/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(9*d^(5/3)) + (5*c^(1/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9*d^(5/3)) - (7*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(2*3^(3/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (7*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3*3^(1/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^1*sqrt(c + d*x^3))/(8*c - d*x^3)^2, x, 14, sqrt(c + d*x^3)/(24*c*d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^2*sqrt(c + d*x^3))/(24*c*(8*c - d*x^3)) + atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3))/(48*sqrt(3)*c^(5/6)*d^(2/3)) - atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3)))/(144*c^(5/6)*d^(2/3)) + atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(144*c^(5/6)*d^(2/3)) - (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(16*3^(3/4)*c^(2/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + ((c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(12*sqrt(2)*3^(1/4)*c^(2/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^2*(8*c - d*x^3)^2), x, 15, -(sqrt(c + d*x^3)/(48*c^2*x)) + (d^(1/3)*sqrt(c + d*x^3))/(48*c^2*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + sqrt(c + d*x^3)/(24*c*x*(8*c - d*x^3)) - (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(48*sqrt(3)*c^(11/6)) + (d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(144*c^(11/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(144*c^(11/6)) - (sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(32*3^(3/4)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(24*sqrt(2)*3^(1/4)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^5*(8*c - d*x^3)^2), x, 16, -((7*sqrt(c + d*x^3))/(768*c^2*x^4)) - (d*sqrt(c + d*x^3))/(96*c^3*x) + (d^(4/3)*sqrt(c + d*x^3))/(96*c^3*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + sqrt(c + d*x^3)/(24*c*x^4*(8*c - d*x^3)) - (17*d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(3072*sqrt(3)*c^(17/6)) + (17*d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(9216*c^(17/6)) - (17*d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(9216*c^(17/6)) - (sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(64*3^(3/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(48*sqrt(2)*3^(1/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [sqrt(c + d*x^3)/(x^8*(8*c - d*x^3)^2), x, 17, -((5*sqrt(c + d*x^3))/(672*c^2*x^7)) - (53*d*sqrt(c + d*x^3))/(21504*c^3*x^4) - (d^2*sqrt(c + d*x^3))/(5376*c^4*x) + (d^(7/3)*sqrt(c + d*x^3))/(5376*c^4*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + sqrt(c + d*x^3)/(24*c*x^7*(8*c - d*x^3)) - (13*d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(12288*sqrt(3)*c^(23/6)) + (13*d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(36864*c^(23/6)) - (13*d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(36864*c^(23/6)) - (sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3584*3^(3/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(2688*sqrt(2)*3^(1/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [(x^11*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 7, (1664*c^3*sqrt(c + d*x^3))/d^4 + (3*x^6*(c + d*x^3)^(3/2))/(7*d^2) + (x^9*(c + d*x^3)^(3/2))/(3*d*(8*c - d*x^3)) + (2*c*(c + d*x^3)^(3/2)*(694*c + 51*d*x^3))/(21*d^4) - (4992*c^(7/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^4]
    @test_int [(x^8*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 7, (160*c^2*sqrt(c + d*x^3))/d^3 + (160*c*(c + d*x^3)^(3/2))/(27*d^3) + (2*(c + d*x^3)^(5/2))/(15*d^3) + (64*c*(c + d*x^3)^(5/2))/(27*d^3*(8*c - d*x^3)) - (480*c^(5/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^3]
    @test_int [(x^5*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 6, (14*c*sqrt(c + d*x^3))/d^2 + (14*(c + d*x^3)^(3/2))/(27*d^2) + (8*(c + d*x^3)^(5/2))/(27*d^2*(8*c - d*x^3)) - (42*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^2]
    @test_int [(x^2*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 5, sqrt(c + d*x^3)/d + (c + d*x^3)^(3/2)/(3*d*(8*c - d*x^3)) - (3*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d]
    @test_int [(c + d*x^3)^(3/2)/(x^1*(8*c - d*x^3)^2), x, 7, (3*sqrt(c + d*x^3))/(8*(8*c - d*x^3)) - (3*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(32*sqrt(c)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(96*sqrt(c))]
    @test_int [(c + d*x^3)^(3/2)/(x^4*(8*c - d*x^3)^2), x, 8, (5*d*sqrt(c + d*x^3))/(96*c*(8*c - d*x^3)) - sqrt(c + d*x^3)/(24*x^3*(8*c - d*x^3)) + (3*d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(128*c^(3/2)) - (7*d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(384*c^(3/2))]
    @test_int [(c + d*x^3)^(3/2)/(x^7*(8*c - d*x^3)^2), x, 9, (7*d^2*sqrt(c + d*x^3))/(512*c^2*(8*c - d*x^3)) - sqrt(c + d*x^3)/(48*x^6*(8*c - d*x^3)) - (23*d*sqrt(c + d*x^3))/(384*c*x^3*(8*c - d*x^3)) + (15*d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(2048*c^(5/2)) - (17*d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(2048*c^(5/2))]

    @test_int [(x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 16, (103*c*x^2*sqrt(c + d*x^3))/(13*d^2) + (19*x^5*sqrt(c + d*x^3))/(39*d) + (5906*c^2*sqrt(c + d*x^3))/(13*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^5*(c + d*x^3)^(3/2))/(3*d*(8*c - d*x^3)) + (108*sqrt(3)*c^(13/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/d^(8/3) - (108*c^(13/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/d^(8/3) + (108*c^(13/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^(8/3) - (2953*3^(1/4)*sqrt(2 - sqrt(3))*c^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(13*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (5906*sqrt(2)*c^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(13*3^(1/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 15, (13*x^2*sqrt(c + d*x^3))/(21*d) + (265*c*sqrt(c + d*x^3))/(7*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^2*(c + d*x^3)^(3/2))/(3*d*(8*c - d*x^3)) + (9*sqrt(3)*c^(7/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/d^(5/3) - (9*c^(7/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/d^(5/3) + (9*c^(7/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/d^(5/3) - (265*3^(1/4)*sqrt(2 - sqrt(3))*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(14*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (265*sqrt(2)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(7*3^(1/4)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(x^1*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2, x, 14, (19*sqrt(c + d*x^3))/(8*d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (3*x^2*sqrt(c + d*x^3))/(8*(8*c - d*x^3)) + (9*sqrt(3)*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(16*d^(2/3)) - (9*c^(1/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(16*d^(2/3)) + (9*c^(1/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(16*d^(2/3)) - (19*3^(1/4)*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(16*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (19*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(4*sqrt(2)*3^(1/4)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)^2), x, 6, -sqrt(c + d*x^3)/(16*c*x) + (d^(1/3)*sqrt(c + d*x^3))/(16*c*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (3*sqrt(c + d*x^3))/(8*x*(8*c - d*x^3)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(32*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(8*sqrt(2)*3^(1/4)*c^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)^2), x, 16, -((13*sqrt(c + d*x^3))/(256*c*x^4)) - (d*sqrt(c + d*x^3))/(32*c^2*x) + (d^(4/3)*sqrt(c + d*x^3))/(32*c^2*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (3*sqrt(c + d*x^3))/(8*x^4*(8*c - d*x^3)) - (9*sqrt(3)*d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(1024*c^(11/6)) + (9*d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(1024*c^(11/6)) - (9*d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1024*c^(11/6)) - (3^(1/4)*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(64*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(16*sqrt(2)*3^(1/4)*c^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [(c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)^2), x, 17, -((11*sqrt(c + d*x^3))/(224*c*x^7)) - (83*d*sqrt(c + d*x^3))/(7168*c^2*x^4) - (19*d^2*sqrt(c + d*x^3))/(1792*c^3*x) + (19*d^(7/3)*sqrt(c + d*x^3))/(1792*c^3*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (3*sqrt(c + d*x^3))/(8*x^7*(8*c - d*x^3)) - (9*sqrt(3)*d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(4096*c^(17/6)) + (9*d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(4096*c^(17/6)) - (9*d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(4096*c^(17/6)) - (19*3^(1/4)*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(3584*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (19*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(896*sqrt(2)*3^(1/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    #= ::Subsubsection::Closed:: =#
    #=q<0*when*8*b*c+a*d=0=#
    #==#

    @test_int [x^11/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 5, (8*x^6*sqrt(c + d*x^3))/(27*d^2*(8*c - d*x^3)) + (2*sqrt(c + d*x^3)*(170*c + 7*d*x^3))/(27*d^4) - (2944*c^(3/2)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*d^4)]
    @test_int [x^8/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 5, (2*sqrt(c + d*x^3))/(3*d^3) + (64*c*sqrt(c + d*x^3))/(27*d^3*(8*c - d*x^3)) - (224*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*d^3)]
    @test_int [x^5/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 4, (8*sqrt(c + d*x^3))/(27*d^2*(8*c - d*x^3)) - (10*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*sqrt(c)*d^2)]
    @test_int [x^2/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 4, sqrt(c + d*x^3)/(27*c*d*(8*c - d*x^3)) + atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(81*c^(3/2)*d)]
    @test_int [1/(x^1*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 7, sqrt(c + d*x^3)/(216*c^2*(8*c - d*x^3)) + (13*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(2592*c^(5/2)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(96*c^(5/2))]
    @test_int [1/(x^4*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 8, (5*d*sqrt(c + d*x^3))/(864*c^3*(8*c - d*x^3)) - sqrt(c + d*x^3)/(24*c^2*x^3*(8*c - d*x^3)) + (11*d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(10368*c^(7/2)) + (d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(384*c^(7/2))]
    @test_int [1/(x^7*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 9, (-35*d^2*sqrt(c + d*x^3))/(13824*c^4*(8*c - d*x^3)) - sqrt(c + d*x^3)/(48*c^2*x^6*(8*c - d*x^3)) + (3*d*sqrt(c + d*x^3))/(128*c^3*x^3*(8*c - d*x^3)) + (31*d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(165888*c^(9/2)) - (19*d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(6144*c^(9/2))]

    @test_int [x^7/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 14, (62*sqrt(c + d*x^3))/(27*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (8*x^2*sqrt(c + d*x^3))/(27*d^2*(8*c - d*x^3)) + (44*c^(1/6)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(27*sqrt(3)*d^(8/3)) - (44*c^(1/6)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(81*d^(8/3)) + (44*c^(1/6)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(81*d^(8/3)) - (31*sqrt(2 - sqrt(3))*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(9*3^(3/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (62*sqrt(2)*c^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^4/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 14, sqrt(c + d*x^3)/(27*c*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^2*sqrt(c + d*x^3))/(27*c*d*(8*c - d*x^3)) + atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3))/(27*sqrt(3)*c^(5/6)*d^(5/3)) - atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3)))/(81*c^(5/6)*d^(5/3)) + atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(81*c^(5/6)*d^(5/3)) - (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(18*3^(3/4)*c^(2/3)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (sqrt(2)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(1/4)*c^(2/3)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^1/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 14, sqrt(c + d*x^3)/(216*c^2*d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (x^2*sqrt(c + d*x^3))/(216*c^2*(8*c - d*x^3)) - (7*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(432*sqrt(3)*c^(11/6)*d^(2/3)) + (7*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(1296*c^(11/6)*d^(2/3)) - (7*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(1296*c^(11/6)*d^(2/3)) - (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(144*3^(3/4)*c^(5/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + ((c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(108*sqrt(2)*3^(1/4)*c^(5/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 15, -((7*sqrt(c + d*x^3))/(432*c^3*x)) + (7*d^(1/3)*sqrt(c + d*x^3))/(432*c^3*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + sqrt(c + d*x^3)/(216*c^2*x*(8*c - d*x^3)) - (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(216*sqrt(3)*c^(17/6)) + (d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(648*c^(17/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(648*c^(17/6)) - (7*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(288*3^(3/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (7*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(216*sqrt(2)*3^(1/4)*c^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^5*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 16, -((31*sqrt(c + d*x^3))/(6912*c^3*x^4)) + (5*d*sqrt(c + d*x^3))/(864*c^4*x) - (5*d^(4/3)*sqrt(c + d*x^3))/(864*c^4*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + sqrt(c + d*x^3)/(216*c^2*x^4*(8*c - d*x^3)) - (25*d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(27648*sqrt(3)*c^(23/6)) + (25*d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(82944*c^(23/6)) - (25*d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(82944*c^(23/6)) + (5*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(576*3^(3/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (5*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(432*sqrt(2)*3^(1/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^8*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 17, -((17*sqrt(c + d*x^3))/(6048*c^3*x^7)) + (391*d*sqrt(c + d*x^3))/(193536*c^4*x^4) - (289*d^2*sqrt(c + d*x^3))/(48384*c^5*x) + (289*d^(7/3)*sqrt(c + d*x^3))/(48384*c^5*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + sqrt(c + d*x^3)/(216*c^2*x^7*(8*c - d*x^3)) - (17*d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(110592*sqrt(3)*c^(29/6)) + (17*d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(331776*c^(29/6)) - (17*d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(331776*c^(29/6)) - (289*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(32256*3^(3/4)*c^(14/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (289*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(24192*sqrt(2)*3^(1/4)*c^(14/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [x^6/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 2, (x^7*sqrt(1 + (d*x^3)/c)*AppellF1(7/3, 2, 1/2, 10/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(448*c^2*sqrt(c + d*x^3))]
    @test_int [x^3/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 2, 1/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(256*c^2*sqrt(c + d*x^3))]
    @test_int [x^0/((8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 2, 1/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(64*c^2*sqrt(c + d*x^3))]
    @test_int [1/(x^3*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 2, 1/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(128*c^2*x^2*sqrt(c + d*x^3)))]
    @test_int [1/(x^6*(8*c - d*x^3)^2*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(5/3), 2, 1/2, -(2/3), (d*x^3)/(8*c), -((d*x^3)/c)))/(320*c^2*x^5*sqrt(c + d*x^3)))]

    @test_int [x^11/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 5, (8*x^6)/(27*d^2*(8*c - d*x^3)*sqrt(c + d*x^3)) + (2*(38*c + 39*d*x^3))/(81*d^4*sqrt(c + d*x^3)) - (640*sqrt(c)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(243*d^4)]
    @test_int [x^8/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 5, -22/(81*d^3*sqrt(c + d*x^3)) + (64*c)/(27*d^3*(8*c - d*x^3)*sqrt(c + d*x^3)) - (32*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(243*sqrt(c)*d^3)]
    @test_int [x^5/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 5, -2/(81*c*d^2*sqrt(c + d*x^3)) + 8/(27*d^2*(8*c - d*x^3)*sqrt(c + d*x^3)) + (2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(243*c^(3/2)*d^2)]
    @test_int [x^2/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 5, -1/(81*c^2*d*sqrt(c + d*x^3)) + 1/(27*c*d*(8*c - d*x^3)*sqrt(c + d*x^3)) + atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(243*c^(5/2)*d)]
    @test_int [1/(x^1*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 8, 5/(648*c^3*sqrt(c + d*x^3)) + 1/(216*c^2*(8*c - d*x^3)*sqrt(c + d*x^3)) + (7*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(7776*c^(7/2)) - atanh(sqrt(c + d*x^3)/sqrt(c))/(96*c^(7/2))]
    @test_int [1/(x^4*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 9, (-35*d)/(2592*c^4*sqrt(c + d*x^3)) + (5*d)/(864*c^3*(8*c - d*x^3)*sqrt(c + d*x^3)) - 1/(24*c^2*x^3*(8*c - d*x^3)*sqrt(c + d*x^3)) + (5*d*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(31104*c^(9/2)) + (5*d*atanh(sqrt(c + d*x^3)/sqrt(c)))/(384*c^(9/2))]
    @test_int [1/(x^7*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 10, (665*d^2)/(41472*c^5*sqrt(c + d*x^3)) - (71*d^2)/(13824*c^4*(8*c - d*x^3)*sqrt(c + d*x^3)) - 1/(48*c^2*x^6*(8*c - d*x^3)*sqrt(c + d*x^3)) + (17*d)/(384*c^3*x^3*(8*c - d*x^3)*sqrt(c + d*x^3)) + (13*d^2*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(497664*c^(11/2)) - (33*d^2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(2048*c^(11/2))]

    @test_int [x^7/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 15, -((2*x^2)/(81*c*d^2*sqrt(c + d*x^3))) + (8*x^2)/(27*d^2*(8*c - d*x^3)*sqrt(c + d*x^3)) + (2*sqrt(c + d*x^3))/(81*c*d^(8/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) + (4*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(81*sqrt(3)*c^(5/6)*d^(8/3)) - (4*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(243*c^(5/6)*d^(8/3)) + (4*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(243*c^(5/6)*d^(8/3)) - (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(27*3^(3/4)*c^(2/3)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (2*sqrt(2)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(81*3^(1/4)*c^(2/3)*d^(8/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^4/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 15, -(x^2/(81*c^2*d*sqrt(c + d*x^3))) + x^2/(27*c*d*(8*c - d*x^3)*sqrt(c + d*x^3)) + sqrt(c + d*x^3)/(81*c^2*d^(5/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3))/(81*sqrt(3)*c^(11/6)*d^(5/3)) + atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3)))/(243*c^(11/6)*d^(5/3)) - atanh(sqrt(c + d*x^3)/(3*sqrt(c)))/(243*c^(11/6)*d^(5/3)) - (sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(54*3^(3/4)*c^(5/3)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (sqrt(2)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(81*3^(1/4)*c^(5/3)*d^(5/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^1/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 15, (5*x^2)/(648*c^3*sqrt(c + d*x^3)) + x^2/(216*c^2*(8*c - d*x^3)*sqrt(c + d*x^3)) - (5*sqrt(c + d*x^3))/(648*c^3*d^(2/3)*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (5*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(1296*sqrt(3)*c^(17/6)*d^(2/3)) + (5*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(3888*c^(17/6)*d^(2/3)) - (5*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(3888*c^(17/6)*d^(2/3)) + (5*sqrt(2 - sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(432*3^(3/4)*c^(8/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (5*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(324*sqrt(2)*3^(1/4)*c^(8/3)*d^(2/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 16, 5/(648*c^3*x*sqrt(c + d*x^3)) + 1/(216*c^2*x*(8*c - d*x^3)*sqrt(c + d*x^3)) - (31*sqrt(c + d*x^3))/(1296*c^4*x) + (31*d^(1/3)*sqrt(c + d*x^3))/(1296*c^4*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(1296*sqrt(3)*c^(23/6)) + (d^(1/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(3888*c^(23/6)) - (d^(1/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(3888*c^(23/6)) - (31*sqrt(2 - sqrt(3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(864*3^(3/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (31*d^(1/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(648*sqrt(2)*3^(1/4)*c^(11/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^5*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 17, 5/(648*c^3*x^4*sqrt(c + d*x^3)) + 1/(216*c^2*x^4*(8*c - d*x^3)*sqrt(c + d*x^3)) - (253*sqrt(c + d*x^3))/(20736*c^4*x^4) + (77*d*sqrt(c + d*x^3))/(2592*c^5*x) - (77*d^(4/3)*sqrt(c + d*x^3))/(2592*c^5*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (11*d^(4/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(82944*sqrt(3)*c^(29/6)) + (11*d^(4/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(248832*c^(29/6)) - (11*d^(4/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(248832*c^(29/6)) + (77*sqrt(2 - sqrt(3))*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(1728*3^(3/4)*c^(14/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) - (77*d^(4/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(1296*sqrt(2)*3^(1/4)*c^(14/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [1/(x^8*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 18, 5/(648*c^3*x^7*sqrt(c + d*x^3)) + 1/(216*c^2*x^7*(8*c - d*x^3)*sqrt(c + d*x^3)) - (191*sqrt(c + d*x^3))/(18144*c^4*x^7) + (8257*d*sqrt(c + d*x^3))/(580608*c^5*x^4) - (5179*d^2*sqrt(c + d*x^3))/(145152*c^6*x) + (5179*d^(7/3)*sqrt(c + d*x^3))/(145152*c^6*((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)) - (7*d^(7/3)*atan((sqrt(3)*c^(1/6)*(c^(1/3) + d^(1/3)*x))/sqrt(c + d*x^3)))/(331776*sqrt(3)*c^(35/6)) + (7*d^(7/3)*atanh((c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*sqrt(c + d*x^3))))/(995328*c^(35/6)) - (7*d^(7/3)*atanh(sqrt(c + d*x^3)/(3*sqrt(c))))/(995328*c^(35/6)) - (5179*sqrt(2 - sqrt(3))*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.E(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(96768*3^(3/4)*c^(17/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3)) + (5179*d^(7/3)*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(72576*sqrt(2)*3^(1/4)*c^(17/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]

    @test_int [x^6/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, -2, (2*x*(4*c + d*x^3))/(81*c*d^2*(8*c - d*x^3)*sqrt(c + d*x^3)) - (2*sqrt(2 + sqrt(3))*(c^(1/3) + d^(1/3)*x)*sqrt((c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*Elliptic.F(asin(((1 - sqrt(3))*c^(1/3) + d^(1/3)*x)/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)), -7 - 4*sqrt(3)))/(81*3^(1/4)*c*d^(7/3)*sqrt((c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + sqrt(3))*c^(1/3) + d^(1/3)*x)^2)*sqrt(c + d*x^3))]
    @test_int [x^3/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 2, 3/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(256*c^3*sqrt(c + d*x^3))]
    @test_int [x^0/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 2, 3/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(64*c^3*sqrt(c + d*x^3))]
    @test_int [1/(x^3*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 2, 3/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)))/(128*c^3*x^2*sqrt(c + d*x^3)))]
    @test_int [1/(x^6*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-(5/3), 2, 3/2, -(2/3), (d*x^3)/(8*c), -((d*x^3)/c)))/(320*c^3*x^5*sqrt(c + d*x^3)))]

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [(x^8*sqrt(c + d*x^3))/(a + b*x^3)^2, x, 6, -(a*(4*b*c - 5*a*d)*sqrt(c + d*x^3))/(3*b^3*(b*c - a*d)) + (2*(c + d*x^3)^(3/2))/(9*b^2*d) - (a^2*(c + d*x^3)^(3/2))/(3*b^2*(b*c - a*d)*(a + b*x^3)) + (a*(4*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(7/2)*sqrt(b*c - a*d))]
    @test_int [(x^5*sqrt(c + d*x^3))/(a + b*x^3)^2, x, 5, ((2*b*c - 3*a*d)*sqrt(c + d*x^3))/(3*b^2*(b*c - a*d)) + (a*(c + d*x^3)^(3/2))/(3*b*(b*c - a*d)*(a + b*x^3)) - ((2*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(5/2)*sqrt(b*c - a*d))]
    @test_int [(x^2*sqrt(c + d*x^3))/(a + b*x^3)^2, x, 4, -sqrt(c + d*x^3)/(3*b*(a + b*x^3)) - (d*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(3/2)*sqrt(b*c - a*d))]
    @test_int [sqrt(c + d*x^3)/(x^1*(a + b*x^3)^2), x, 7, sqrt(c + d*x^3)/(3*a*(a + b*x^3)) - (2*sqrt(c)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2) + ((2*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*sqrt(b)*sqrt(b*c - a*d))]
    @test_int [sqrt(c + d*x^3)/(x^4*(a + b*x^3)^2), x, 8, (-2*b*sqrt(c + d*x^3))/(3*a^2*(a + b*x^3)) - sqrt(c + d*x^3)/(3*a*x^3*(a + b*x^3)) + ((4*b*c - a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^3*sqrt(c)) - (sqrt(b)*(4*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^3*sqrt(b*c - a*d))]

    @test_int [(x^3*sqrt(c + d*x^3))/(a + b*x^3)^2, x, 2, (x^4*sqrt(c + d*x^3)*AppellF1(4/3, 2, -1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a^2*sqrt(1 + (d*x^3)/c))]
    @test_int [(x^1*sqrt(c + d*x^3))/(a + b*x^3)^2, x, 2, (x^2*sqrt(c + d*x^3)*AppellF1(2/3, 2, -1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*sqrt(1 + (d*x^3)/c))]
    @test_int [x^0*sqrt(c + d*x^3)/(a + b*x^3)^2, x, 2, (x*sqrt(c + d*x^3)*AppellF1(1/3, 2, -(1/2), 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*sqrt(1 + (d*x^3)/c))]
    @test_int [sqrt(c + d*x^3)/(x^2*(a + b*x^3)^2), x, 2, -((sqrt(c + d*x^3)*AppellF1(-1/3, 2, -1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*x*sqrt(1 + (d*x^3)/c)))]
    @test_int [sqrt(c + d*x^3)/(x^3*(a + b*x^3)^2), x, 2, -(sqrt(c + d*x^3)*AppellF1(-2/3, 2, -1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*x^2*sqrt(1 + (d*x^3)/c))]

    @test_int [(x^8*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x, 7, -(a*(4*b*c - 7*a*d)*sqrt(c + d*x^3))/(3*b^4) - (a*(4*b*c - 7*a*d)*(c + d*x^3)^(3/2))/(9*b^3*(b*c - a*d)) + (2*(c + d*x^3)^(5/2))/(15*b^2*d) - (a^2*(c + d*x^3)^(5/2))/(3*b^2*(b*c - a*d)*(a + b*x^3)) + (a*(4*b*c - 7*a*d)*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(9/2))]
    @test_int [(x^5*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x, 6, ((2*b*c - 5*a*d)*sqrt(c + d*x^3))/(3*b^3) + ((2*b*c - 5*a*d)*(c + d*x^3)^(3/2))/(9*b^2*(b*c - a*d)) + (a*(c + d*x^3)^(5/2))/(3*b*(b*c - a*d)*(a + b*x^3)) - ((2*b*c - 5*a*d)*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(7/2))]
    @test_int [(x^2*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x, 5, (d*sqrt(c + d*x^3))/b^2 - (c + d*x^3)^(3/2)/(3*b*(a + b*x^3)) - (d*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/b^(5/2)]
    @test_int [(c + d*x^3)^(3/2)/(x^1*(a + b*x^3)^2), x, 7, ((b*c - a*d)*sqrt(c + d*x^3))/(3*a*b*(a + b*x^3)) - (2*c^(3/2)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2) + (sqrt(b*c - a*d)*(2*b*c + a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*b^(3/2))]
    @test_int [(c + d*x^3)^(3/2)/(x^4*(a + b*x^3)^2), x, 8, -((2*b*c - a*d)*sqrt(c + d*x^3))/(3*a^2*(a + b*x^3)) - (c*sqrt(c + d*x^3))/(3*a*x^3*(a + b*x^3)) + (sqrt(c)*(4*b*c - 3*a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^3) - (sqrt(b*c - a*d)*(4*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^3*sqrt(b))]

    @test_int [(x^3*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x, 2, (c*x^4*sqrt(c + d*x^3)*AppellF1(4/3, 2, -3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a^2*sqrt(1 + (d*x^3)/c))]
    @test_int [(x^1*(c + d*x^3)^(3/2))/(a + b*x^3)^2, x, 2, (c*x^2*sqrt(c + d*x^3)*AppellF1(2/3, 2, -3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*sqrt(1 + (d*x^3)/c))]
    @test_int [x^0*(c + d*x^3)^(3/2)/(a + b*x^3)^2, x, 2, (c*x*sqrt(c + d*x^3)*AppellF1(1/3, 2, -(3/2), 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*sqrt(1 + (d*x^3)/c))]
    @test_int [(c + d*x^3)^(3/2)/(x^2*(a + b*x^3)^2), x, 2, -((c*sqrt(c + d*x^3)*AppellF1(-1/3, 2, -3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*x*sqrt(1 + (d*x^3)/c)))]
    @test_int [(c + d*x^3)^(3/2)/(x^3*(a + b*x^3)^2), x, 2, -(c*sqrt(c + d*x^3)*AppellF1(-2/3, 2, -3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*x^2*sqrt(1 + (d*x^3)/c))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x^8/((a + b*x^3)^2*sqrt(c + d*x^3)), x, 5, (2*sqrt(c + d*x^3))/(3*b^2*d) - (a^2*sqrt(c + d*x^3))/(3*b^2*(b*c - a*d)*(a + b*x^3)) + (a*(4*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [x^5/((a + b*x^3)^2*sqrt(c + d*x^3)), x, 4, (a*sqrt(c + d*x^3))/(3*b*(b*c - a*d)*(a + b*x^3)) - ((2*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [x^2/((a + b*x^3)^2*sqrt(c + d*x^3)), x, 4, -sqrt(c + d*x^3)/(3*(b*c - a*d)*(a + b*x^3)) + (d*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*sqrt(b)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^1*(a + b*x^3)^2*sqrt(c + d*x^3)), x, 7, (b*sqrt(c + d*x^3))/(3*a*(b*c - a*d)*(a + b*x^3)) - (2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2*sqrt(c)) + (sqrt(b)*(2*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*(b*c - a*d)^(3/2))]
    @test_int [1/(x^4*(a + b*x^3)^2*sqrt(c + d*x^3)), x, 8, -(b*(2*b*c - a*d)*sqrt(c + d*x^3))/(3*a^2*c*(b*c - a*d)*(a + b*x^3)) - sqrt(c + d*x^3)/(3*a*c*x^3*(a + b*x^3)) + ((4*b*c + a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^3*(b*c - a*d)^(3/2))]

    @test_int [x^3/((a + b*x^3)^2*sqrt(c + d*x^3)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 2, 1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a^2*sqrt(c + d*x^3))]
    @test_int [x^1/((a + b*x^3)^2*sqrt(c + d*x^3)), x, 2, (x^2*sqrt(1 + (d*x^3)/c)*AppellF1(2/3, 2, 1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*sqrt(c + d*x^3))]
    @test_int [x^0/((a + b*x^3)^2*sqrt(c + d*x^3)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 2, 1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(a + b*x^3)^2*sqrt(c + d*x^3)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-1/3, 2, 1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*x*sqrt(c + d*x^3)))]
    @test_int [1/(x^3*(a + b*x^3)^2*sqrt(c + d*x^3)), x, 2, -(sqrt(1 + (d*x^3)/c)*AppellF1(-2/3, 2, 1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*x^2*sqrt(c + d*x^3))]

    @test_int [x^8/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 5, -(2*b^2*c^2 + a^2*d^2)/(3*b^2*d*(b*c - a*d)^2*sqrt(c + d*x^3)) - a^2/(3*b^2*(b*c - a*d)*(a + b*x^3)*sqrt(c + d*x^3)) + (a*(4*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*b^(3/2)*(b*c - a*d)^(5/2))]
    @test_int [x^5/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 5, (2*b*c + a*d)/(3*b*(b*c - a*d)^2*sqrt(c + d*x^3)) + a/(3*b*(b*c - a*d)*(a + b*x^3)*sqrt(c + d*x^3)) - ((2*b*c + a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*sqrt(b)*(b*c - a*d)^(5/2))]
    @test_int [x^2/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 5, -(d/((b*c - a*d)^2*sqrt(c + d*x^3))) - 1/(3*(b*c - a*d)*(a + b*x^3)*sqrt(c + d*x^3)) + (sqrt(b)*d*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(b*c - a*d)^(5/2)]
    @test_int [1/(x^1*(a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 8, (d*(b*c + 2*a*d))/(3*a*c*(b*c - a*d)^2*sqrt(c + d*x^3)) + b/(3*a*(b*c - a*d)*(a + b*x^3)*sqrt(c + d*x^3)) - (2*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^2*c^(3/2)) + (b^(3/2)*(2*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^2*(b*c - a*d)^(5/2))]
    @test_int [1/(x^4*(a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 9, -(d*(2*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2))/(3*a^2*c^2*(b*c - a*d)^2*sqrt(c + d*x^3)) - (b*(2*b*c - a*d))/(3*a^2*c*(b*c - a*d)*(a + b*x^3)*sqrt(c + d*x^3)) - 1/(3*a*c*x^3*(a + b*x^3)*sqrt(c + d*x^3)) + ((4*b*c + 3*a*d)*atanh(sqrt(c + d*x^3)/sqrt(c)))/(3*a^3*c^(5/2)) - (b^(5/2)*(4*b*c - 7*a*d)*atanh((sqrt(b)*sqrt(c + d*x^3))/sqrt(b*c - a*d)))/(3*a^3*(b*c - a*d)^(5/2))]

    @test_int [x^3/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 2, (x^4*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 2, 3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*a^2*c*sqrt(c + d*x^3))]
    @test_int [x^1/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 2, (x^2*sqrt(1 + (d*x^3)/c)*AppellF1(2/3, 2, 3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*c*sqrt(c + d*x^3))]
    @test_int [x^0/((a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 2, (x*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 2, 3/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*c*sqrt(c + d*x^3))]
    @test_int [1/(x^2*(a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 2, -((sqrt(1 + (d*x^3)/c)*AppellF1(-1/3, 2, 3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a^2*c*x*sqrt(c + d*x^3)))]
    @test_int [1/(x^3*(a + b*x^3)^2*(c + d*x^3)^(3/2)), x, 2, -(sqrt(1 + (d*x^3)/c)*AppellF1(-2/3, 2, 3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a^2*c*x^2*sqrt(c + d*x^3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^(p/2)*(c+d*x^3)^q*with*m*symbolic=#

    @test_int [(e*x)^m*(a + b*x^3)^(5/2)*(A + B*x^3), x, 3, (2*B*(e*x)^(1 + m)*(a + b*x^3)^(7/2))/(b*e*(23 + 2*m)) - (a^2*(2*a*B*(1 + m) - A*b*(23 + 2*m))*(e*x)^(1 + m)*sqrt(a + b*x^3)*HypergeometricFunctions._₂F₁(-(5/2), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(b*e*(1 + m)*(23 + 2*m)*sqrt(1 + (b*x^3)/a))]
    @test_int [(e*x)^m*(a + b*x^3)^(3/2)*(A + B*x^3), x, 3, (2*B*(e*x)^(1 + m)*(a + b*x^3)^(5/2))/(b*e*(17 + 2*m)) - (a*(2*a*B*(1 + m) - A*b*(17 + 2*m))*(e*x)^(1 + m)*sqrt(a + b*x^3)*HypergeometricFunctions._₂F₁(-(3/2), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(b*e*(1 + m)*(17 + 2*m)*sqrt(1 + (b*x^3)/a))]
    @test_int [(e*x)^m*(a + b*x^3)^(1/2)*(A + B*x^3), x, 3, (2*B*(e*x)^(1 + m)*(a + b*x^3)^(3/2))/(b*e*(11 + 2*m)) - ((2*a*B*(1 + m) - A*b*(11 + 2*m))*(e*x)^(1 + m)*sqrt(a + b*x^3)*HypergeometricFunctions._₂F₁(-(1/2), (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(b*e*(1 + m)*(11 + 2*m)*sqrt(1 + (b*x^3)/a))]
    @test_int [((e*x)^m*(A + B*x^3))/(a + b*x^3)^(1/2), x, 3, (2*B*(e*x)^(1 + m)*sqrt(a + b*x^3))/(b*e*(5 + 2*m)) - ((2*a*B*(1 + m) - A*b*(5 + 2*m))*(e*x)^(1 + m)*sqrt(1 + (b*x^3)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(b*e*(1 + m)*(5 + 2*m)*sqrt(a + b*x^3))]
    @test_int [((e*x)^m*(A + B*x^3))/(a + b*x^3)^(3/2), x, 3, (2*(A*b - a*B)*(e*x)^(1 + m))/(3*a*b*e*sqrt(a + b*x^3)) + ((2*a*B*(1 + m) + A*(b - 2*b*m))*(e*x)^(1 + m)*sqrt(1 + (b*x^3)/a)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(3*a*b*e*(1 + m)*sqrt(a + b*x^3))]
    @test_int [((e*x)^m*(A + B*x^3))/(a + b*x^3)^(5/2), x, 3, (2*(A*b - a*B)*(e*x)^(1 + m))/(9*a*b*e*(a + b*x^3)^(3/2)) + ((A*b*(7 - 2*m) + 2*a*B*(1 + m))*(e*x)^(1 + m)*sqrt(1 + (b*x^3)/a)*HypergeometricFunctions._₂F₁(3/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)))/(9*a^2*b*e*(1 + m)*sqrt(a + b*x^3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^(p/2)*(c+d*x^3)^(q/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^(p/2)*(c+d*x^3)^(q/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^5/(sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 5, (sqrt(a + b*x^3)*sqrt(c + d*x^3))/(3*b*d) - ((b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x^3))/(sqrt(b)*sqrt(c + d*x^3))))/(3*b^(3/2)*d^(3/2))]
    @test_int [x^2/(sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 4, (2*atanh((sqrt(d)*sqrt(a + b*x^3))/(sqrt(b)*sqrt(c + d*x^3))))/(3*sqrt(b)*sqrt(d))]
    @test_int [1/(x^1*sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, -((2*atanh((sqrt(c)*sqrt(a + b*x^3))/(sqrt(a)*sqrt(c + d*x^3))))/(3*sqrt(a)*sqrt(c)))]
    @test_int [1/(x^4*sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 4, -((sqrt(a + b*x^3)*sqrt(c + d*x^3))/(3*a*c*x^3)) + ((b*c + a*d)*atanh((sqrt(c)*sqrt(a + b*x^3))/(sqrt(a)*sqrt(c + d*x^3))))/(3*a^(3/2)*c^(3/2))]

    @test_int [x^4/(sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, (x^5*sqrt(1 + (b*x^3)/a)*sqrt(1 + (d*x^3)/c)*AppellF1(5/3, 1/2, 1/2, 8/3, -((b*x^3)/a), -((d*x^3)/c)))/(5*sqrt(a + b*x^3)*sqrt(c + d*x^3))]
    @test_int [x^3/(sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, (x^4*sqrt(1 + (b*x^3)/a)*sqrt(1 + (d*x^3)/c)*AppellF1(4/3, 1/2, 1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*sqrt(a + b*x^3)*sqrt(c + d*x^3))]
    @test_int [x^1/(sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, (x^2*sqrt(1 + (b*x^3)/a)*sqrt(1 + (d*x^3)/c)*AppellF1(2/3, 1/2, 1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*sqrt(a + b*x^3)*sqrt(c + d*x^3))]
    @test_int [x^0/(sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, (x*sqrt(1 + (b*x^3)/a)*sqrt(1 + (d*x^3)/c)*AppellF1(1/3, 1/2, 1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(sqrt(a + b*x^3)*sqrt(c + d*x^3))]
    @test_int [1/(x^2*sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, -((sqrt(1 + (b*x^3)/a)*sqrt(1 + (d*x^3)/c)*AppellF1(-(1/3), 1/2, 1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(x*sqrt(a + b*x^3)*sqrt(c + d*x^3)))]
    @test_int [1/(x^3*sqrt(a + b*x^3)*sqrt(c + d*x^3)), x, 3, -((sqrt(1 + (b*x^3)/a)*sqrt(1 + (d*x^3)/c)*AppellF1(-(2/3), 1/2, 1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*x^2*sqrt(a + b*x^3)*sqrt(c + d*x^3)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x^3)^(p/2)*(c+d*x^3)^q=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^3)^(p/2)*(c+d*x^3)^1=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [(e*x)^(7/2)*sqrt(a + b*x^3)*(A + B*x^3), x, 7, (a*(2*A*b - a*B)*e^2*(e*x)^(3/2)*sqrt(a + b*x^3))/(24*b^2) + ((2*A*b - a*B)*(e*x)^(9/2)*sqrt(a + b*x^3))/(12*b*e) + (B*(e*x)^(9/2)*(a + b*x^3)^(3/2))/(9*b*e) - (a^2*(2*A*b - a*B)*e^(7/2)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(24*b^(5/2))]
    @test_int [(e*x)^(5/2)*sqrt(a + b*x^3)*(A + B*x^3), x, 5, (3*a*(16*A*b - 7*a*B)*e^2*sqrt(e*x)*sqrt(a + b*x^3))/(320*b^2) + ((16*A*b - 7*a*B)*(e*x)^(7/2)*sqrt(a + b*x^3))/(80*b*e) + (B*(e*x)^(7/2)*(a + b*x^3)^(3/2))/(8*b*e) - (3^(3/4)*a^(5/3)*(16*A*b - 7*a*B)*e^2*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(640*b^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(e*x)^(3/2)*sqrt(a + b*x^3)*(A + B*x^3), x, 6, ((14*A*b - 5*a*B)*(e*x)^(5/2)*sqrt(a + b*x^3))/(56*b*e) + (3*(1 + sqrt(3))*a*(14*A*b - 5*a*B)*e*sqrt(e*x)*sqrt(a + b*x^3))/(112*b^(5/3)*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + (B*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(7*b*e) - (3*3^(1/4)*a^(4/3)*(14*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(112*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*(1 - sqrt(3))*a^(4/3)*(14*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(224*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(e*x)*sqrt(a + b*x^3)*(A + B*x^3), x, 6, ((4*A*b - a*B)*(e*x)^(3/2)*sqrt(a + b*x^3))/(12*b*e) + (B*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(6*b*e) + (a*(4*A*b - a*B)*sqrt(e)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(12*b^(3/2))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/sqrt(e*x), x, 4, ((10*A*b - a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(20*b*e) + (B*sqrt(e*x)*(a + b*x^3)^(3/2))/(5*b*e) + (3^(3/4)*a^(2/3)*(10*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(40*b*e*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/(e*x)^(3/2), x, 6, ((8*A*b + a*B)*(e*x)^(5/2)*sqrt(a + b*x^3))/(4*a*e^4) + (3*(1 + sqrt(3))*(8*A*b + a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(8*b^(2/3)*e^2*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) - (2*A*(a + b*x^3)^(3/2))/(a*e*sqrt(e*x)) - (3*3^(1/4)*a^(1/3)*(8*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(8*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*(1 - sqrt(3))*a^(1/3)*(8*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(16*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/(e*x)^(5/2), x, 6, ((2*A*b + a*B)*(e*x)^(3/2)*sqrt(a + b*x^3))/(3*a*e^4) - (2*A*(a + b*x^3)^(3/2))/(3*a*e*(e*x)^(3/2)) + ((2*A*b + a*B)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(3*sqrt(b)*e^(5/2))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/(e*x)^(7/2), x, 4, ((4*A*b + 5*a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(10*a*e^4) - (2*A*(a + b*x^3)^(3/2))/(5*a*e*(e*x)^(5/2)) + (3^(3/4)*(4*A*b + 5*a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(20*a^(1/3)*e^4*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^(9/2), x, 6, -((2*(2*A*b + 7*a*B)*sqrt(a + b*x^3))/(7*a*sqrt(x))) + (3*(1 + sqrt(3))*b^(1/3)*(2*A*b + 7*a*B)*sqrt(x)*sqrt(a + b*x^3))/(7*a*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) - (2*A*(a + b*x^3)^(3/2))/(7*a*x^(7/2)) - (3*3^(1/4)*b^(1/3)*(2*A*b + 7*a*B)*sqrt(x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(7*a^(2/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (3^(3/4)*(1 - sqrt(3))*b^(1/3)*(2*A*b + 7*a*B)*sqrt(x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(14*a^(2/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^(11/2), x, 6, (-2*B*sqrt(a + b*x^3))/(3*x^(3/2)) - (2*A*(a + b*x^3)^(3/2))/(9*a*x^(9/2)) + (2*sqrt(b)*B*atanh((sqrt(b)*x^(3/2))/sqrt(a + b*x^3)))/3]
    @test_int [(sqrt(a + b*x^3)*(A + B*x^3))/x^(13/2), x, 4, (2*(2*A*b - 11*a*B)*sqrt(a + b*x^3))/(55*a*x^(5/2)) - (2*A*(a + b*x^3)^(3/2))/(11*a*x^(11/2)) - (3^(3/4)*b*(2*A*b - 11*a*B)*sqrt(x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(55*a^(4/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(e*x)^(7/2)*(a + b*x^3)^(3/2)*(A + B*x^3), x, 8, (a^2*(8*A*b - 3*a*B)*e^2*(e*x)^(3/2)*sqrt(a + b*x^3))/(192*b^2) + (a*(8*A*b - 3*a*B)*(e*x)^(9/2)*sqrt(a + b*x^3))/(96*b*e) + ((8*A*b - 3*a*B)*(e*x)^(9/2)*(a + b*x^3)^(3/2))/(72*b*e) + (B*(e*x)^(9/2)*(a + b*x^3)^(5/2))/(12*b*e) - (a^3*(8*A*b - 3*a*B)*e^(7/2)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(192*b^(5/2))]
    @test_int [(e*x)^(5/2)*(a + b*x^3)^(3/2)*(A + B*x^3), x, 6, (27*a^2*(22*A*b - 7*a*B)*e^2*sqrt(e*x)*sqrt(a + b*x^3))/(7040*b^2) + (9*a*(22*A*b - 7*a*B)*(e*x)^(7/2)*sqrt(a + b*x^3))/(1760*b*e) + ((22*A*b - 7*a*B)*(e*x)^(7/2)*(a + b*x^3)^(3/2))/(176*b*e) + (B*(e*x)^(7/2)*(a + b*x^3)^(5/2))/(11*b*e) - (9*3^(3/4)*a^(8/3)*(22*A*b - 7*a*B)*e^2*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(14080*b^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(e*x)^(3/2)*(a + b*x^3)^(3/2)*(A + B*x^3), x, 7, (9*a*(4*A*b - a*B)*(e*x)^(5/2)*sqrt(a + b*x^3))/(224*b*e) + (27*(1 + sqrt(3))*a^2*(4*A*b - a*B)*e*sqrt(e*x)*sqrt(a + b*x^3))/(448*b^(5/3)*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + ((4*A*b - a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(28*b*e) + (B*(e*x)^(5/2)*(a + b*x^3)^(5/2))/(10*b*e) - (27*3^(1/4)*a^(7/3)*(4*A*b - a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(448*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (9*3^(3/4)*(1 - sqrt(3))*a^(7/3)*(4*A*b - a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(896*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(e*x)*(a + b*x^3)^(3/2)*(A + B*x^3), x, 7, (a*(6*A*b - a*B)*(e*x)^(3/2)*sqrt(a + b*x^3))/(24*b*e) + ((6*A*b - a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(36*b*e) + (B*(e*x)^(3/2)*(a + b*x^3)^(5/2))/(9*b*e) + (a^2*(6*A*b - a*B)*sqrt(e)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(24*b^(3/2))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/sqrt(e*x), x, 5, (9*a*(16*A*b - a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(320*b*e) + ((16*A*b - a*B)*sqrt(e*x)*(a + b*x^3)^(3/2))/(80*b*e) + (B*sqrt(e*x)*(a + b*x^3)^(5/2))/(8*b*e) + (9*3^(3/4)*a^(5/3)*(16*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(640*b*e*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/(e*x)^(3/2), x, 7, (9*(14*A*b + a*B)*(e*x)^(5/2)*sqrt(a + b*x^3))/(56*e^4) + (27*(1 + sqrt(3))*a*(14*A*b + a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(112*b^(2/3)*e^2*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + ((14*A*b + a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(7*a*e^4) - (2*A*(a + b*x^3)^(5/2))/(a*e*sqrt(e*x)) - (27*3^(1/4)*a^(4/3)*(14*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(112*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (9*3^(3/4)*(1 - sqrt(3))*a^(4/3)*(14*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(224*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/(e*x)^(5/2), x, 7, ((4*A*b + a*B)*(e*x)^(3/2)*sqrt(a + b*x^3))/(4*e^4) + ((4*A*b + a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(6*a*e^4) - (2*A*(a + b*x^3)^(5/2))/(3*a*e*(e*x)^(3/2)) + (a*(4*A*b + a*B)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(4*sqrt(b)*e^(5/2))]
    @test_int [((a + b*x^3)^(3/2)*(A + B*x^3))/(e*x)^(7/2), x, 5, (9*(2*A*b + a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(20*e^4) + ((2*A*b + a*B)*sqrt(e*x)*(a + b*x^3)^(3/2))/(5*a*e^4) - (2*A*(a + b*x^3)^(5/2))/(5*a*e*(e*x)^(5/2)) + (9*3^(3/4)*a^(2/3)*(2*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(40*e^4*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [(e*x)^(7/2)*(a + b*x^3)^(5/2)*(A + B*x^3), x, 9, (a^3*(10*A*b - 3*a*B)*e^2*(e*x)^(3/2)*sqrt(a + b*x^3))/(384*b^2) + (a^2*(10*A*b - 3*a*B)*(e*x)^(9/2)*sqrt(a + b*x^3))/(192*b*e) + (a*(10*A*b - 3*a*B)*(e*x)^(9/2)*(a + b*x^3)^(3/2))/(144*b*e) + ((10*A*b - 3*a*B)*(e*x)^(9/2)*(a + b*x^3)^(5/2))/(120*b*e) + (B*(e*x)^(9/2)*(a + b*x^3)^(7/2))/(15*b*e) - (a^4*(10*A*b - 3*a*B)*e^(7/2)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(384*b^(5/2))]
    @test_int [(e*x)^(5/2)*(a + b*x^3)^(5/2)*(A + B*x^3), x, 7, (81*a^3*(4*A*b - a*B)*e^2*sqrt(e*x)*sqrt(a + b*x^3))/(5632*b^2) + (27*a^2*(4*A*b - a*B)*(e*x)^(7/2)*sqrt(a + b*x^3))/(1408*b*e) + (15*a*(4*A*b - a*B)*(e*x)^(7/2)*(a + b*x^3)^(3/2))/(704*b*e) + ((4*A*b - a*B)*(e*x)^(7/2)*(a + b*x^3)^(5/2))/(44*b*e) + (B*(e*x)^(7/2)*(a + b*x^3)^(7/2))/(14*b*e) - (27*3^(3/4)*a^(11/3)*(4*A*b - a*B)*e^2*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(11264*b^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(e*x)^(3/2)*(a + b*x^3)^(5/2)*(A + B*x^3), x, 8, (27*a^2*(26*A*b - 5*a*B)*(e*x)^(5/2)*sqrt(a + b*x^3))/(5824*b*e) + (81*(1 + sqrt(3))*a^3*(26*A*b - 5*a*B)*e*sqrt(e*x)*sqrt(a + b*x^3))/(11648*b^(5/3)*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + (3*a*(26*A*b - 5*a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(728*b*e) + ((26*A*b - 5*a*B)*(e*x)^(5/2)*(a + b*x^3)^(5/2))/(260*b*e) + (B*(e*x)^(5/2)*(a + b*x^3)^(7/2))/(13*b*e) - (81*3^(1/4)*a^(10/3)*(26*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(11648*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (27*3^(3/4)*(1 - sqrt(3))*a^(10/3)*(26*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(23296*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [sqrt(e*x)*(a + b*x^3)^(5/2)*(A + B*x^3), x, 8, (5*a^2*(8*A*b - a*B)*(e*x)^(3/2)*sqrt(a + b*x^3))/(192*b*e) + (5*a*(8*A*b - a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(288*b*e) + ((8*A*b - a*B)*(e*x)^(3/2)*(a + b*x^3)^(5/2))/(72*b*e) + (B*(e*x)^(3/2)*(a + b*x^3)^(7/2))/(12*b*e) + (5*a^3*(8*A*b - a*B)*sqrt(e)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(192*b^(3/2))]
    @test_int [((a + b*x^3)^(5/2)*(A + B*x^3))/sqrt(e*x), x, 6, (27*a^2*(22*A*b - a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(1408*b*e) + (3*a*(22*A*b - a*B)*sqrt(e*x)*(a + b*x^3)^(3/2))/(352*b*e) + ((22*A*b - a*B)*sqrt(e*x)*(a + b*x^3)^(5/2))/(176*b*e) + (B*sqrt(e*x)*(a + b*x^3)^(7/2))/(11*b*e) + (27*3^(3/4)*a^(8/3)*(22*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(2816*b*e*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(5/2)*(A + B*x^3))/(e*x)^(3/2), x, 8, (27*a*(20*A*b + a*B)*(e*x)^(5/2)*sqrt(a + b*x^3))/(224*e^4) + (81*(1 + sqrt(3))*a^2*(20*A*b + a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(448*b^(2/3)*e^2*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + (3*(20*A*b + a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(28*e^4) + ((20*A*b + a*B)*(e*x)^(5/2)*(a + b*x^3)^(5/2))/(10*a*e^4) - (2*A*(a + b*x^3)^(7/2))/(a*e*sqrt(e*x)) - (81*3^(1/4)*a^(7/3)*(20*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(448*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (27*3^(3/4)*(1 - sqrt(3))*a^(7/3)*(20*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(896*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((a + b*x^3)^(5/2)*(A + B*x^3))/(e*x)^(5/2), x, 8, (5*a*(6*A*b + a*B)*(e*x)^(3/2)*sqrt(a + b*x^3))/(24*e^4) + (5*(6*A*b + a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(36*e^4) + ((6*A*b + a*B)*(e*x)^(3/2)*(a + b*x^3)^(5/2))/(9*a*e^4) - (2*A*(a + b*x^3)^(7/2))/(3*a*e*(e*x)^(3/2)) + (5*a^2*(6*A*b + a*B)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(24*sqrt(b)*e^(5/2))]
    @test_int [((a + b*x^3)^(5/2)*(A + B*x^3))/(e*x)^(7/2), x, 6, (27*a*(16*A*b + 5*a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(320*e^4) + (3*(16*A*b + 5*a*B)*sqrt(e*x)*(a + b*x^3)^(3/2))/(80*e^4) + ((16*A*b + 5*a*B)*sqrt(e*x)*(a + b*x^3)^(5/2))/(40*a*e^4) - (2*A*(a + b*x^3)^(7/2))/(5*a*e*(e*x)^(5/2)) + (27*3^(3/4)*a^(5/3)*(16*A*b + 5*a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(640*e^4*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [((e*x)^(7/2)*(A + B*x^3))/sqrt(a + b*x^3), x, 6, ((4*A*b - 3*a*B)*e^2*(e*x)^(3/2)*sqrt(a + b*x^3))/(12*b^2) + (B*(e*x)^(9/2)*sqrt(a + b*x^3))/(6*b*e) - (a*(4*A*b - 3*a*B)*e^(7/2)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(12*b^(5/2))]
    @test_int [((e*x)^(5/2)*(A + B*x^3))/sqrt(a + b*x^3), x, 4, ((10*A*b - 7*a*B)*e^2*sqrt(e*x)*sqrt(a + b*x^3))/(20*b^2) + (B*(e*x)^(7/2)*sqrt(a + b*x^3))/(5*b*e) - (a^(2/3)*(10*A*b - 7*a*B)*e^2*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(40*3^(1/4)*b^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((e*x)^(3/2)*(A + B*x^3))/sqrt(a + b*x^3), x, 5, (B*(e*x)^(5/2)*sqrt(a + b*x^3))/(4*b*e) + ((1 + sqrt(3))*(8*A*b - 5*a*B)*e*sqrt(e*x)*sqrt(a + b*x^3))/(8*b^(5/3)*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) - (3^(1/4)*a^(1/3)*(8*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(8*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - ((1 - sqrt(3))*a^(1/3)*(8*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(16*3^(1/4)*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(e*x)*(A + B*x^3))/sqrt(a + b*x^3), x, 5, (B*(e*x)^(3/2)*sqrt(a + b*x^3))/(3*b*e) + ((2*A*b - a*B)*sqrt(e)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(3*b^(3/2))]
    @test_int [(A + B*x^3)/(sqrt(e*x)*sqrt(a + b*x^3)), x, 3, (B*sqrt(e*x)*sqrt(a + b*x^3))/(2*b*e) + ((4*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(4*3^(1/4)*a^(1/3)*b*e*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(3/2)*sqrt(a + b*x^3)), x, 5, -((2*A*sqrt(a + b*x^3))/(a*e*sqrt(e*x))) + ((1 + sqrt(3))*(2*A*b + a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(a*b^(2/3)*e^2*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) - (3^(1/4)*(2*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(a^(2/3)*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - ((1 - sqrt(3))*(2*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(2*3^(1/4)*a^(2/3)*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(5/2)*sqrt(a + b*x^3)), x, 5, (-2*A*sqrt(a + b*x^3))/(3*a*e*(e*x)^(3/2)) + (2*B*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(3*sqrt(b)*e^(5/2))]
    @test_int [(A + B*x^3)/((e*x)^(7/2)*sqrt(a + b*x^3)), x, 3, -((2*A*sqrt(a + b*x^3))/(5*a*e*(e*x)^(5/2))) - ((2*A*b - 5*a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(5*3^(1/4)*a^(4/3)*e^4*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [((e*x)^(7/2)*(A + B*x^3))/(a + b*x^3)^(3/2), x, 6, -(((2*A*b - 3*a*B)*e^2*(e*x)^(3/2))/(3*b^2*sqrt(a + b*x^3))) + (B*(e*x)^(9/2))/(3*b*e*sqrt(a + b*x^3)) + ((2*A*b - 3*a*B)*e^(7/2)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(3*b^(5/2))]
    @test_int [((e*x)^(5/2)*(A + B*x^3))/(a + b*x^3)^(3/2), x, 4, -(((4*A*b - 7*a*B)*e^2*sqrt(e*x))/(6*b^2*sqrt(a + b*x^3))) + (B*(e*x)^(7/2))/(2*b*e*sqrt(a + b*x^3)) + ((4*A*b - 7*a*B)*e^2*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(12*3^(1/4)*a^(1/3)*b^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((e*x)^(3/2)*(A + B*x^3))/(a + b*x^3)^(3/2), x, 5, (2*(A*b - a*B)*(e*x)^(5/2))/(3*a*b*e*sqrt(a + b*x^3)) - ((1 + sqrt(3))*(2*A*b - 5*a*B)*e*sqrt(e*x)*sqrt(a + b*x^3))/(3*a*b^(5/3)*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + ((2*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(3^(3/4)*a^(2/3)*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) + ((1 - sqrt(3))*(2*A*b - 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(6*3^(1/4)*a^(2/3)*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(e*x)*(A + B*x^3))/(a + b*x^3)^(3/2), x, 5, (2*(A*b - a*B)*(e*x)^(3/2))/(3*a*b*e*sqrt(a + b*x^3)) + (2*B*sqrt(e)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(3*b^(3/2))]
    @test_int [(A + B*x^3)/(sqrt(e*x)*(a + b*x^3)^(3/2)), x, 3, (2*(A*b - a*B)*sqrt(e*x))/(3*a*b*e*sqrt(a + b*x^3)) + ((2*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(3*3^(1/4)*a^(4/3)*b*e*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(3/2)), x, 6, -((2*A)/(a*e*sqrt(e*x)*sqrt(a + b*x^3))) - (2*(4*A*b - a*B)*(e*x)^(5/2))/(3*a^2*e^4*sqrt(a + b*x^3)) + (2*(1 + sqrt(3))*(4*A*b - a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(3*a^2*b^(2/3)*e^2*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) - (2*(4*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(3^(3/4)*a^(5/3)*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - ((1 - sqrt(3))*(4*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(3*3^(1/4)*a^(5/3)*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(3/2)), x, 2, (-2*A)/(3*a*e*(e*x)^(3/2)*sqrt(a + b*x^3)) - (2*(2*A*b - a*B)*(e*x)^(3/2))/(3*a^2*e^4*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(3/2)), x, 4, -((2*A)/(5*a*e*(e*x)^(5/2)*sqrt(a + b*x^3))) - (2*(8*A*b - 5*a*B)*sqrt(e*x))/(15*a^2*e^4*sqrt(a + b*x^3)) - (2*(8*A*b - 5*a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(15*3^(1/4)*a^(7/3)*e^4*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    @test_int [((e*x)^(7/2)*(A + B*x^3))/(a + b*x^3)^(5/2), x, 6, (2*(A*b - a*B)*(e*x)^(9/2))/(9*a*b*e*(a + b*x^3)^(3/2)) - (2*B*e^2*(e*x)^(3/2))/(3*b^2*sqrt(a + b*x^3)) + (2*B*e^(7/2)*atanh((sqrt(b)*(e*x)^(3/2))/(e^(3/2)*sqrt(a + b*x^3))))/(3*b^(5/2))]
    @test_int [((e*x)^(5/2)*(A + B*x^3))/(a + b*x^3)^(5/2), x, 4, (2*(A*b - a*B)*(e*x)^(7/2))/(9*a*b*e*(a + b*x^3)^(3/2)) - (2*(2*A*b + 7*a*B)*e^2*sqrt(e*x))/(27*a*b^2*sqrt(a + b*x^3)) + ((2*A*b + 7*a*B)*e^2*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(27*3^(1/4)*a^(4/3)*b^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [((e*x)^(3/2)*(A + B*x^3))/(a + b*x^3)^(5/2), x, 6, (2*(A*b - a*B)*(e*x)^(5/2))/(9*a*b*e*(a + b*x^3)^(3/2)) + (2*(4*A*b + 5*a*B)*(e*x)^(5/2))/(27*a^2*b*e*sqrt(a + b*x^3)) - (2*(1 + sqrt(3))*(4*A*b + 5*a*B)*e*sqrt(e*x)*sqrt(a + b*x^3))/(27*a^2*b^(5/3)*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) + (2*(4*A*b + 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(9*3^(3/4)*a^(5/3)*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) + ((1 - sqrt(3))*(4*A*b + 5*a*B)*e*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(27*3^(1/4)*a^(5/3)*b^(5/3)*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(sqrt(e*x)*(A + B*x^3))/(a + b*x^3)^(5/2), x, 2, (2*(A*b - a*B)*(e*x)^(3/2))/(9*a*b*e*(a + b*x^3)^(3/2)) + (2*(2*A*b + a*B)*(e*x)^(3/2))/(9*a^2*b*e*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/(sqrt(e*x)*(a + b*x^3)^(5/2)), x, 4, (2*(A*b - a*B)*sqrt(e*x))/(9*a*b*e*(a + b*x^3)^(3/2)) + (2*(8*A*b + a*B)*sqrt(e*x))/(27*a^2*b*e*sqrt(a + b*x^3)) + (2*(8*A*b + a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(27*3^(1/4)*a^(7/3)*b*e*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(5/2)), x, 7, -((2*A)/(a*e*sqrt(e*x)*(a + b*x^3)^(3/2))) - (2*(10*A*b - a*B)*(e*x)^(5/2))/(9*a^2*e^4*(a + b*x^3)^(3/2)) - (8*(10*A*b - a*B)*(e*x)^(5/2))/(27*a^3*e^4*sqrt(a + b*x^3)) + (8*(1 + sqrt(3))*(10*A*b - a*B)*sqrt(e*x)*sqrt(a + b*x^3))/(27*a^3*b^(2/3)*e^2*(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)) - (8*(10*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.E(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(9*3^(3/4)*a^(8/3)*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3)) - (4*(1 - sqrt(3))*(10*A*b - a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(27*3^(1/4)*a^(8/3)*b^(2/3)*e^2*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(5/2)), x, 3, -((2*A)/(3*a*e*(e*x)^(3/2)*(a + b*x^3)^(3/2))) - (2*(4*A*b - a*B)*(e*x)^(3/2))/(9*a^2*e^4*(a + b*x^3)^(3/2)) - (4*(4*A*b - a*B)*(e*x)^(3/2))/(9*a^3*e^4*sqrt(a + b*x^3))]
    @test_int [(A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(5/2)), x, 5, -((2*A)/(5*a*e*(e*x)^(5/2)*(a + b*x^3)^(3/2))) - (2*(14*A*b - 5*a*B)*sqrt(e*x))/(45*a^2*e^4*(a + b*x^3)^(3/2)) - (16*(14*A*b - 5*a*B)*sqrt(e*x))/(135*a^3*e^4*sqrt(a + b*x^3)) - (16*(14*A*b - 5*a*B)*sqrt(e*x)*(a^(1/3) + b^(1/3)*x)*sqrt((a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*Elliptic.F(acos((a^(1/3) + (1 - sqrt(3))*b^(1/3)*x)/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)), (1/4)*(2 + sqrt(3))))/(135*3^(1/4)*a^(10/3)*e^4*sqrt((b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + sqrt(3))*b^(1/3)*x)^2)*sqrt(a + b*x^3))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^3)^(p/3)*(c+d*x^3)^q=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^(p/3) / (c+d*x^3)*when*b*c+a*d=0=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^11*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 8, -((a^3*(a + b*x^3)^(1/3))/(b^4*d)) - (a^2*(a + b*x^3)^(4/3))/(4*b^4*d) + (a*(a + b*x^3)^(7/3))/(7*b^4*d) - (a + b*x^3)^(10/3)/(10*b^4*d) + (2^(1/3)*a^(10/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^4*d) + (a^(10/3)*log(a - b*x^3))/(3*2^(2/3)*b^4*d) - (a^(10/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(2/3)*b^4*d)]
    @test_int [x^8*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 8, -((a^2*(a + b*x^3)^(1/3))/(b^3*d)) - (a + b*x^3)^(7/3)/(7*b^3*d) + (2^(1/3)*a^(7/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^3*d) + (a^(7/3)*log(a - b*x^3))/(3*2^(2/3)*b^3*d) - (a^(7/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(2/3)*b^3*d)]
    @test_int [x^5*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 7, -((a*(a + b*x^3)^(1/3))/(b^2*d)) - (a + b*x^3)^(4/3)/(4*b^2*d) + (2^(1/3)*a^(4/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^2*d) + (a^(4/3)*log(a - b*x^3))/(3*2^(2/3)*b^2*d) - (a^(4/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(2/3)*b^2*d)]
    @test_int [x^2*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 6, -((a + b*x^3)^(1/3)/(b*d)) + (2^(1/3)*a^(1/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b*d) + (a^(1/3)*log(a - b*x^3))/(3*2^(2/3)*b*d) - (a^(1/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(2/3)*b*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^1*(a*d - b*d*x^3)), x, 10, -(atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(2/3)*d)) + (2^(1/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(2/3)*d) - log(x)/(2*a^(2/3)*d) + log(a - b*x^3)/(3*2^(2/3)*a^(2/3)*d) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(2/3)*d) - log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3))/(2^(2/3)*a^(2/3)*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^4*(a*d - b*d*x^3)), x, 13, (b*(a + b*x^3)^(1/3))/(3*a^2*d) - (a + b*x^3)^(4/3)/(3*a^2*d*x^3) - (4*b*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*d) + (2^(1/3)*b*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(5/3)*d) - (2*b*log(x))/(3*a^(5/3)*d) + (b*log(a - b*x^3))/(3*2^(2/3)*a^(5/3)*d) + (2*b*log(a^(1/3) - (a + b*x^3)^(1/3)))/(3*a^(5/3)*d) - (b*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(2/3)*a^(5/3)*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^7*(a*d - b*d*x^3)), x, 12, -((2*b*(a + b*x^3)^(1/3))/(9*a^2*d*x^3)) - (a + b*x^3)^(4/3)/(6*a^2*d*x^6) - (11*b^2*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(8/3)*d) + (2^(1/3)*b^2*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(8/3)*d) - (11*b^2*log(x))/(18*a^(8/3)*d) + (b^2*log(a - b*x^3))/(3*2^(2/3)*a^(8/3)*d) + (11*b^2*log(a^(1/3) - (a + b*x^3)^(1/3)))/(18*a^(8/3)*d) - (b^2*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(2/3)*a^(8/3)*d)]

    @test_int [x^7*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 6, -((7*a*x^2*(a + b*x^3)^(1/3))/(18*b^2*d)) - (x^5*(a + b*x^3)^(1/3))/(6*b*d) + (11*a^2*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(8/3)*d) - (2^(1/3)*a^2*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(8/3)*d) + (a^2*log(a*d - b*d*x^3))/(3*2^(2/3)*b^(8/3)*d) + (11*a^2*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(18*b^(8/3)*d) - (a^2*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(2/3)*b^(8/3)*d)]
    @test_int [x^4*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 5, -((x^2*(a + b*x^3)^(1/3))/(3*b*d)) + (4*a*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(5/3)*d) - (2^(1/3)*a*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(5/3)*d) + (a*log(a*d - b*d*x^3))/(3*2^(2/3)*b^(5/3)*d) + (2*a*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(3*b^(5/3)*d) - (a*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(2/3)*b^(5/3)*d)]
    @test_int [x^1*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 3, atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(2/3)*d) - (2^(1/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(2/3)*d) + log(a*d - b*d*x^3)/(3*2^(2/3)*b^(2/3)*d) + log(b^(1/3)*x - (a + b*x^3)^(1/3))/(2*b^(2/3)*d) - log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3))/(2^(2/3)*b^(2/3)*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^2*(a*d - b*d*x^3)), x, 3, -((a + b*x^3)^(1/3)/(a*d*x)) - (2^(1/3)*b^(1/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a*d) + (b^(1/3)*log(a*d - b*d*x^3))/(3*2^(2/3)*a*d) - (b^(1/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(2/3)*a*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^5*(a*d - b*d*x^3)), x, 4, -((a + b*x^3)^(1/3)/(4*a*d*x^4)) - (5*b*(a + b*x^3)^(1/3))/(4*a^2*d*x) - (2^(1/3)*b^(4/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^2*d) + (b^(4/3)*log(a*d - b*d*x^3))/(3*2^(2/3)*a^2*d) - (b^(4/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(2/3)*a^2*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^8*(a*d - b*d*x^3)), x, 5, -((a + b*x^3)^(1/3)/(7*a*d*x^7)) - (2*b*(a + b*x^3)^(1/3))/(7*a^2*d*x^4) - (8*b^2*(a + b*x^3)^(1/3))/(7*a^3*d*x) - (2^(1/3)*b^(7/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^3*d) + (b^(7/3)*log(a*d - b*d*x^3))/(3*2^(2/3)*a^3*d) - (b^(7/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(2/3)*a^3*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^11*(a*d - b*d*x^3)), x, 6, -((a + b*x^3)^(1/3)/(10*a*d*x^10)) - (11*b*(a + b*x^3)^(1/3))/(70*a^2*d*x^7) - (37*b^2*(a + b*x^3)^(1/3))/(140*a^3*d*x^4) - (169*b^3*(a + b*x^3)^(1/3))/(140*a^4*d*x) - (2^(1/3)*b^(10/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^4*d) + (b^(10/3)*log(a*d - b*d*x^3))/(3*2^(2/3)*a^4*d) - (b^(10/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(2/3)*a^4*d)]

    @test_int [x^6*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 22, -((3*a*x*(a + b*x^3)^(1/3))/(5*b^2*d)) - (x^4*(a + b*x^3)^(1/3))/(5*b*d) - (2^(1/3)*a^(5/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(7/3)*d) - (a^(5/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(2/3)*sqrt(3)*b^(7/3)*d) - (2*a^2*x*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, -((b*x^3)/a)))/(5*b^2*d*(a + b*x^3)^(2/3)) - (a^(5/3)*log(2^(2/3) - (a^(1/3) + b^(1/3)*x)/(a + b*x^3)^(1/3)))/(3*2^(2/3)*b^(7/3)*d) + (a^(5/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(2/3)*b^(7/3)*d) - (2^(1/3)*a^(5/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*b^(7/3)*d) + (a^(5/3)*log(2*2^(1/3) + (a^(1/3) + b^(1/3)*x)^2/(a + b*x^3)^(2/3) + (2^(2/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(6*2^(2/3)*b^(7/3)*d)]
    @test_int [x^3*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 21, -((x*(a + b*x^3)^(1/3))/(2*b*d)) - (2^(1/3)*a^(2/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(4/3)*d) - (a^(2/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(2/3)*sqrt(3)*b^(4/3)*d) - (a*x*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, -((b*x^3)/a)))/(2*b*d*(a + b*x^3)^(2/3)) - (a^(2/3)*log(2^(2/3) - (a^(1/3) + b^(1/3)*x)/(a + b*x^3)^(1/3)))/(3*2^(2/3)*b^(4/3)*d) + (a^(2/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(2/3)*b^(4/3)*d) - (2^(1/3)*a^(2/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*b^(4/3)*d) + (a^(2/3)*log(2*2^(1/3) + (a^(1/3) + b^(1/3)*x)^2/(a + b*x^3)^(2/3) + (2^(2/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(6*2^(2/3)*b^(4/3)*d)]
    @test_int [x^0*(a + b*x^3)^(1/3)/(a*d - b*d*x^3), x, 14, -((2^(1/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^(1/3)*b^(1/3)*d)) - atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)*a^(1/3)*b^(1/3)*d) - log(2^(2/3) - (a^(1/3) + b^(1/3)*x)/(a + b*x^3)^(1/3))/(3*2^(2/3)*a^(1/3)*b^(1/3)*d) + log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/(3*2^(2/3)*a^(1/3)*b^(1/3)*d) - (2^(1/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*a^(1/3)*b^(1/3)*d) + log(2*2^(1/3) + (a^(1/3) + b^(1/3)*x)^2/(a + b*x^3)^(2/3) + (2^(2/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/(6*2^(2/3)*a^(1/3)*b^(1/3)*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^3*(a*d - b*d*x^3)), x, 21, -((a + b*x^3)^(1/3)/(2*a*d*x^2)) - (2^(1/3)*b^(2/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^(4/3)*d) - (b^(2/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(2/3)*sqrt(3)*a^(4/3)*d) + (b*x*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, -((b*x^3)/a)))/(2*a*d*(a + b*x^3)^(2/3)) - (b^(2/3)*log(2^(2/3) - (a^(1/3) + b^(1/3)*x)/(a + b*x^3)^(1/3)))/(3*2^(2/3)*a^(4/3)*d) + (b^(2/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(2/3)*a^(4/3)*d) - (2^(1/3)*b^(2/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*a^(4/3)*d) + (b^(2/3)*log(2*2^(1/3) + (a^(1/3) + b^(1/3)*x)^2/(a + b*x^3)^(2/3) + (2^(2/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(6*2^(2/3)*a^(4/3)*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^6*(a*d - b*d*x^3)), x, 22, -((a + b*x^3)^(1/3)/(5*a*d*x^5)) - (3*b*(a + b*x^3)^(1/3))/(5*a^2*d*x^2) - (2^(1/3)*b^(5/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^(7/3)*d) - (b^(5/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(2/3)*sqrt(3)*a^(7/3)*d) + (2*b^2*x*(1 + (b*x^3)/a)^(2/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, -((b*x^3)/a)))/(5*a^2*d*(a + b*x^3)^(2/3)) - (b^(5/3)*log(2^(2/3) - (a^(1/3) + b^(1/3)*x)/(a + b*x^3)^(1/3)))/(3*2^(2/3)*a^(7/3)*d) + (b^(5/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(2/3)*a^(7/3)*d) - (2^(1/3)*b^(5/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*a^(7/3)*d) + (b^(5/3)*log(2*2^(1/3) + (a^(1/3) + b^(1/3)*x)^2/(a + b*x^3)^(2/3) + (2^(2/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(6*2^(2/3)*a^(7/3)*d)]

    @test_int [x^11*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 8, -((a^3*(a + b*x^3)^(2/3))/(2*b^4*d)) - (a^2*(a + b*x^3)^(5/3))/(5*b^4*d) + (a*(a + b*x^3)^(8/3))/(8*b^4*d) - (a + b*x^3)^(11/3)/(11*b^4*d) - (2^(2/3)*a^(11/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^4*d) + (a^(11/3)*log(a - b*x^3))/(3*2^(1/3)*b^4*d) - (a^(11/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(1/3)*b^4*d)]
    @test_int [x^8*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 8, -((a^2*(a + b*x^3)^(2/3))/(2*b^3*d)) - (a + b*x^3)^(8/3)/(8*b^3*d) - (2^(2/3)*a^(8/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^3*d) + (a^(8/3)*log(a - b*x^3))/(3*2^(1/3)*b^3*d) - (a^(8/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(1/3)*b^3*d)]
    @test_int [x^5*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 7, -((a*(a + b*x^3)^(2/3))/(2*b^2*d)) - (a + b*x^3)^(5/3)/(5*b^2*d) - (2^(2/3)*a^(5/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b^2*d) + (a^(5/3)*log(a - b*x^3))/(3*2^(1/3)*b^2*d) - (a^(5/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(1/3)*b^2*d)]
    @test_int [x^2*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 6, -((a + b*x^3)^(2/3)/(2*b*d)) - (2^(2/3)*a^(2/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*b*d) + (a^(2/3)*log(a - b*x^3))/(3*2^(1/3)*b*d) - (a^(2/3)*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(1/3)*b*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^1*(a*d - b*d*x^3)), x, 10, atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(1/3)*d) - (2^(2/3)*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(1/3)*d) - log(x)/(2*a^(1/3)*d) + log(a - b*x^3)/(3*2^(1/3)*a^(1/3)*d) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(1/3)*d) - log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3))/(2^(1/3)*a^(1/3)*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^4*(a*d - b*d*x^3)), x, 13, (b*(a + b*x^3)^(2/3))/(3*a^2*d) - (a + b*x^3)^(5/3)/(3*a^2*d*x^3) + (5*b*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*d) - (2^(2/3)*b*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(4/3)*d) - (5*b*log(x))/(6*a^(4/3)*d) + (b*log(a - b*x^3))/(3*2^(1/3)*a^(4/3)*d) + (5*b*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(4/3)*d) - (b*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(1/3)*a^(4/3)*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^7*(a*d - b*d*x^3)), x, 12, -((5*b*(a + b*x^3)^(2/3))/(18*a^2*d*x^3)) - (a + b*x^3)^(5/3)/(6*a^2*d*x^6) + (14*b^2*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(7/3)*d) - (2^(2/3)*b^2*atan((a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*a^(7/3)*d) - (7*b^2*log(x))/(9*a^(7/3)*d) + (b^2*log(a - b*x^3))/(3*2^(1/3)*a^(7/3)*d) + (7*b^2*log(a^(1/3) - (a + b*x^3)^(1/3)))/(9*a^(7/3)*d) - (b^2*log(2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)))/(2^(1/3)*a^(7/3)*d)]

    @test_int [x^6*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 5, -((4*a*x*(a + b*x^3)^(2/3))/(9*b^2*d)) - (x^4*(a + b*x^3)^(2/3))/(6*b*d) - (14*a^2*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(7/3)*d) + (2^(2/3)*a^2*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(7/3)*d) + (a^2*log(a*d - b*d*x^3))/(3*2^(1/3)*b^(7/3)*d) - (a^2*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(1/3)*b^(7/3)*d) + (7*a^2*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(9*b^(7/3)*d)]
    @test_int [x^3*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 4, -((x*(a + b*x^3)^(2/3))/(3*b*d)) - (5*a*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(4/3)*d) + (2^(2/3)*a*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(4/3)*d) + (a*log(a*d - b*d*x^3))/(3*2^(1/3)*b^(4/3)*d) - (a*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(1/3)*b^(4/3)*d) + (5*a*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(6*b^(4/3)*d)]
    @test_int [x^0*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 3, -(atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(1/3)*d)) + (2^(2/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(1/3)*d) + log(a*d - b*d*x^3)/(3*2^(1/3)*b^(1/3)*d) - log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3))/(2^(1/3)*b^(1/3)*d) + log((-b^(1/3))*x + (a + b*x^3)^(1/3))/(2*b^(1/3)*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^3*(a*d - b*d*x^3)), x, 3, -((a + b*x^3)^(2/3)/(2*a*d*x^2)) + (2^(2/3)*b^(2/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a*d) + (b^(2/3)*log(a*d - b*d*x^3))/(3*2^(1/3)*a*d) - (b^(2/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(1/3)*a*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^6*(a*d - b*d*x^3)), x, 4, -((a + b*x^3)^(2/3)/(5*a*d*x^5)) - (7*b*(a + b*x^3)^(2/3))/(10*a^2*d*x^2) + (2^(2/3)*b^(5/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^2*d) + (b^(5/3)*log(a*d - b*d*x^3))/(3*2^(1/3)*a^2*d) - (b^(5/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(1/3)*a^2*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^9*(a*d - b*d*x^3)), x, 5, -((a + b*x^3)^(2/3)/(8*a*d*x^8)) - (b*(a + b*x^3)^(2/3))/(4*a^2*d*x^5) - (5*b^2*(a + b*x^3)^(2/3))/(8*a^3*d*x^2) + (2^(2/3)*b^(8/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^3*d) + (b^(8/3)*log(a*d - b*d*x^3))/(3*2^(1/3)*a^3*d) - (b^(8/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(1/3)*a^3*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^12*(a*d - b*d*x^3)), x, 6, -((a + b*x^3)^(2/3)/(11*a*d*x^11)) - (13*b*(a + b*x^3)^(2/3))/(88*a^2*d*x^8) - (49*b^2*(a + b*x^3)^(2/3))/(220*a^3*d*x^5) - (293*b^3*(a + b*x^3)^(2/3))/(440*a^4*d*x^2) + (2^(2/3)*b^(11/3)*atan((1 + (2*2^(1/3)*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^4*d) + (b^(11/3)*log(a*d - b*d*x^3))/(3*2^(1/3)*a^4*d) - (b^(11/3)*log(2^(1/3)*b^(1/3)*x - (a + b*x^3)^(1/3)))/(2^(1/3)*a^4*d)]

    @test_int [x^7*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 14, -((9*a*x^2*(a + b*x^3)^(2/3))/(28*b^2*d)) - (x^5*(a + b*x^3)^(2/3))/(7*b*d) + (2^(2/3)*a^(7/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(8/3)*d) + (a^(7/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(1/3)*sqrt(3)*b^(8/3)*d) - (19*a^2*x^2*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, -((b*x^3)/a)))/(28*b^2*d*(a + b*x^3)^(1/3)) + (a^(7/3)*log(((a^(1/3) - b^(1/3)*x)^2*(a^(1/3) + b^(1/3)*x))/a))/(6*2^(1/3)*b^(8/3)*d) + (a^(7/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(1/3)*b^(8/3)*d) - (2^(2/3)*a^(7/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*b^(8/3)*d) - (a^(7/3)*log((b^(1/3)*(a^(1/3) + b^(1/3)*x))/a^(1/3) - (2^(2/3)*b^(1/3)*(a + b*x^3)^(1/3))/a^(1/3)))/(2*2^(1/3)*b^(8/3)*d)]
    @test_int [x^4*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 13, -((x^2*(a + b*x^3)^(2/3))/(4*b*d)) + (2^(2/3)*a^(4/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(5/3)*d) + (a^(4/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(1/3)*sqrt(3)*b^(5/3)*d) - (3*a*x^2*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, -((b*x^3)/a)))/(4*b*d*(a + b*x^3)^(1/3)) + (a^(4/3)*log(((a^(1/3) - b^(1/3)*x)^2*(a^(1/3) + b^(1/3)*x))/a))/(6*2^(1/3)*b^(5/3)*d) + (a^(4/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(1/3)*b^(5/3)*d) - (2^(2/3)*a^(4/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*b^(5/3)*d) - (a^(4/3)*log((b^(1/3)*(a^(1/3) + b^(1/3)*x))/a^(1/3) - (2^(2/3)*b^(1/3)*(a + b*x^3)^(1/3))/a^(1/3)))/(2*2^(1/3)*b^(5/3)*d)]
    @test_int [x^1*(a + b*x^3)^(2/3)/(a*d - b*d*x^3), x, 11, (2^(2/3)*a^(1/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*b^(2/3)*d) + (a^(1/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(1/3)*sqrt(3)*b^(2/3)*d) - (x^2*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, -((b*x^3)/a)))/(2*d*(a + b*x^3)^(1/3)) + (a^(1/3)*log(((a^(1/3) - b^(1/3)*x)^2*(a^(1/3) + b^(1/3)*x))/a))/(6*2^(1/3)*b^(2/3)*d) + (a^(1/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(1/3)*b^(2/3)*d) - (2^(2/3)*a^(1/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*b^(2/3)*d) - (a^(1/3)*log((b^(1/3)*(a^(1/3) + b^(1/3)*x))/a^(1/3) - (2^(2/3)*b^(1/3)*(a + b*x^3)^(1/3))/a^(1/3)))/(2*2^(1/3)*b^(2/3)*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^2*(a*d - b*d*x^3)), x, 13, -((a + b*x^3)^(2/3)/(a*d*x)) + (2^(2/3)*b^(1/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^(2/3)*d) + (b^(1/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(1/3)*sqrt(3)*a^(2/3)*d) + (b*x^2*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, -((b*x^3)/a)))/(2*a*d*(a + b*x^3)^(1/3)) + (b^(1/3)*log(((a^(1/3) - b^(1/3)*x)^2*(a^(1/3) + b^(1/3)*x))/a))/(6*2^(1/3)*a^(2/3)*d) + (b^(1/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(1/3)*a^(2/3)*d) - (2^(2/3)*b^(1/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*a^(2/3)*d) - (b^(1/3)*log((b^(1/3)*(a^(1/3) + b^(1/3)*x))/a^(1/3) - (2^(2/3)*b^(1/3)*(a + b*x^3)^(1/3))/a^(1/3)))/(2*2^(1/3)*a^(2/3)*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^5*(a*d - b*d*x^3)), x, 14, -((a + b*x^3)^(2/3)/(4*a*d*x^4)) - (3*b*(a + b*x^3)^(2/3))/(2*a^2*d*x) + (2^(2/3)*b^(4/3)*atan((1 - (2*2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*a^(5/3)*d) + (b^(4/3)*atan((1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3))/sqrt(3)))/(2^(1/3)*sqrt(3)*a^(5/3)*d) + (3*b^2*x^2*(1 + (b*x^3)/a)^(1/3)*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, -((b*x^3)/a)))/(4*a^2*d*(a + b*x^3)^(1/3)) + (b^(4/3)*log(((a^(1/3) - b^(1/3)*x)^2*(a^(1/3) + b^(1/3)*x))/a))/(6*2^(1/3)*a^(5/3)*d) + (b^(4/3)*log(1 + (2^(2/3)*(a^(1/3) + b^(1/3)*x)^2)/(a + b*x^3)^(2/3) - (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*2^(1/3)*a^(5/3)*d) - (2^(2/3)*b^(4/3)*log(1 + (2^(1/3)*(a^(1/3) + b^(1/3)*x))/(a + b*x^3)^(1/3)))/(3*a^(5/3)*d) - (b^(4/3)*log((b^(1/3)*(a^(1/3) + b^(1/3)*x))/a^(1/3) - (2^(2/3)*b^(1/3)*(a + b*x^3)^(1/3))/a^(1/3)))/(2*2^(1/3)*a^(5/3)*d)]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^14/((1 - x^3)^(1/3)*(1 + x^3)), x, 7, (2/5)*(1 - x^3)^(5/3) - (1/4)*(1 - x^3)^(8/3) + (1/11)*(1 - x^3)^(11/3) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - log(1 + x^3)/(6*2^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [x^11/((1 - x^3)^(1/3)*(1 + x^3)), x, 7, (-(1/2))*(1 - x^3)^(2/3) + (1/5)*(1 - x^3)^(5/3) - (1/8)*(1 - x^3)^(8/3) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + log(1 + x^3)/(6*2^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [x^8/((1 - x^3)^(1/3)*(1 + x^3)), x, 7, (1/5)*(1 - x^3)^(5/3) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - log(1 + x^3)/(6*2^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [x^5/((1 - x^3)^(1/3)*(1 + x^3)), x, 6, (-(1/2))*(1 - x^3)^(2/3) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + log(1 + x^3)/(6*2^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [x^2/((1 - x^3)^(1/3)*(1 + x^3)), x, 5, atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - log(1 + x^3)/(6*2^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [1/(x^1*(1 - x^3)^(1/3)*(1 + x^3)), x, 10, atan((1 + 2*(1 - x^3)^(1/3))/sqrt(3))/sqrt(3) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - log(x)/2 + log(1 + x^3)/(6*2^(1/3)) + (1/2)*log(1 - (1 - x^3)^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [1/(x^4*(1 - x^3)^(1/3)*(1 + x^3)), x, 11, -((1 - x^3)^(2/3)/(3*x^3)) - (2*atan((1 + 2*(1 - x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + log(x)/3 - log(1 + x^3)/(6*2^(1/3)) - (1/3)*log(1 - (1 - x^3)^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(1/3))]

    @test_int [x^6/((1 - x^3)^(1/3)*(1 + x^3)), x, 4, (-(1/3))*x*(1 - x^3)^(2/3) + (2*atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - log(1 + x^3)/(6*2^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(1/3)) - (1/3)*log(x + (1 - x^3)^(1/3))]
    @test_int [x^3/((1 - x^3)^(1/3)*(1 + x^3)), x, 3, -(atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3))/sqrt(3)) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + log(1 + x^3)/(6*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(1/3)) + (1/2)*log(x + (1 - x^3)^(1/3))]
    @test_int [x^0/((1 - x^3)^(1/3)*(1 + x^3)), x, 1, -(atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))) - log(1 + x^3)/(6*2^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [1/(x^3*(1 - x^3)^(1/3)*(1 + x^3)), x, 3, -((1 - x^3)^(2/3)/(2*x^2)) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + log(1 + x^3)/(6*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [1/(x^6*(1 - x^3)^(1/3)*(1 + x^3)), x, 4, -((1 - x^3)^(2/3)/(5*x^5)) + (1 - x^3)^(2/3)/(5*x^2) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - log(1 + x^3)/(6*2^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(1/3))]
    @test_int [1/(x^9*(1 - x^3)^(1/3)*(1 + x^3)), x, 5, -((1 - x^3)^(2/3)/(8*x^8)) + (1 - x^3)^(2/3)/(20*x^5) - (17*(1 - x^3)^(2/3))/(40*x^2) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + log(1 + x^3)/(6*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(1/3))]

    @test_int [x^7/((1 - x^3)^(1/3)*(1 + x^3)), x, 12, (-(1/4))*x^2*(1 - x^3)^(2/3) + atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - (1/4)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) + log((1 - x)*(1 + x)^2)/(12*2^(1/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(1/3)) - log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^4/((1 - x^3)^(1/3)*(1 + x^3)), x, 10, -(atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3))) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + (1/2)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) - log((1 - x)*(1 + x)^2)/(12*2^(1/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(1/3)) + log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^1/((1 - x^3)^(1/3)*(1 + x^3)), x, 8, atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log((1 - x)*(1 + x)^2)/(12*2^(1/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(1/3)) - log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^2*(1 - x^3)^(1/3)*(1 + x^3)), x, 12, -((1 - x^3)^(2/3)/x) - atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - (1/2)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) - log((1 - x)*(1 + x)^2)/(12*2^(1/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(1/3)) + log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^5*(1 - x^3)^(1/3)*(1 + x^3)), x, 14, -((1 - x^3)^(2/3)/(4*x^4)) + (1 - x^3)^(2/3)/(2*x) + atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(1/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + (1/4)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) + log((1 - x)*(1 + x)^2)/(12*2^(1/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(1/3)) - log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(4*2^(1/3))]

    @test_int [x^11/((1 - x^3)^(2/3)*(1 + x^3)), x, 7, -(1 - x^3)^(1/3) + (1/4)*(1 - x^3)^(4/3) - (1/7)*(1 - x^3)^(7/3) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + log(1 + x^3)/(6*2^(2/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [x^8/((1 - x^3)^(2/3)*(1 + x^3)), x, 7, (1/4)*(1 - x^3)^(4/3) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) - log(1 + x^3)/(6*2^(2/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [x^5/((1 - x^3)^(2/3)*(1 + x^3)), x, 6, -(1 - x^3)^(1/3) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + log(1 + x^3)/(6*2^(2/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [x^2/((1 - x^3)^(2/3)*(1 + x^3)), x, 5, -(atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))) - log(1 + x^3)/(6*2^(2/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [1/(x^1*(1 - x^3)^(2/3)*(1 + x^3)), x, 10, -(atan((1 + 2*(1 - x^3)^(1/3))/sqrt(3))/sqrt(3)) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) - log(x)/2 + log(1 + x^3)/(6*2^(2/3)) + (1/2)*log(1 - (1 - x^3)^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [1/(x^4*(1 - x^3)^(2/3)*(1 + x^3)), x, 11, -((1 - x^3)^(1/3)/(3*x^3)) + atan((1 + 2*(1 - x^3)^(1/3))/sqrt(3))/(3*sqrt(3)) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + log(x)/6 - log(1 + x^3)/(6*2^(2/3)) - (1/6)*log(1 - (1 - x^3)^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(2*2^(2/3))]

    @test_int [x^7/((1 - x^3)^(2/3)*(1 + x^3)), x, 5, (-(1/3))*x^2*(1 - x^3)^(1/3) + atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3))/(3*sqrt(3)) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + log(1 + x^3)/(6*2^(2/3)) + (1/6)*log(-x - (1 - x^3)^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [x^4/((1 - x^3)^(2/3)*(1 + x^3)), x, 3, -(atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3))/sqrt(3)) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) - log(1 + x^3)/(6*2^(2/3)) - (1/2)*log(-x - (1 - x^3)^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [x^1/((1 - x^3)^(2/3)*(1 + x^3)), x, 1, -(atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))) + log(1 + x^3)/(6*2^(2/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [1/(x^2*(1 - x^3)^(2/3)*(1 + x^3)), x, 2, -((1 - x^3)^(1/3)/x) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) - log(1 + x^3)/(6*2^(2/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(2/3))]
    @test_int [1/(x^5*(1 - x^3)^(2/3)*(1 + x^3)), x, 4, -((1 - x^3)^(1/3)/(4*x^4)) + (1 - x^3)^(1/3)/(4*x) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + log(1 + x^3)/(6*2^(2/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(2*2^(2/3))]

    @test_int [x^6/((1 - x^3)^(2/3)*(1 + x^3)), x, 15, (-(1/2))*x*(1 - x^3)^(1/3) + atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(2/3)*sqrt(3)) + log(2^(2/3) - (1 - x)/(1 - x^3)^(1/3))/(6*2^(2/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(2/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(2/3)) - log(2*2^(1/3) + (1 - x)^2/(1 - x^3)^(2/3) + (2^(2/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(2/3))]
    @test_int [x^3/((1 - x^3)^(2/3)*(1 + x^3)), x, 18, -(atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3))) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(2/3)*sqrt(3)) + (1/2)*x*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, x^3) - log(2^(2/3) - (1 - x)/(1 - x^3)^(1/3))/(6*2^(2/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(2/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(2/3)) + log(2*2^(1/3) + (1 - x)^2/(1 - x^3)^(2/3) + (2^(2/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(2/3))]
    @test_int [x^0/((1 - x^3)^(2/3)*(1 + x^3)), x, 16, atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(2/3)*sqrt(3)) + (1/2)*x*HypergeometricFunctions._₂F₁(1/3, 2/3, 4/3, x^3) + log(2^(2/3) - (1 - x)/(1 - x^3)^(1/3))/(6*2^(2/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(2/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(2/3)) - log(2*2^(1/3) + (1 - x)^2/(1 - x^3)^(2/3) + (2^(2/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(2/3))]
    @test_int [1/(x^3*(1 - x^3)^(2/3)*(1 + x^3)), x, 16, -((1 - x^3)^(1/3)/(2*x^2)) - atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2^(2/3)*sqrt(3)) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(2/3)*sqrt(3)) - log(2^(2/3) - (1 - x)/(1 - x^3)^(1/3))/(6*2^(2/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(2/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(3*2^(2/3)) + log(2*2^(1/3) + (1 - x)^2/(1 - x^3)^(2/3) + (2^(2/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(2/3))]

    @test_int [x^14/((1 - x^3)^(4/3)*(1 + x^3)), x, 11, 1/(2*(1 - x^3)^(1/3)) + (1 - x^3)^(2/3) - (2/5)*(1 - x^3)^(5/3) + (1/8)*(1 - x^3)^(8/3) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(1 + x^3)/(12*2^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^11/((1 - x^3)^(4/3)*(1 + x^3)), x, 11, 1/(2*(1 - x^3)^(1/3)) + (1/2)*(1 - x^3)^(2/3) - (1/5)*(1 - x^3)^(5/3) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log(1 + x^3)/(12*2^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^8/((1 - x^3)^(4/3)*(1 + x^3)), x, 9, 1/(2*(1 - x^3)^(1/3)) + (1/2)*(1 - x^3)^(2/3) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(1 + x^3)/(12*2^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^5/((1 - x^3)^(4/3)*(1 + x^3)), x, 6, 1/(2*(1 - x^3)^(1/3)) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log(1 + x^3)/(12*2^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^2/((1 - x^3)^(4/3)*(1 + x^3)), x, 6, 1/(2*(1 - x^3)^(1/3)) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(1 + x^3)/(12*2^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^1*(1 - x^3)^(4/3)*(1 + x^3)), x, 11, 1/(2*(1 - x^3)^(1/3)) + atan((1 + 2*(1 - x^3)^(1/3))/sqrt(3))/sqrt(3) - atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(x)/2 + log(1 + x^3)/(12*2^(1/3)) + (1/2)*log(1 - (1 - x^3)^(1/3)) - log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^4*(1 - x^3)^(4/3)*(1 + x^3)), x, 13, 5/(6*(1 - x^3)^(1/3)) - 1/(3*x^3*(1 - x^3)^(1/3)) + atan((1 + 2*(1 - x^3)^(1/3))/sqrt(3))/(3*sqrt(3)) + atan((1 + 2^(2/3)*(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(x)/6 - log(1 + x^3)/(12*2^(1/3)) + (1/6)*log(1 - (1 - x^3)^(1/3)) + log(2^(1/3) - (1 - x^3)^(1/3))/(4*2^(1/3))]

    @test_int [x^9/((1 - x^3)^(4/3)*(1 + x^3)), x, 5, x^4/(2*(1 - x^3)^(1/3)) + (5/6)*x*(1 - x^3)^(2/3) + atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3))/(3*sqrt(3)) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log(1 + x^3)/(12*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3)) - (1/6)*log(x + (1 - x^3)^(1/3))]
    @test_int [x^6/((1 - x^3)^(4/3)*(1 + x^3)), x, 4, x/(2*(1 - x^3)^(1/3)) + atan((1 - (2*x)/(1 - x^3)^(1/3))/sqrt(3))/sqrt(3) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(1 + x^3)/(12*2^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3)) - (1/2)*log(x + (1 - x^3)^(1/3))]
    @test_int [x^3/((1 - x^3)^(4/3)*(1 + x^3)), x, 2, x/(2*(1 - x^3)^(1/3)) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log(1 + x^3)/(12*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [x^0/((1 - x^3)^(4/3)*(1 + x^3)), x, 2, x/(2*(1 - x^3)^(1/3)) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(1 + x^3)/(12*2^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^3*(1 - x^3)^(4/3)*(1 + x^3)), x, 4, 1/(2*x^2*(1 - x^3)^(1/3)) - (1 - x^3)^(2/3)/x^2 + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log(1 + x^3)/(12*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^6*(1 - x^3)^(4/3)*(1 + x^3)), x, 5, 1/(2*x^5*(1 - x^3)^(1/3)) - (7*(1 - x^3)^(2/3))/(10*x^5) - (4*(1 - x^3)^(2/3))/(5*x^2) - atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - log(1 + x^3)/(12*2^(1/3)) + log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3))]
    @test_int [1/(x^9*(1 - x^3)^(4/3)*(1 + x^3)), x, 6, 1/(2*x^8*(1 - x^3)^(1/3)) - (5*(1 - x^3)^(2/3))/(8*x^8) - (13*(1 - x^3)^(2/3))/(20*x^5) - (49*(1 - x^3)^(2/3))/(40*x^2) + atan((1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + log(1 + x^3)/(12*2^(1/3)) - log((-2^(1/3))*x - (1 - x^3)^(1/3))/(4*2^(1/3))]

    @test_int [x^10/((1 - x^3)^(4/3)*(1 + x^3)), x, 13, x^5/(2*(1 - x^3)^(1/3)) + (3/4)*x^2*(1 - x^3)^(2/3) - atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(4*2^(1/3)*sqrt(3)) - (1/2)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) - log((1 - x)*(1 + x)^2)/(24*2^(1/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(1/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) + log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(8*2^(1/3))]
    @test_int [x^7/((1 - x^3)^(4/3)*(1 + x^3)), x, 12, x^2/(2*(1 - x^3)^(1/3)) + atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(4*2^(1/3)*sqrt(3)) - (3/4)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) + log((1 - x)*(1 + x)^2)/(24*2^(1/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(1/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) - log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(8*2^(1/3))]
    @test_int [x^4/((1 - x^3)^(4/3)*(1 + x^3)), x, 12, x^2/(2*(1 - x^3)^(1/3)) - atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(4*2^(1/3)*sqrt(3)) - (1/4)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) - log((1 - x)*(1 + x)^2)/(24*2^(1/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(1/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) + log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(8*2^(1/3))]
    @test_int [x^1/((1 - x^3)^(4/3)*(1 + x^3)), x, 11, x^2/(2*(1 - x^3)^(1/3)) + atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(4*2^(1/3)*sqrt(3)) - (1/4)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) + log((1 - x)*(1 + x)^2)/(24*2^(1/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(1/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) - log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(8*2^(1/3))]
    @test_int [1/(x^2*(1 - x^3)^(4/3)*(1 + x^3)), x, 13, 1/(2*x*(1 - x^3)^(1/3)) - (3*(1 - x^3)^(2/3))/(2*x) - atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) - atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(4*2^(1/3)*sqrt(3)) - (3/4)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) - log((1 - x)*(1 + x)^2)/(24*2^(1/3)) - log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(1/3)) + log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) + log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(8*2^(1/3))]
    @test_int [1/(x^5*(1 - x^3)^(4/3)*(1 + x^3)), x, 14, 1/(2*x^4*(1 - x^3)^(1/3)) - (3*(1 - x^3)^(2/3))/(4*x^4) - (1 - x^3)^(2/3)/x + atan((1 - (2*2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(2*2^(1/3)*sqrt(3)) + atan((1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/sqrt(3))/(4*2^(1/3)*sqrt(3)) - (1/2)*x^2*HypergeometricFunctions._₂F₁(1/3, 2/3, 5/3, x^3) + log((1 - x)*(1 + x)^2)/(24*2^(1/3)) + log(1 + (2^(2/3)*(1 - x)^2)/(1 - x^3)^(2/3) - (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(12*2^(1/3)) - log(1 + (2^(1/3)*(1 - x))/(1 - x^3)^(1/3))/(6*2^(1/3)) - log(-1 + x + 2^(2/3)*(1 - x^3)^(1/3))/(8*2^(1/3))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^3)^(p/3) / (c+d*x^3)=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^11*(a + b*x^3)^(1/3)/(c + d*x^3), x, 8, -((c^3*(a + b*x^3)^(1/3))/d^4) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(4/3))/(4*b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(7/3))/(7*b^3*d^2) + (a + b*x^3)^(10/3)/(10*b^3*d) - (c^3*(b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(13/3)) - (c^3*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*d^(13/3)) + (c^3*(b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(13/3))]
    @test_int [x^8*(a + b*x^3)^(1/3)/(c + d*x^3), x, 8, (c^2*(a + b*x^3)^(1/3))/d^3 - ((b*c + a*d)*(a + b*x^3)^(4/3))/(4*b^2*d^2) + (a + b*x^3)^(7/3)/(7*b^2*d) + (c^2*(b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(10/3)) + (c^2*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*d^(10/3)) - (c^2*(b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(10/3))]
    @test_int [x^5*(a + b*x^3)^(1/3)/(c + d*x^3), x, 7, -((c*(a + b*x^3)^(1/3))/d^2) + (a + b*x^3)^(4/3)/(4*b*d) - (c*(b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(7/3)) - (c*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*d^(7/3)) + (c*(b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(7/3))]
    @test_int [x^2*(a + b*x^3)^(1/3)/(c + d*x^3), x, 6, (a + b*x^3)^(1/3)/d + ((b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(4/3)) + ((b*c - a*d)^(1/3)*log(c + d*x^3))/(6*d^(4/3)) - ((b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(4/3))]
    @test_int [(a + b*x^3)^(1/3)/(x^1*(c + d*x^3)), x, 10, -((a^(1/3)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*c)) - ((b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c*d^(1/3)) - (a^(1/3)*log(x))/(2*c) - ((b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c*d^(1/3)) + (a^(1/3)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(2*c) + ((b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c*d^(1/3))]
    @test_int [(a + b*x^3)^(1/3)/(x^4*(c + d*x^3)), x, 13, (d*(a + b*x^3)^(1/3))/c^2 + ((b*c - 3*a*d)*(a + b*x^3)^(1/3))/(3*a*c^2) - (a + b*x^3)^(4/3)/(3*a*c*x^3) - ((b*c - 3*a*d)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(2/3)*c^2) + (d^(2/3)*(b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^2) - ((b*c - 3*a*d)*log(x))/(6*a^(2/3)*c^2) + (d^(2/3)*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^2) + ((b*c - 3*a*d)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(2/3)*c^2) - (d^(2/3)*(b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^2)]
    @test_int [(a + b*x^3)^(1/3)/(x^7*(c + d*x^3)), x, 12, ((b*c + 3*a*d)*(a + b*x^3)^(1/3))/(9*a*c^2*x^3) - (a + b*x^3)^(4/3)/(6*a*c*x^6) + ((b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(5/3)*c^3) - (d^(5/3)*(b*c - a*d)^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^3) + ((b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*log(x))/(18*a^(5/3)*c^3) - (d^(5/3)*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^3) - ((b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(18*a^(5/3)*c^3) + (d^(5/3)*(b*c - a*d)^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^3)]

    @test_int [x^7*(a + b*x^3)^(1/3)/(c + d*x^3), x, 6, -(((6*b*c - a*d)*x^2*(a + b*x^3)^(1/3))/(18*b*d^2)) + (x^5*(a + b*x^3)^(1/3))/(6*d) - ((9*b^2*c^2 - 3*a*b*c*d - a^2*d^2)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(5/3)*d^3) + (c^(5/3)*(b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^3) - (c^(5/3)*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*d^3) - ((9*b^2*c^2 - 3*a*b*c*d - a^2*d^2)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(18*b^(5/3)*d^3) + (c^(5/3)*(b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^3)]
    @test_int [x^4*(a + b*x^3)^(1/3)/(c + d*x^3), x, 5, (x^2*(a + b*x^3)^(1/3))/(3*d) + ((3*b*c - a*d)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(2/3)*d^2) - (c^(2/3)*(b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^2) + (c^(2/3)*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*d^2) + ((3*b*c - a*d)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(6*b^(2/3)*d^2) - (c^(2/3)*(b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^2)]
    @test_int [x^1*(a + b*x^3)^(1/3)/(c + d*x^3), x, 3, -((b^(1/3)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*d)) + ((b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(1/3)*d) - ((b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^(1/3)*d) - (b^(1/3)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(2*d) + ((b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(1/3)*d)]
    @test_int [(a + b*x^3)^(1/3)/(x^2*(c + d*x^3)), x, 3, -((a + b*x^3)^(1/3)/(c*x)) - ((b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(4/3)) + ((b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^(4/3)) - ((b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(4/3))]
    @test_int [(a + b*x^3)^(1/3)/(x^5*(c + d*x^3)), x, 4, -((a + b*x^3)^(1/3)/(4*c*x^4)) - ((b*c - 4*a*d)*(a + b*x^3)^(1/3))/(4*a*c^2*x) + (d*(b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(7/3)) - (d*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^(7/3)) + (d*(b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(7/3))]
    @test_int [(a + b*x^3)^(1/3)/(x^8*(c + d*x^3)), x, 5, -((a + b*x^3)^(1/3)/(7*c*x^7)) - ((b*c - 7*a*d)*(a + b*x^3)^(1/3))/(28*a*c^2*x^4) + ((3*b^2*c^2 + 7*a*b*c*d - 28*a^2*d^2)*(a + b*x^3)^(1/3))/(28*a^2*c^3*x) - (d^2*(b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(10/3)) + (d^2*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^(10/3)) - (d^2*(b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(10/3))]
    @test_int [(a + b*x^3)^(1/3)/(x^11*(c + d*x^3)), x, 6, -((a + b*x^3)^(1/3)/(10*c*x^10)) - ((b*c - 10*a*d)*(a + b*x^3)^(1/3))/(70*a*c^2*x^7) + ((3*b^2*c^2 + 5*a*b*c*d - 35*a^2*d^2)*(a + b*x^3)^(1/3))/(140*a^2*c^3*x^4) - ((9*b^3*c^3 + 15*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 140*a^3*d^3)*(a + b*x^3)^(1/3))/(140*a^3*c^4*x) + (d^3*(b*c - a*d)^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(13/3)) - (d^3*(b*c - a*d)^(1/3)*log(c + d*x^3))/(6*c^(13/3)) + (d^3*(b*c - a*d)^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(13/3))]

    @test_int [x^6*(a + b*x^3)^(1/3)/(c + d*x^3), x, 2, (x^7*(a + b*x^3)^(1/3)*AppellF1(7/3, -(1/3), 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)))/(7*c*(1 + (b*x^3)/a)^(1/3))]
    @test_int [x^3*(a + b*x^3)^(1/3)/(c + d*x^3), x, 2, (x^4*(a + b*x^3)^(1/3)*AppellF1(4/3, -(1/3), 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*c*(1 + (b*x^3)/a)^(1/3))]
    @test_int [x^0*(a + b*x^3)^(1/3)/(c + d*x^3), x, 2, (x*(a + b*x^3)^(1/3)*AppellF1(1/3, -(1/3), 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(c*(1 + (b*x^3)/a)^(1/3))]
    @test_int [(a + b*x^3)^(1/3)/(x^3*(c + d*x^3)), x, 2, -(((a + b*x^3)^(1/3)*AppellF1(-(2/3), -(1/3), 1, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*c*x^2*(1 + (b*x^3)/a)^(1/3)))]
    @test_int [(a + b*x^3)^(1/3)/(x^6*(c + d*x^3)), x, 2, -(((a + b*x^3)^(1/3)*AppellF1(-(5/3), -(1/3), 1, -(2/3), -((b*x^3)/a), -((d*x^3)/c)))/(5*c*x^5*(1 + (b*x^3)/a)^(1/3)))]

    @test_int [x^11*(a + b*x^3)^(2/3)/(c + d*x^3), x, 8, -((c^3*(a + b*x^3)^(2/3))/(2*d^4)) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(5/3))/(5*b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(8/3))/(8*b^3*d^2) + (a + b*x^3)^(11/3)/(11*b^3*d) - (c^3*(b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(14/3)) + (c^3*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*d^(14/3)) - (c^3*(b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(14/3))]
    @test_int [x^8*(a + b*x^3)^(2/3)/(c + d*x^3), x, 8, (c^2*(a + b*x^3)^(2/3))/(2*d^3) - ((b*c + a*d)*(a + b*x^3)^(5/3))/(5*b^2*d^2) + (a + b*x^3)^(8/3)/(8*b^2*d) + (c^2*(b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(11/3)) - (c^2*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*d^(11/3)) + (c^2*(b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(11/3))]
    @test_int [x^5*(a + b*x^3)^(2/3)/(c + d*x^3), x, 7, -((c*(a + b*x^3)^(2/3))/(2*d^2)) + (a + b*x^3)^(5/3)/(5*b*d) - (c*(b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(8/3)) + (c*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*d^(8/3)) - (c*(b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(8/3))]
    @test_int [x^2*(a + b*x^3)^(2/3)/(c + d*x^3), x, 6, (a + b*x^3)^(2/3)/(2*d) + ((b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(5/3)) - ((b*c - a*d)^(2/3)*log(c + d*x^3))/(6*d^(5/3)) + ((b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(5/3))]
    @test_int [(a + b*x^3)^(2/3)/(x^1*(c + d*x^3)), x, 10, (a^(2/3)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*c) - ((b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c*d^(2/3)) - (a^(2/3)*log(x))/(2*c) + ((b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c*d^(2/3)) + (a^(2/3)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(2*c) - ((b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c*d^(2/3))]
    @test_int [(a + b*x^3)^(2/3)/(x^4*(c + d*x^3)), x, 13, (d*(a + b*x^3)^(2/3))/(2*c^2) + ((2*b*c - 3*a*d)*(a + b*x^3)^(2/3))/(6*a*c^2) - (a + b*x^3)^(5/3)/(3*a*c*x^3) + ((2*b*c - 3*a*d)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(1/3)*c^2) + (d^(1/3)*(b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^2) - ((2*b*c - 3*a*d)*log(x))/(6*a^(1/3)*c^2) - (d^(1/3)*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^2) + ((2*b*c - 3*a*d)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(1/3)*c^2) + (d^(1/3)*(b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^2)]
    @test_int [(a + b*x^3)^(2/3)/(x^7*(c + d*x^3)), x, 12, ((b*c + 6*a*d)*(a + b*x^3)^(2/3))/(18*a*c^2*x^3) - (a + b*x^3)^(5/3)/(6*a*c*x^6) - ((b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(4/3)*c^3) - (d^(4/3)*(b*c - a*d)^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^3) + ((b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*log(x))/(18*a^(4/3)*c^3) + (d^(4/3)*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^3) - ((b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(18*a^(4/3)*c^3) - (d^(4/3)*(b*c - a*d)^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^3)]

    @test_int [x^6*(a + b*x^3)^(2/3)/(c + d*x^3), x, 5, -(((3*b*c - a*d)*x*(a + b*x^3)^(2/3))/(9*b*d^2)) + (x^4*(a + b*x^3)^(2/3))/(6*d) + ((9*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(4/3)*d^3) - (c^(4/3)*(b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^3) - (c^(4/3)*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*d^3) + (c^(4/3)*(b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^3) - ((9*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(18*b^(4/3)*d^3)]
    @test_int [x^3*(a + b*x^3)^(2/3)/(c + d*x^3), x, 4, (x*(a + b*x^3)^(2/3))/(3*d) - ((3*b*c - 2*a*d)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(1/3)*d^2) + (c^(1/3)*(b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^2) + (c^(1/3)*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*d^2) - (c^(1/3)*(b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^2) + ((3*b*c - 2*a*d)*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(6*b^(1/3)*d^2)]
    @test_int [x^0*(a + b*x^3)^(2/3)/(c + d*x^3), x, 3, (b^(2/3)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*d) - ((b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(2/3)*d) - ((b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^(2/3)*d) + ((b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(2/3)*d) - (b^(2/3)*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(2*d)]
    @test_int [(a + b*x^3)^(2/3)/(x^3*(c + d*x^3)), x, 3, -((a + b*x^3)^(2/3)/(2*c*x^2)) + ((b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(5/3)) + ((b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^(5/3)) - ((b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(5/3))]
    @test_int [(a + b*x^3)^(2/3)/(x^6*(c + d*x^3)), x, 4, -((a + b*x^3)^(2/3)/(5*c*x^5)) - ((2*b*c - 5*a*d)*(a + b*x^3)^(2/3))/(10*a*c^2*x^2) - (d*(b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(8/3)) - (d*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^(8/3)) + (d*(b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(8/3))]
    @test_int [(a + b*x^3)^(2/3)/(x^9*(c + d*x^3)), x, 5, -((a + b*x^3)^(2/3)/(8*c*x^8)) - ((b*c - 4*a*d)*(a + b*x^3)^(2/3))/(20*a*c^2*x^5) + ((3*b^2*c^2 + 8*a*b*c*d - 20*a^2*d^2)*(a + b*x^3)^(2/3))/(40*a^2*c^3*x^2) + (d^2*(b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(11/3)) + (d^2*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^(11/3)) - (d^2*(b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(11/3))]
    @test_int [(a + b*x^3)^(2/3)/(x^12*(c + d*x^3)), x, 6, -((a + b*x^3)^(2/3)/(11*c*x^11)) - ((2*b*c - 11*a*d)*(a + b*x^3)^(2/3))/(88*a*c^2*x^8) + ((6*b^2*c^2 + 11*a*b*c*d - 44*a^2*d^2)*(a + b*x^3)^(2/3))/(220*a^2*c^3*x^5) - ((18*b^3*c^3 + 33*a*b^2*c^2*d + 88*a^2*b*c*d^2 - 220*a^3*d^3)*(a + b*x^3)^(2/3))/(440*a^3*c^4*x^2) - (d^3*(b*c - a*d)^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(14/3)) - (d^3*(b*c - a*d)^(2/3)*log(c + d*x^3))/(6*c^(14/3)) + (d^3*(b*c - a*d)^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(14/3))]

    @test_int [x^7*(a + b*x^3)^(2/3)/(c + d*x^3), x, 2, (x^8*(a + b*x^3)^(2/3)*AppellF1(8/3, -(2/3), 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)))/(8*c*(1 + (b*x^3)/a)^(2/3))]
    @test_int [x^4*(a + b*x^3)^(2/3)/(c + d*x^3), x, 2, (x^5*(a + b*x^3)^(2/3)*AppellF1(5/3, -(2/3), 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)))/(5*c*(1 + (b*x^3)/a)^(2/3))]
    @test_int [x^1*(a + b*x^3)^(2/3)/(c + d*x^3), x, 2, (x^2*(a + b*x^3)^(2/3)*AppellF1(2/3, -(2/3), 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*c*(1 + (b*x^3)/a)^(2/3))]
    @test_int [(a + b*x^3)^(2/3)/(x^2*(c + d*x^3)), x, 2, -(((a + b*x^3)^(2/3)*AppellF1(-(1/3), -(2/3), 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(c*x*(1 + (b*x^3)/a)^(2/3)))]
    @test_int [(a + b*x^3)^(2/3)/(x^5*(c + d*x^3)), x, 2, -(((a + b*x^3)^(2/3)*AppellF1(-(4/3), -(2/3), 1, -(1/3), -((b*x^3)/a), -((d*x^3)/c)))/(4*c*x^4*(1 + (b*x^3)/a)^(2/3)))]

    @test_int [x^8*(a + b*x^3)^(4/3)/(c + d*x^3), x, 9, -((c^2*(b*c - a*d)*(a + b*x^3)^(1/3))/d^4) + (c^2*(a + b*x^3)^(4/3))/(4*d^3) - ((b*c + a*d)*(a + b*x^3)^(7/3))/(7*b^2*d^2) + (a + b*x^3)^(10/3)/(10*b^2*d) - (c^2*(b*c - a*d)^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(13/3)) - (c^2*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*d^(13/3)) + (c^2*(b*c - a*d)^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(13/3))]
    @test_int [x^5*(a + b*x^3)^(4/3)/(c + d*x^3), x, 8, (c*(b*c - a*d)*(a + b*x^3)^(1/3))/d^3 - (c*(a + b*x^3)^(4/3))/(4*d^2) + (a + b*x^3)^(7/3)/(7*b*d) + (c*(b*c - a*d)^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(10/3)) + (c*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*d^(10/3)) - (c*(b*c - a*d)^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(10/3))]
    @test_int [x^2*(a + b*x^3)^(4/3)/(c + d*x^3), x, 7, -(((b*c - a*d)*(a + b*x^3)^(1/3))/d^2) + (a + b*x^3)^(4/3)/(4*d) - ((b*c - a*d)^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(7/3)) - ((b*c - a*d)^(4/3)*log(c + d*x^3))/(6*d^(7/3)) + ((b*c - a*d)^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(7/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^1*(c + d*x^3)), x, 11, (b*(a + b*x^3)^(1/3))/d - (a^(4/3)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(sqrt(3)*c) + ((b*c - a*d)^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c*d^(4/3)) - (a^(4/3)*log(x))/(2*c) + ((b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c*d^(4/3)) + (a^(4/3)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(2*c) - ((b*c - a*d)^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c*d^(4/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^4*(c + d*x^3)), x, 15, ((4*b*c - 3*a*d)*(a + b*x^3)^(1/3))/(3*c^2) - ((b*c - a*d)*(a + b*x^3)^(1/3))/c^2 + (d*(a + b*x^3)^(4/3))/(4*c^2) + ((4*b*c - 3*a*d)*(a + b*x^3)^(4/3))/(12*a*c^2) - (a + b*x^3)^(7/3)/(3*a*c*x^3) - (a^(1/3)*(4*b*c - 3*a*d)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*c^2) - ((b*c - a*d)^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^2*d^(1/3)) - (a^(1/3)*(4*b*c - 3*a*d)*log(x))/(6*c^2) - ((b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^2*d^(1/3)) + (a^(1/3)*(4*b*c - 3*a*d)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*c^2) + ((b*c - a*d)^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^2*d^(1/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^7*(c + d*x^3)), x, 14, (d*(b*c - a*d)*(a + b*x^3)^(1/3))/c^3 + ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*(a + b*x^3)^(1/3))/(9*a*c^3) - ((b*c - 6*a*d)*(a + b*x^3)^(4/3))/(18*a*c^2*x^3) - (a + b*x^3)^(7/3)/(6*a*c*x^6) - ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(9*sqrt(3)*a^(2/3)*c^3) + (d^(2/3)*(b*c - a*d)^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^3) - ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*log(x))/(18*a^(2/3)*c^3) + (d^(2/3)*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^3) + ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(18*a^(2/3)*c^3) - (d^(2/3)*(b*c - a*d)^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^3)]

    @test_int [x^4*(a + b*x^3)^(4/3)/(c + d*x^3), x, 6, -(((6*b*c - 7*a*d)*x^2*(a + b*x^3)^(1/3))/(18*d^2)) + (b*x^5*(a + b*x^3)^(1/3))/(6*d) - ((9*b^2*c^2 - 12*a*b*c*d + 2*a^2*d^2)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(9*sqrt(3)*b^(2/3)*d^3) + (c^(2/3)*(b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^3) - (c^(2/3)*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*d^3) - ((9*b^2*c^2 - 12*a*b*c*d + 2*a^2*d^2)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(18*b^(2/3)*d^3) + (c^(2/3)*(b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^3)]
    @test_int [x^1*(a + b*x^3)^(4/3)/(c + d*x^3), x, 5, (b*x^2*(a + b*x^3)^(1/3))/(3*d) + (b^(1/3)*(3*b*c - 4*a*d)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*d^2) - ((b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(1/3)*d^2) + ((b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^(1/3)*d^2) + (b^(1/3)*(3*b*c - 4*a*d)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(6*d^2) - ((b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(1/3)*d^2)]
    @test_int [(a + b*x^3)^(4/3)/(x^2*(c + d*x^3)), x, 5, -((a*(a + b*x^3)^(1/3))/(c*x)) - (b^(4/3)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(sqrt(3)*d) + ((b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(4/3)*d) - ((b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^(4/3)*d) - (b^(4/3)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(2*d) + ((b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(4/3)*d)]
    @test_int [(a + b*x^3)^(4/3)/(x^5*(c + d*x^3)), x, 4, -((a*(a + b*x^3)^(1/3))/(4*c*x^4)) - ((5*b*c - 4*a*d)*(a + b*x^3)^(1/3))/(4*c^2*x) - ((b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(7/3)) + ((b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^(7/3)) - ((b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(7/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^8*(c + d*x^3)), x, 5, -((a*(a + b*x^3)^(1/3))/(7*c*x^7)) - ((8*b*c - 7*a*d)*(a + b*x^3)^(1/3))/(28*c^2*x^4) - ((4*b^2*c^2 - 35*a*b*c*d + 28*a^2*d^2)*(a + b*x^3)^(1/3))/(28*a*c^3*x) + (d*(b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(10/3)) - (d*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^(10/3)) + (d*(b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(10/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^11*(c + d*x^3)), x, 6, -((a*(a + b*x^3)^(1/3))/(10*c*x^10)) - ((11*b*c - 10*a*d)*(a + b*x^3)^(1/3))/(70*c^2*x^7) - ((2*b^2*c^2 - 40*a*b*c*d + 35*a^2*d^2)*(a + b*x^3)^(1/3))/(140*a*c^3*x^4) + ((6*b^3*c^3 + 20*a*b^2*c^2*d - 175*a^2*b*c*d^2 + 140*a^3*d^3)*(a + b*x^3)^(1/3))/(140*a^2*c^4*x) - (d^2*(b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(13/3)) + (d^2*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^(13/3)) - (d^2*(b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(13/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^14*(c + d*x^3)), x, 7, -((a*(a + b*x^3)^(1/3))/(13*c*x^13)) - ((14*b*c - 13*a*d)*(a + b*x^3)^(1/3))/(130*c^2*x^10) - ((4*b^2*c^2 - 143*a*b*c*d + 130*a^2*d^2)*(a + b*x^3)^(1/3))/(910*a*c^3*x^7) + ((12*b^3*c^3 + 26*a*b^2*c^2*d - 520*a^2*b*c*d^2 + 455*a^3*d^3)*(a + b*x^3)^(1/3))/(1820*a^2*c^4*x^4) - ((36*b^4*c^4 + 78*a*b^3*c^3*d + 260*a^2*b^2*c^2*d^2 - 2275*a^3*b*c*d^3 + 1820*a^4*d^4)*(a + b*x^3)^(1/3))/(1820*a^3*c^5*x) + (d^3*(b*c - a*d)^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(16/3)) - (d^3*(b*c - a*d)^(4/3)*log(c + d*x^3))/(6*c^(16/3)) + (d^3*(b*c - a*d)^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(16/3))]

    @test_int [x^6*(a + b*x^3)^(4/3)/(c + d*x^3), x, 2, (a*x^7*(a + b*x^3)^(1/3)*AppellF1(7/3, -(4/3), 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)))/(7*c*(1 + (b*x^3)/a)^(1/3))]
    @test_int [x^3*(a + b*x^3)^(4/3)/(c + d*x^3), x, 2, (a*x^4*(a + b*x^3)^(1/3)*AppellF1(4/3, -(4/3), 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*c*(1 + (b*x^3)/a)^(1/3))]
    @test_int [x^0*(a + b*x^3)^(4/3)/(c + d*x^3), x, 2, (a*x*(a + b*x^3)^(1/3)*AppellF1(1/3, -(4/3), 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(c*(1 + (b*x^3)/a)^(1/3))]
    @test_int [(a + b*x^3)^(4/3)/(x^3*(c + d*x^3)), x, 2, -((a*(a + b*x^3)^(1/3)*AppellF1(-(2/3), -(4/3), 1, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*c*x^2*(1 + (b*x^3)/a)^(1/3)))]
    @test_int [(a + b*x^3)^(4/3)/(x^6*(c + d*x^3)), x, 2, -((a*(a + b*x^3)^(1/3)*AppellF1(-(5/3), -(4/3), 1, -(2/3), -((b*x^3)/a), -((d*x^3)/c)))/(5*c*x^5*(1 + (b*x^3)/a)^(1/3)))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^14/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 7, -(((b*c + a*d)*(b^2*c^2 + a^2*d^2)*(a + b*x^3)^(2/3))/(2*b^4*d^4)) + ((b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*(a + b*x^3)^(5/3))/(5*b^4*d^3) - ((b*c + 3*a*d)*(a + b*x^3)^(8/3))/(8*b^4*d^2) + (a + b*x^3)^(11/3)/(11*b^4*d) - (c^4*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(14/3)*(b*c - a*d)^(1/3)) + (c^4*log(c + d*x^3))/(6*d^(14/3)*(b*c - a*d)^(1/3)) - (c^4*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(14/3)*(b*c - a*d)^(1/3))]
    @test_int [x^11/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 7, ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(2/3))/(2*b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(5/3))/(5*b^3*d^2) + (a + b*x^3)^(8/3)/(8*b^3*d) + (c^3*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(11/3)*(b*c - a*d)^(1/3)) - (c^3*log(c + d*x^3))/(6*d^(11/3)*(b*c - a*d)^(1/3)) + (c^3*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(11/3)*(b*c - a*d)^(1/3))]
    @test_int [x^8/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 7, -(((b*c + a*d)*(a + b*x^3)^(2/3))/(2*b^2*d^2)) + (a + b*x^3)^(5/3)/(5*b^2*d) - (c^2*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(8/3)*(b*c - a*d)^(1/3)) + (c^2*log(c + d*x^3))/(6*d^(8/3)*(b*c - a*d)^(1/3)) - (c^2*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(8/3)*(b*c - a*d)^(1/3))]
    @test_int [x^5/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 6, (a + b*x^3)^(2/3)/(2*b*d) + (c*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(5/3)*(b*c - a*d)^(1/3)) - (c*log(c + d*x^3))/(6*d^(5/3)*(b*c - a*d)^(1/3)) + (c*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(5/3)*(b*c - a*d)^(1/3))]
    @test_int [x^2/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 5, -(atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3))/(sqrt(3)*d^(2/3)*(b*c - a*d)^(1/3))) + log(c + d*x^3)/(6*d^(2/3)*(b*c - a*d)^(1/3)) - log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3))/(2*d^(2/3)*(b*c - a*d)^(1/3))]
    @test_int [1/(x^1*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 10, atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(1/3)*c) + (d^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c*(b*c - a*d)^(1/3)) - log(x)/(2*a^(1/3)*c) - (d^(1/3)*log(c + d*x^3))/(6*c*(b*c - a*d)^(1/3)) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(1/3)*c) + (d^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c*(b*c - a*d)^(1/3))]
    @test_int [1/(x^4*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 11, -((a + b*x^3)^(2/3)/(3*a*c*x^3)) - ((b*c + 3*a*d)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(4/3)*c^2) - (d^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^2*(b*c - a*d)^(1/3)) + ((b*c + 3*a*d)*log(x))/(6*a^(4/3)*c^2) + (d^(4/3)*log(c + d*x^3))/(6*c^2*(b*c - a*d)^(1/3)) - ((b*c + 3*a*d)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(4/3)*c^2) - (d^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^2*(b*c - a*d)^(1/3))]

    @test_int [x^6/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 4, (x*(a + b*x^3)^(2/3))/(3*b*d) - ((3*b*c + a*d)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(4/3)*d^2) + (c^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^2*(b*c - a*d)^(1/3)) + (c^(4/3)*log(c + d*x^3))/(6*d^2*(b*c - a*d)^(1/3)) - (c^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^2*(b*c - a*d)^(1/3)) + ((3*b*c + a*d)*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(6*b^(4/3)*d^2)]
    @test_int [x^3/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 3, atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(1/3)*d) - (c^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d*(b*c - a*d)^(1/3)) - (c^(1/3)*log(c + d*x^3))/(6*d*(b*c - a*d)^(1/3)) + (c^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d*(b*c - a*d)^(1/3)) - log((-b^(1/3))*x + (a + b*x^3)^(1/3))/(2*b^(1/3)*d)]
    @test_int [x^0/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 1, atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3))/(sqrt(3)*c^(2/3)*(b*c - a*d)^(1/3)) + log(c + d*x^3)/(6*c^(2/3)*(b*c - a*d)^(1/3)) - log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3))/(2*c^(2/3)*(b*c - a*d)^(1/3))]
    @test_int [1/(x^3*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 3, -((a + b*x^3)^(2/3)/(2*a*c*x^2)) - (d*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(5/3)*(b*c - a*d)^(1/3)) - (d*log(c + d*x^3))/(6*c^(5/3)*(b*c - a*d)^(1/3)) + (d*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(5/3)*(b*c - a*d)^(1/3))]
    @test_int [1/(x^6*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 4, -((a + b*x^3)^(2/3)/(5*a*c*x^5)) + ((3*b*c + 5*a*d)*(a + b*x^3)^(2/3))/(10*a^2*c^2*x^2) + (d^2*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(8/3)*(b*c - a*d)^(1/3)) + (d^2*log(c + d*x^3))/(6*c^(8/3)*(b*c - a*d)^(1/3)) - (d^2*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(8/3)*(b*c - a*d)^(1/3))]
    @test_int [1/(x^9*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 5, -((a + b*x^3)^(2/3)/(8*a*c*x^8)) + ((3*b*c + 4*a*d)*(a + b*x^3)^(2/3))/(20*a^2*c^2*x^5) - ((9*b^2*c^2 + 12*a*b*c*d + 20*a^2*d^2)*(a + b*x^3)^(2/3))/(40*a^3*c^3*x^2) - (d^3*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(11/3)*(b*c - a*d)^(1/3)) - (d^3*log(c + d*x^3))/(6*c^(11/3)*(b*c - a*d)^(1/3)) + (d^3*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(11/3)*(b*c - a*d)^(1/3))]

    @test_int [x^7/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 2, (x^8*(1 + (b*x^3)/a)^(1/3)*AppellF1(8/3, 1/3, 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)))/(8*c*(a + b*x^3)^(1/3))]
    @test_int [x^4/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 2, (x^5*(1 + (b*x^3)/a)^(1/3)*AppellF1(5/3, 1/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)))/(5*c*(a + b*x^3)^(1/3))]
    @test_int [x^1/((a + b*x^3)^(1/3)*(c + d*x^3)), x, 2, (x^2*(1 + (b*x^3)/a)^(1/3)*AppellF1(2/3, 1/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*c*(a + b*x^3)^(1/3))]
    @test_int [1/(x^2*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 2, -(((1 + (b*x^3)/a)^(1/3)*AppellF1(-(1/3), 1/3, 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(c*x*(a + b*x^3)^(1/3)))]
    @test_int [1/(x^5*(a + b*x^3)^(1/3)*(c + d*x^3)), x, 2, -(((1 + (b*x^3)/a)^(1/3)*AppellF1(-(4/3), 1/3, 1, -(1/3), -((b*x^3)/a), -((d*x^3)/c)))/(4*c*x^4*(a + b*x^3)^(1/3)))]

    @test_int [x^11/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 7, ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(1/3))/(b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(4/3))/(4*b^3*d^2) + (a + b*x^3)^(7/3)/(7*b^3*d) + (c^3*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(10/3)*(b*c - a*d)^(2/3)) + (c^3*log(c + d*x^3))/(6*d^(10/3)*(b*c - a*d)^(2/3)) - (c^3*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(10/3)*(b*c - a*d)^(2/3))]
    @test_int [x^8/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 7, -(((b*c + a*d)*(a + b*x^3)^(1/3))/(b^2*d^2)) + (a + b*x^3)^(4/3)/(4*b^2*d) - (c^2*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(7/3)*(b*c - a*d)^(2/3)) - (c^2*log(c + d*x^3))/(6*d^(7/3)*(b*c - a*d)^(2/3)) + (c^2*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(7/3)*(b*c - a*d)^(2/3))]
    @test_int [x^5/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 6, (a + b*x^3)^(1/3)/(b*d) + (c*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(4/3)*(b*c - a*d)^(2/3)) + (c*log(c + d*x^3))/(6*d^(4/3)*(b*c - a*d)^(2/3)) - (c*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(4/3)*(b*c - a*d)^(2/3))]
    @test_int [x^2/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 5, -(atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3))/(sqrt(3)*d^(1/3)*(b*c - a*d)^(2/3))) - log(c + d*x^3)/(6*d^(1/3)*(b*c - a*d)^(2/3)) + log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3))/(2*d^(1/3)*(b*c - a*d)^(2/3))]
    @test_int [1/(x^1*(a + b*x^3)^(2/3)*(c + d*x^3)), x, 10, -(atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(2/3)*c)) + (d^(2/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c*(b*c - a*d)^(2/3)) - log(x)/(2*a^(2/3)*c) + (d^(2/3)*log(c + d*x^3))/(6*c*(b*c - a*d)^(2/3)) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(2/3)*c) - (d^(2/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c*(b*c - a*d)^(2/3))]
    @test_int [1/(x^4*(a + b*x^3)^(2/3)*(c + d*x^3)), x, 11, -((a + b*x^3)^(1/3)/(3*a*c*x^3)) + ((2*b*c + 3*a*d)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(5/3)*c^2) - (d^(5/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^2*(b*c - a*d)^(2/3)) + ((2*b*c + 3*a*d)*log(x))/(6*a^(5/3)*c^2) - (d^(5/3)*log(c + d*x^3))/(6*c^2*(b*c - a*d)^(2/3)) - ((2*b*c + 3*a*d)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(5/3)*c^2) + (d^(5/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^2*(b*c - a*d)^(2/3))]

    @test_int [x^7/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 5, (x^2*(a + b*x^3)^(1/3))/(3*b*d) + ((3*b*c + 2*a*d)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(5/3)*d^2) - (c^(5/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^2*(b*c - a*d)^(2/3)) + (c^(5/3)*log(c + d*x^3))/(6*d^2*(b*c - a*d)^(2/3)) + ((3*b*c + 2*a*d)*log(b^(1/3)*x - (a + b*x^3)^(1/3)))/(6*b^(5/3)*d^2) - (c^(5/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^2*(b*c - a*d)^(2/3))]
    @test_int [x^4/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 3, -(atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(2/3)*d)) + (c^(2/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d*(b*c - a*d)^(2/3)) - (c^(2/3)*log(c + d*x^3))/(6*d*(b*c - a*d)^(2/3)) - log(b^(1/3)*x - (a + b*x^3)^(1/3))/(2*b^(2/3)*d) + (c^(2/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d*(b*c - a*d)^(2/3))]
    @test_int [x^1/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 1, -(atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3))/(sqrt(3)*c^(1/3)*(b*c - a*d)^(2/3))) + log(c + d*x^3)/(6*c^(1/3)*(b*c - a*d)^(2/3)) - log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3))/(2*c^(1/3)*(b*c - a*d)^(2/3))]
    @test_int [1/(x^2*(a + b*x^3)^(2/3)*(c + d*x^3)), x, 3, -((a + b*x^3)^(1/3)/(a*c*x)) + (d*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(4/3)*(b*c - a*d)^(2/3)) - (d*log(c + d*x^3))/(6*c^(4/3)*(b*c - a*d)^(2/3)) + (d*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(4/3)*(b*c - a*d)^(2/3))]
    @test_int [1/(x^5*(a + b*x^3)^(2/3)*(c + d*x^3)), x, 4, -((a + b*x^3)^(1/3)/(4*a*c*x^4)) + ((3*b*c + 4*a*d)*(a + b*x^3)^(1/3))/(4*a^2*c^2*x) - (d^2*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(7/3)*(b*c - a*d)^(2/3)) + (d^2*log(c + d*x^3))/(6*c^(7/3)*(b*c - a*d)^(2/3)) - (d^2*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(7/3)*(b*c - a*d)^(2/3))]

    @test_int [x^6/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 2, (x^7*(1 + (b*x^3)/a)^(2/3)*AppellF1(7/3, 2/3, 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)))/(7*c*(a + b*x^3)^(2/3))]
    @test_int [x^3/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 2, (x^4*(1 + (b*x^3)/a)^(2/3)*AppellF1(4/3, 2/3, 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)))/(4*c*(a + b*x^3)^(2/3))]
    @test_int [x^0/((a + b*x^3)^(2/3)*(c + d*x^3)), x, 2, (x*(1 + (b*x^3)/a)^(2/3)*AppellF1(1/3, 2/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)))/(c*(a + b*x^3)^(2/3))]
    @test_int [1/(x^3*(a + b*x^3)^(2/3)*(c + d*x^3)), x, 2, -(((1 + (b*x^3)/a)^(2/3)*AppellF1(-(2/3), 2/3, 1, 1/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*c*x^2*(a + b*x^3)^(2/3)))]

    @test_int [x^14/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 11, -(a^4/(b^4*(b*c - a*d)*(a + b*x^3)^(1/3))) + (a^2*(a + b*x^3)^(2/3))/(2*b^4*d) + (a*(b*c + a*d)*(a + b*x^3)^(2/3))/(2*b^4*d^2) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(2/3))/(2*b^4*d^3) - (2*a*(a + b*x^3)^(5/3))/(5*b^4*d) - ((b*c + a*d)*(a + b*x^3)^(5/3))/(5*b^4*d^2) + (a + b*x^3)^(8/3)/(8*b^4*d) + (c^4*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(11/3)*(b*c - a*d)^(4/3)) - (c^4*log(c + d*x^3))/(6*d^(11/3)*(b*c - a*d)^(4/3)) + (c^4*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(11/3)*(b*c - a*d)^(4/3))]
    @test_int [x^11/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 9, a^3/(b^3*(b*c - a*d)*(a + b*x^3)^(1/3)) - (a*(a + b*x^3)^(2/3))/(2*b^3*d) - ((b*c + a*d)*(a + b*x^3)^(2/3))/(2*b^3*d^2) + (a + b*x^3)^(5/3)/(5*b^3*d) - (c^3*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(8/3)*(b*c - a*d)^(4/3)) + (c^3*log(c + d*x^3))/(6*d^(8/3)*(b*c - a*d)^(4/3)) - (c^3*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(8/3)*(b*c - a*d)^(4/3))]
    @test_int [x^8/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 7, -(a^2/(b^2*(b*c - a*d)*(a + b*x^3)^(1/3))) + (a + b*x^3)^(2/3)/(2*b^2*d) + (c^2*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(5/3)*(b*c - a*d)^(4/3)) - (c^2*log(c + d*x^3))/(6*d^(5/3)*(b*c - a*d)^(4/3)) + (c^2*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(5/3)*(b*c - a*d)^(4/3))]
    @test_int [x^5/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 6, a/(b*(b*c - a*d)*(a + b*x^3)^(1/3)) - (c*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*d^(2/3)*(b*c - a*d)^(4/3)) + (c*log(c + d*x^3))/(6*d^(2/3)*(b*c - a*d)^(4/3)) - (c*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*d^(2/3)*(b*c - a*d)^(4/3))]
    @test_int [x^2/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 6, -(1/((b*c - a*d)*(a + b*x^3)^(1/3))) + (d^(1/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*(b*c - a*d)^(4/3)) - (d^(1/3)*log(c + d*x^3))/(6*(b*c - a*d)^(4/3)) + (d^(1/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*(b*c - a*d)^(4/3))]
    @test_int [1/(x^1*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 11, b/(a*(b*c - a*d)*(a + b*x^3)^(1/3)) + atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3)))/(sqrt(3)*a^(4/3)*c) - (d^(4/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c*(b*c - a*d)^(4/3)) - log(x)/(2*a^(4/3)*c) + (d^(4/3)*log(c + d*x^3))/(6*c*(b*c - a*d)^(4/3)) + log(a^(1/3) - (a + b*x^3)^(1/3))/(2*a^(4/3)*c) - (d^(4/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c*(b*c - a*d)^(4/3))]
    @test_int [1/(x^4*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 13, -(d^2/(c^2*(b*c - a*d)*(a + b*x^3)^(1/3))) - (4*b*c + 3*a*d)/(3*a^2*c^2*(a + b*x^3)^(1/3)) - 1/(3*a*c*x^3*(a + b*x^3)^(1/3)) - ((4*b*c + 3*a*d)*atan((a^(1/3) + 2*(a + b*x^3)^(1/3))/(sqrt(3)*a^(1/3))))/(3*sqrt(3)*a^(7/3)*c^2) + (d^(7/3)*atan((1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/sqrt(3)))/(sqrt(3)*c^2*(b*c - a*d)^(4/3)) + ((4*b*c + 3*a*d)*log(x))/(6*a^(7/3)*c^2) - (d^(7/3)*log(c + d*x^3))/(6*c^2*(b*c - a*d)^(4/3)) - ((4*b*c + 3*a*d)*log(a^(1/3) - (a + b*x^3)^(1/3)))/(6*a^(7/3)*c^2) + (d^(7/3)*log((b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)))/(2*c^2*(b*c - a*d)^(4/3))]

    @test_int [x^9/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 5, (a*x^4)/(b*(b*c - a*d)*(a + b*x^3)^(1/3)) + ((b*c - 4*a*d)*x*(a + b*x^3)^(2/3))/(3*b^2*d*(b*c - a*d)) - ((3*b*c + 4*a*d)*atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3)))/(3*sqrt(3)*b^(7/3)*d^2) + (c^(7/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d^2*(b*c - a*d)^(4/3)) + (c^(7/3)*log(c + d*x^3))/(6*d^2*(b*c - a*d)^(4/3)) - (c^(7/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d^2*(b*c - a*d)^(4/3)) + ((3*b*c + 4*a*d)*log((-b^(1/3))*x + (a + b*x^3)^(1/3)))/(6*b^(7/3)*d^2)]
    @test_int [x^6/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 4, (a*x)/(b*(b*c - a*d)*(a + b*x^3)^(1/3)) + atan((1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/sqrt(3))/(sqrt(3)*b^(4/3)*d) - (c^(4/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*d*(b*c - a*d)^(4/3)) - (c^(4/3)*log(c + d*x^3))/(6*d*(b*c - a*d)^(4/3)) + (c^(4/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*d*(b*c - a*d)^(4/3)) - log((-b^(1/3))*x + (a + b*x^3)^(1/3))/(2*b^(4/3)*d)]
    @test_int [x^3/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 3, -(x/((b*c - a*d)*(a + b*x^3)^(1/3))) + (c^(1/3)*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*(b*c - a*d)^(4/3)) + (c^(1/3)*log(c + d*x^3))/(6*(b*c - a*d)^(4/3)) - (c^(1/3)*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*(b*c - a*d)^(4/3))]
    @test_int [x^0/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, (b*x)/(a*(b*c - a*d)*(a + b*x^3)^(1/3)) - (d*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(2/3)*(b*c - a*d)^(4/3)) - (d*log(c + d*x^3))/(6*c^(2/3)*(b*c - a*d)^(4/3)) + (d*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(2/3)*(b*c - a*d)^(4/3))]
    @test_int [1/(x^3*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 4, b/(a*(b*c - a*d)*x^2*(a + b*x^3)^(1/3)) - ((3*b*c - a*d)*(a + b*x^3)^(2/3))/(2*a^2*c*(b*c - a*d)*x^2) + (d^2*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(5/3)*(b*c - a*d)^(4/3)) + (d^2*log(c + d*x^3))/(6*c^(5/3)*(b*c - a*d)^(4/3)) - (d^2*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(5/3)*(b*c - a*d)^(4/3))]
    @test_int [1/(x^6*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 5, b/(a*(b*c - a*d)*x^5*(a + b*x^3)^(1/3)) - ((6*b*c - a*d)*(a + b*x^3)^(2/3))/(5*a^2*c*(b*c - a*d)*x^5) + ((18*b^2*c^2 - 3*a*b*c*d - 5*a^2*d^2)*(a + b*x^3)^(2/3))/(10*a^3*c^2*(b*c - a*d)*x^2) - (d^3*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(8/3)*(b*c - a*d)^(4/3)) - (d^3*log(c + d*x^3))/(6*c^(8/3)*(b*c - a*d)^(4/3)) + (d^3*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(8/3)*(b*c - a*d)^(4/3))]
    @test_int [1/(x^9*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 6, b/(a*(b*c - a*d)*x^8*(a + b*x^3)^(1/3)) - ((9*b*c - a*d)*(a + b*x^3)^(2/3))/(8*a^2*c*(b*c - a*d)*x^8) + ((9*b*c - 4*a*d)*(3*b*c + a*d)*(a + b*x^3)^(2/3))/(20*a^3*c^2*(b*c - a*d)*x^5) - ((81*b^3*c^3 - 9*a*b^2*c^2*d - 12*a^2*b*c*d^2 - 20*a^3*d^3)*(a + b*x^3)^(2/3))/(40*a^4*c^3*(b*c - a*d)*x^2) + (d^4*atan((1 + (2*(b*c - a*d)^(1/3)*x)/(c^(1/3)*(a + b*x^3)^(1/3)))/sqrt(3)))/(sqrt(3)*c^(11/3)*(b*c - a*d)^(4/3)) + (d^4*log(c + d*x^3))/(6*c^(11/3)*(b*c - a*d)^(4/3)) - (d^4*log(((b*c - a*d)^(1/3)*x)/c^(1/3) - (a + b*x^3)^(1/3)))/(2*c^(11/3)*(b*c - a*d)^(4/3))]

    @test_int [x^10/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, (x^11*(1 + (b*x^3)/a)^(1/3)*AppellF1(11/3, 4/3, 1, 14/3, -((b*x^3)/a), -((d*x^3)/c)))/(11*a*c*(a + b*x^3)^(1/3))]
    @test_int [x^7/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, (x^8*(1 + (b*x^3)/a)^(1/3)*AppellF1(8/3, 4/3, 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)))/(8*a*c*(a + b*x^3)^(1/3))]
    @test_int [x^4/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, (x^5*(1 + (b*x^3)/a)^(1/3)*AppellF1(5/3, 4/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)))/(5*a*c*(a + b*x^3)^(1/3))]
    @test_int [x^1/((a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, (x^2*(1 + (b*x^3)/a)^(1/3)*AppellF1(2/3, 4/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)))/(2*a*c*(a + b*x^3)^(1/3))]
    @test_int [1/(x^2*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, -(((1 + (b*x^3)/a)^(1/3)*AppellF1(-(1/3), 4/3, 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)))/(a*c*x*(a + b*x^3)^(1/3)))]
    @test_int [1/(x^5*(a + b*x^3)^(4/3)*(c + d*x^3)), x, 2, -(((1 + (b*x^3)/a)^(1/3)*AppellF1(-(4/3), 4/3, 1, -(1/3), -((b*x^3)/a), -((d*x^3)/c)))/(4*a*c*x^4*(a + b*x^3)^(1/3)))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^4)^p*(c+d*x^4)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^4)^p*(c+d*x^4)^q=#

    #= ::Subsubsection:: =#
    #=q>0=#

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x^15/((a + b*x^4)*(c + d*x^4)), x, 3, -(((b*c + a*d)*x^4)/(4*b^2*d^2)) + x^8/(8*b*d) - (a^3*log(a + b*x^4))/(4*b^3*(b*c - a*d)) + (c^3*log(c + d*x^4))/(4*d^3*(b*c - a*d))]
    @test_int [x^11/((a + b*x^4)*(c + d*x^4)), x, 3, x^4/(4*b*d) + (a^2*log(a + b*x^4))/(4*b^2*(b*c - a*d)) - (c^2*log(c + d*x^4))/(4*d^2*(b*c - a*d))]
    @test_int [x^7/((a + b*x^4)*(c + d*x^4)), x, 3, -((a*log(a + b*x^4))/(4*b*(b*c - a*d))) + (c*log(c + d*x^4))/(4*d*(b*c - a*d))]
    @test_int [x^3/((a + b*x^4)*(c + d*x^4)), x, 4, log(a + b*x^4)/(4*(b*c - a*d)) - log(c + d*x^4)/(4*(b*c - a*d))]
    @test_int [1/(x^1*(a + b*x^4)*(c + d*x^4)), x, 3, log(x)/(a*c) - (b*log(a + b*x^4))/(4*a*(b*c - a*d)) + (d*log(c + d*x^4))/(4*c*(b*c - a*d))]
    @test_int [1/(x^5*(a + b*x^4)*(c + d*x^4)), x, 3, -(1/(4*a*c*x^4)) - ((b*c + a*d)*log(x))/(a^2*c^2) + (b^2*log(a + b*x^4))/(4*a^2*(b*c - a*d)) - (d^2*log(c + d*x^4))/(4*c^2*(b*c - a*d))]

    @test_int [x^13/((a + b*x^4)*(c + d*x^4)), x, 6, -(((b*c + a*d)*x^2)/(2*b^2*d^2)) + x^6/(6*b*d) - (a^(5/2)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*b^(5/2)*(b*c - a*d)) + (c^(5/2)*atan((sqrt(d)*x^2)/sqrt(c)))/(2*d^(5/2)*(b*c - a*d))]
    @test_int [x^9/((a + b*x^4)*(c + d*x^4)), x, 5, x^2/(2*b*d) + (a^(3/2)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*b^(3/2)*(b*c - a*d)) - (c^(3/2)*atan((sqrt(d)*x^2)/sqrt(c)))/(2*d^(3/2)*(b*c - a*d))]
    @test_int [x^5/((a + b*x^4)*(c + d*x^4)), x, 4, -((sqrt(a)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(b)*(b*c - a*d))) + (sqrt(c)*atan((sqrt(d)*x^2)/sqrt(c)))/(2*sqrt(d)*(b*c - a*d))]
    @test_int [x^1/((a + b*x^4)*(c + d*x^4)), x, 4, (sqrt(b)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*sqrt(a)*(b*c - a*d)) - (sqrt(d)*atan((sqrt(d)*x^2)/sqrt(c)))/(2*sqrt(c)*(b*c - a*d))]
    @test_int [1/(x^3*(a + b*x^4)*(c + d*x^4)), x, 5, -(1/(2*a*c*x^2)) - (b^(3/2)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*a^(3/2)*(b*c - a*d)) + (d^(3/2)*atan((sqrt(d)*x^2)/sqrt(c)))/(2*c^(3/2)*(b*c - a*d))]
    @test_int [1/(x^7*(a + b*x^4)*(c + d*x^4)), x, 6, -(1/(6*a*c*x^6)) + (b*c + a*d)/(2*a^2*c^2*x^2) + (b^(5/2)*atan((sqrt(b)*x^2)/sqrt(a)))/(2*a^(5/2)*(b*c - a*d)) - (d^(5/2)*atan((sqrt(d)*x^2)/sqrt(c)))/(2*c^(5/2)*(b*c - a*d))]

    @test_int [x^8/((a + b*x^4)*(c + d*x^4)), x, 20, x/(b*d) - (a^(5/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(5/4)*(b*c - a*d)) + (a^(5/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(5/4)*(b*c - a*d)) + (c^(5/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*d^(5/4)*(b*c - a*d)) - (c^(5/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*d^(5/4)*(b*c - a*d)) - (a^(5/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(5/4)*(b*c - a*d)) + (a^(5/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(5/4)*(b*c - a*d)) + (c^(5/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*d^(5/4)*(b*c - a*d)) - (c^(5/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*d^(5/4)*(b*c - a*d))]
    @test_int [x^6/((a + b*x^4)*(c + d*x^4)), x, 19, (a^(3/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(3/4)*(b*c - a*d)) - (a^(3/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(3/4)*(b*c - a*d)) - (c^(3/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*d^(3/4)*(b*c - a*d)) + (c^(3/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*d^(3/4)*(b*c - a*d)) - (a^(3/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(3/4)*(b*c - a*d)) + (a^(3/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(3/4)*(b*c - a*d)) + (c^(3/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*d^(3/4)*(b*c - a*d)) - (c^(3/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*d^(3/4)*(b*c - a*d))]
    @test_int [x^4/((a + b*x^4)*(c + d*x^4)), x, 19, (a^(1/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(1/4)*(b*c - a*d)) - (a^(1/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*b^(1/4)*(b*c - a*d)) - (c^(1/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*d^(1/4)*(b*c - a*d)) + (c^(1/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*d^(1/4)*(b*c - a*d)) + (a^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(1/4)*(b*c - a*d)) - (a^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*b^(1/4)*(b*c - a*d)) - (c^(1/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*d^(1/4)*(b*c - a*d)) + (c^(1/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*d^(1/4)*(b*c - a*d))]
    @test_int [x^2/((a + b*x^4)*(c + d*x^4)), x, 19, -((b^(1/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(1/4)*(b*c - a*d))) + (b^(1/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(1/4)*(b*c - a*d)) + (d^(1/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(1/4)*(b*c - a*d)) - (d^(1/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(1/4)*(b*c - a*d)) + (b^(1/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(1/4)*(b*c - a*d)) - (b^(1/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(1/4)*(b*c - a*d)) - (d^(1/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(1/4)*(b*c - a*d)) + (d^(1/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(1/4)*(b*c - a*d))]
    @test_int [x^0/((a + b*x^4)*(c + d*x^4)), x, 19, -((b^(3/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*(b*c - a*d))) + (b^(3/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(3/4)*(b*c - a*d)) + (d^(3/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(3/4)*(b*c - a*d)) - (d^(3/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(3/4)*(b*c - a*d)) - (b^(3/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*(b*c - a*d)) + (b^(3/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(3/4)*(b*c - a*d)) + (d^(3/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(3/4)*(b*c - a*d)) - (d^(3/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(3/4)*(b*c - a*d))]
    @test_int [1/(x^2*(a + b*x^4)*(c + d*x^4)), x, 21, -(1/(a*c*x)) + (b^(5/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(5/4)*(b*c - a*d)) - (b^(5/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(5/4)*(b*c - a*d)) - (d^(5/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(5/4)*(b*c - a*d)) + (d^(5/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(5/4)*(b*c - a*d)) - (b^(5/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(5/4)*(b*c - a*d)) + (b^(5/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(5/4)*(b*c - a*d)) + (d^(5/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(5/4)*(b*c - a*d)) - (d^(5/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(5/4)*(b*c - a*d))]
    @test_int [1/(x^4*(a + b*x^4)*(c + d*x^4)), x, 20, -(1/(3*a*c*x^3)) + (b^(7/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(7/4)*(b*c - a*d)) - (b^(7/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(7/4)*(b*c - a*d)) - (d^(7/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(7/4)*(b*c - a*d)) + (d^(7/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(7/4)*(b*c - a*d)) + (b^(7/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(7/4)*(b*c - a*d)) - (b^(7/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(7/4)*(b*c - a*d)) - (d^(7/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(7/4)*(b*c - a*d)) + (d^(7/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(7/4)*(b*c - a*d))]
    @test_int [1/(x^6*(a + b*x^4)*(c + d*x^4)), x, 22, -(1/(5*a*c*x^5)) + (b*c + a*d)/(a^2*c^2*x) - (b^(9/4)*atan(1 - (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(9/4)*(b*c - a*d)) + (b^(9/4)*atan(1 + (sqrt(2)*b^(1/4)*x)/a^(1/4)))/(2*sqrt(2)*a^(9/4)*(b*c - a*d)) + (d^(9/4)*atan(1 - (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(9/4)*(b*c - a*d)) - (d^(9/4)*atan(1 + (sqrt(2)*d^(1/4)*x)/c^(1/4)))/(2*sqrt(2)*c^(9/4)*(b*c - a*d)) + (b^(9/4)*log(sqrt(a) - sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(9/4)*(b*c - a*d)) - (b^(9/4)*log(sqrt(a) + sqrt(2)*a^(1/4)*b^(1/4)*x + sqrt(b)*x^2))/(4*sqrt(2)*a^(9/4)*(b*c - a*d)) - (d^(9/4)*log(sqrt(c) - sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(9/4)*(b*c - a*d)) + (d^(9/4)*log(sqrt(c) + sqrt(2)*c^(1/4)*d^(1/4)*x + sqrt(d)*x^2))/(4*sqrt(2)*c^(9/4)*(b*c - a*d))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^4)^p*(c+d*x^4)^(q/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^4)^p*(c+d*x^4)^(1/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^7*sqrt(c + d*x^4)/(a + b*x^4), x, 5, -((a*sqrt(c + d*x^4))/(2*b^2)) + (c + d*x^4)^(3/2)/(6*b*d) + (a*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*b^(5/2))]
    @test_int [x^5*sqrt(c + d*x^4)/(a + b*x^4), x, 7, (x^2*sqrt(c + d*x^4))/(4*b) - (sqrt(a)*sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*b^2) + ((b*c - 2*a*d)*atanh((sqrt(d)*x^2)/sqrt(c + d*x^4)))/(4*b^2*sqrt(d))]
    @test_int [x^3*sqrt(c + d*x^4)/(a + b*x^4), x, 4, sqrt(c + d*x^4)/(2*b) - (sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*b^(3/2))]
    @test_int [x^1*sqrt(c + d*x^4)/(a + b*x^4), x, 6, (sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*sqrt(a)*b) + (sqrt(d)*atanh((sqrt(d)*x^2)/sqrt(c + d*x^4)))/(2*b)]
    @test_int [sqrt(c + d*x^4)/(x^1*(a + b*x^4)), x, 6, -((sqrt(c)*atanh(sqrt(c + d*x^4)/sqrt(c)))/(2*a)) + (sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*a*sqrt(b))]
    @test_int [sqrt(c + d*x^4)/(x^3*(a + b*x^4)), x, 5, -(sqrt(c + d*x^4)/(2*a*x^2)) - (sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*a^(3/2))]
    @test_int [sqrt(c + d*x^4)/(x^5*(a + b*x^4)), x, 7, -(sqrt(c + d*x^4)/(4*a*x^4)) + ((2*b*c - a*d)*atanh(sqrt(c + d*x^4)/sqrt(c)))/(4*a^2*sqrt(c)) - (sqrt(b)*sqrt(b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*a^2)]
    @test_int [sqrt(c + d*x^4)/(x^7*(a + b*x^4)), x, 6, -(sqrt(c + d*x^4)/(6*a*x^6)) + ((3*b*c - a*d)*sqrt(c + d*x^4))/(6*a^2*c*x^2) + (b*sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*a^(5/2))]

    @test_int [x^6*sqrt(c + d*x^4)/(a + b*x^4), x, 13, (x^3*sqrt(c + d*x^4))/(5*b) + ((2*b*c - 5*a*d)*x*sqrt(c + d*x^4))/(5*b^2*sqrt(d)*(sqrt(c) + sqrt(d)*x^2)) - (a*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*atan((sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*x)/sqrt(c + d*x^4)))/(4*b^2) - (a*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*b^2) - (c^(1/4)*(2*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(5*b^2*d^(3/4)*sqrt(c + d*x^4)) + (c^(1/4)*(b^2*c^2 + a*b*c*d - 5*a^2*d^2)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(5*b^2*d^(3/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (a*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(5/2)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) - a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - (a*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(c)*(sqrt(b) - (sqrt(-a)*sqrt(d))/sqrt(c))^2)/(4*sqrt(-a)*sqrt(b)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(5/2)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), (x^3*sqrt(c + d*x^4))/(5*b) + ((2*b*c - 5*a*d)*x*sqrt(c + d*x^4))/(5*b^2*sqrt(d)*(sqrt(c) + sqrt(d)*x^2)) + ((-a)^(3/4)*sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(9/4)) + ((-a)^(3/4)*sqrt((-b)*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(9/4)) - (c^(1/4)*(2*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(5*b^2*d^(3/4)*sqrt(c + d*x^4)) + (c^(1/4)*(2*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(10*b^2*d^(3/4)*sqrt(c + d*x^4)) + (a*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (a*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (sqrt(-a)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(5/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(-a)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(5/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [x^4*sqrt(c + d*x^4)/(a + b*x^4), x, 10, (x*sqrt(c + d*x^4))/(3*b) - ((b*c - a*d)*atan((sqrt((sqrt(-a)*((b*c)/a - d))/sqrt(b))*x)/sqrt(c + d*x^4)))/(4*b^2*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))) - ((b*c - a*d)*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*b^2*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))) + (c^(3/4)*(b*c - 2*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(3*b*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), (x*sqrt(c + d*x^4))/(3*b) - ((-a)^(1/4)*sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(7/4)) + ((-a)^(1/4)*sqrt((-b)*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(7/4)) + ((2*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(6*b^2*c^(1/4)*d^(1/4)*sqrt(c + d*x^4)) - (a*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(-a)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [x^2*sqrt(c + d*x^4)/(a + b*x^4), x, 11, (sqrt(d)*x*sqrt(c + d*x^4))/(b*(sqrt(c) + sqrt(d)*x^2)) + (sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*atan((sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*x)/sqrt(c + d*x^4)))/(4*b) + (sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*b) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(b*sqrt(c + d*x^4)) + (a*c^(1/4)*d^(5/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(b*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(3/2)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) - a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(c)*(sqrt(b) - (sqrt(-a)*sqrt(d))/sqrt(c))^2)/(4*sqrt(-a)*sqrt(b)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(3/2)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), (sqrt(d)*x*sqrt(c + d*x^4))/(b*(sqrt(c) + sqrt(d)*x^2)) + (sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(1/4)*b^(5/4)) + (sqrt((-b)*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(1/4)*b^(5/4)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(b*sqrt(c + d*x^4)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*b*sqrt(c + d*x^4)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [x^0*sqrt(c + d*x^4)/(a + b*x^4), x, 9, ((b*c - a*d)*atan((sqrt((sqrt(-a)*((b*c)/a - d))/sqrt(b))*x)/sqrt(c + d*x^4)))/(4*a*b*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))) + ((b*c - a*d)*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*a*b*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))) + (c^(3/4)*d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/((b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*b*c^(1/4)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*b*c^(1/4)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), -((sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(3/4)*b^(3/4))) + (sqrt((-b)*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(3/4)*b^(3/4)) + (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*b*c^(1/4)*sqrt(c + d*x^4)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*sqrt(-a)*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*b*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*b*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [sqrt(c + d*x^4)/(x^2*(a + b*x^4)), x, 13, -(sqrt(c + d*x^4)/(a*x)) + (sqrt(d)*x*sqrt(c + d*x^4))/(a*(sqrt(c) + sqrt(d)*x^2)) - (sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*atan((sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*x)/sqrt(c + d*x^4)))/(4*a) - (sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*a) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(a*sqrt(c + d*x^4)) + (b*c^(5/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(a*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(b)*c^(1/4)*((-a)^(3/2)*sqrt(b)*sqrt(c) + a^2*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(c)*(sqrt(b) - (sqrt(-a)*sqrt(d))/sqrt(c))^2)/(4*sqrt(-a)*sqrt(b)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*sqrt(b)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), -(sqrt(c + d*x^4)/(a*x)) + (sqrt(d)*x*sqrt(c + d*x^4))/(a*(sqrt(c) + sqrt(d)*x^2)) + (sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(5/4)*b^(1/4)) + (sqrt((-b)*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(5/4)*b^(1/4)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(a*sqrt(c + d*x^4)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*a*sqrt(c + d*x^4)) + ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*(-a)^(3/2)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*(-a)^(3/2)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [sqrt(c + d*x^4)/(x^4*(a + b*x^4)), x, 10, -(sqrt(c + d*x^4)/(3*a*x^3)) - ((b*c - a*d)*atan((sqrt((sqrt(-a)*((b*c)/a - d))/sqrt(b))*x)/sqrt(c + d*x^4)))/(4*a^2*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))) - ((b*c - a*d)*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*a^2*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))) - (d^(3/4)*(2*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(3*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), -(sqrt(c + d*x^4)/(3*a*x^3)) - (b^(1/4)*sqrt(b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(7/4)) + (b^(1/4)*sqrt((-b)*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(7/4)) - (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(6*a*c^(1/4)*sqrt(c + d*x^4)) - (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*(-a)^(3/2)*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x^4)^p*(c+d*x^4)^(1/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(e*x)^(3/2)*sqrt(c + d*x^4)/(a + b*x^4), x, 3, (2*(e*x)^(5/2)*sqrt(c + d*x^4)*AppellF1(5/8, 1, -(1/2), 13/8, -((b*x^4)/a), -((d*x^4)/c)))/(5*a*e*sqrt(1 + (d*x^4)/c))]
    @test_int [(e*x)^(1/2)*sqrt(c + d*x^4)/(a + b*x^4), x, 3, (2*(e*x)^(3/2)*sqrt(c + d*x^4)*AppellF1(3/8, 1, -(1/2), 11/8, -((b*x^4)/a), -((d*x^4)/c)))/(3*a*e*sqrt(1 + (d*x^4)/c))]
    @test_int [sqrt(c + d*x^4)/((e*x)^(1/2)*(a + b*x^4)), x, 3, (2*sqrt(e*x)*sqrt(c + d*x^4)*AppellF1(1/8, 1, -(1/2), 9/8, -((b*x^4)/a), -((d*x^4)/c)))/(a*e*sqrt(1 + (d*x^4)/c))]
    @test_int [sqrt(c + d*x^4)/((e*x)^(3/2)*(a + b*x^4)), x, 3, -((2*sqrt(c + d*x^4)*AppellF1(-(1/8), 1, -(1/2), 7/8, -((b*x^4)/a), -((d*x^4)/c)))/(a*e*sqrt(e*x)*sqrt(1 + (d*x^4)/c)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^4)^p / (c+d*x^4)^(1/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^11/((a + b*x^4)*sqrt(c + d*x^4)), x, 5, -(((b*c + a*d)*sqrt(c + d*x^4))/(2*b^2*d^2)) + (c + d*x^4)^(3/2)/(6*b*d^2) - (a^2*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*b^(5/2)*sqrt(b*c - a*d))]
    @test_int [x^7/((a + b*x^4)*sqrt(c + d*x^4)), x, 4, sqrt(c + d*x^4)/(2*b*d) + (a*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*b^(3/2)*sqrt(b*c - a*d))]
    @test_int [x^3/((a + b*x^4)*sqrt(c + d*x^4)), x, 3, -(atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d))/(2*sqrt(b)*sqrt(b*c - a*d)))]
    @test_int [1/(x^1*(a + b*x^4)*sqrt(c + d*x^4)), x, 6, -(atanh(sqrt(c + d*x^4)/sqrt(c))/(2*a*sqrt(c))) + (sqrt(b)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*a*sqrt(b*c - a*d))]
    @test_int [1/(x^5*(a + b*x^4)*sqrt(c + d*x^4)), x, 7, -(sqrt(c + d*x^4)/(4*a*c*x^4)) + ((2*b*c + a*d)*atanh(sqrt(c + d*x^4)/sqrt(c)))/(4*a^2*c^(3/2)) - (b^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(2*a^2*sqrt(b*c - a*d))]

    @test_int [x^9/((a + b*x^4)*sqrt(c + d*x^4)), x, 7, (x^2*sqrt(c + d*x^4))/(4*b*d) + (a^(3/2)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*b^2*sqrt(b*c - a*d)) - ((b*c + 2*a*d)*atanh((sqrt(d)*x^2)/sqrt(c + d*x^4)))/(4*b^2*d^(3/2))]
    @test_int [x^5/((a + b*x^4)*sqrt(c + d*x^4)), x, 6, -((sqrt(a)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*b*sqrt(b*c - a*d))) + atanh((sqrt(d)*x^2)/sqrt(c + d*x^4))/(2*b*sqrt(d))]
    @test_int [x^1/((a + b*x^4)*sqrt(c + d*x^4)), x, 3, atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4)))/(2*sqrt(a)*sqrt(b*c - a*d))]
    @test_int [1/(x^3*(a + b*x^4)*sqrt(c + d*x^4)), x, 5, -(sqrt(c + d*x^4)/(2*a*c*x^2)) - (b*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*a^(3/2)*sqrt(b*c - a*d))]
    @test_int [1/(x^7*(a + b*x^4)*sqrt(c + d*x^4)), x, 6, -(sqrt(c + d*x^4)/(6*a*c*x^6)) + ((3*b*c + 2*a*d)*sqrt(c + d*x^4))/(6*a^2*c^2*x^2) + (b^2*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(2*a^(5/2)*sqrt(b*c - a*d))]

    @test_int [x^8/((a + b*x^4)*sqrt(c + d*x^4)), x, 10, (x*sqrt(c + d*x^4))/(3*b*d) - ((-a)^(5/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(7/4)*sqrt(b*c - a*d)) - ((-a)^(5/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(7/4)*sqrt((-b)*c + a*d)) + (a^2*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (a*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((b*c + 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(6*b^2*c^(1/4)*d^(5/4)*sqrt(c + d*x^4)) + (a*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (a*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [x^4/((a + b*x^4)*sqrt(c + d*x^4)), x, 9, -(atan((sqrt((sqrt(-a)*((b*c)/a - d))/sqrt(b))*x)/sqrt(c + d*x^4))/(4*b*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b)))))) - atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4))/(4*b*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))) + (c^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), -(((-a)^(1/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(3/4)*sqrt(b*c - a*d))) - ((-a)^(1/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(3/4)*sqrt((-b)*c + a*d)) + ((sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*b*c^(1/4)*d^(1/4)*sqrt(c + d*x^4)) - (a*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [x^0/((a + b*x^4)*sqrt(c + d*x^4)), x, 7, atan((sqrt((sqrt(-a)*((b*c)/a - d))/sqrt(b))*x)/sqrt(c + d*x^4))/(4*a*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))) + atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4))/(4*a*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))) + (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), -((b^(1/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(3/4)*sqrt(b*c - a*d))) - (b^(1/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(3/4)*sqrt((-b)*c + a*d)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [1/(x^4*(a + b*x^4)*sqrt(c + d*x^4)), x, 10, -(sqrt(c + d*x^4)/(3*a*c*x^3)) - (b*atan((sqrt((sqrt(-a)*((b*c)/a - d))/sqrt(b))*x)/sqrt(c + d*x^4)))/(4*a^2*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))) - (b*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*a^2*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))) - (d^(3/4)*(4*b*c + a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(6*a*c^(5/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), -(sqrt(c + d*x^4)/(3*a*c*x^3)) - (b^(5/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(7/4)*sqrt(b*c - a*d)) - (b^(5/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(7/4)*sqrt((-b)*c + a*d)) - (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(6*a*c^(5/4)*sqrt(c + d*x^4)) - (b*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]

    @test_int [x^6/((a + b*x^4)*sqrt(c + d*x^4)), x, 11, (x*sqrt(c + d*x^4))/(b*sqrt(d)*(sqrt(c) + sqrt(d)*x^2)) - (a*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*atan((sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*x)/sqrt(c + d*x^4)))/(4*b*(b*c - a*d)) - (a*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*b*(b*c - a*d)) - (c^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(b*d^(3/4)*sqrt(c + d*x^4)) + (c^(1/4)*(b*c + 2*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*b*d^(3/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (a*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(3/2)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) - a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) - (a*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(c)*(sqrt(b) - (sqrt(-a)*sqrt(d))/sqrt(c))^2)/(4*sqrt(-a)*sqrt(b)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(3/2)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), (x*sqrt(c + d*x^4))/(b*sqrt(d)*(sqrt(c) + sqrt(d)*x^2)) + ((-a)^(3/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(5/4)*sqrt(b*c - a*d)) - ((-a)^(3/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*b^(5/4)*sqrt((-b)*c + a*d)) - (c^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(b*d^(3/4)*sqrt(c + d*x^4)) + (c^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*b*d^(3/4)*sqrt(c + d*x^4)) + (a*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (a*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (sqrt(-a)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(-a)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [x^2/((a + b*x^4)*sqrt(c + d*x^4)), x, 7, (sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*atan((sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*x)/sqrt(c + d*x^4)))/(4*(b*c - a*d)) + (sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*(b*c - a*d)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(b)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) - a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(c)*(sqrt(b) - (sqrt(-a)*sqrt(d))/sqrt(c))^2)/(4*sqrt(-a)*sqrt(b)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(b)*c^(1/4)*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*sqrt(c + d*x^4)), atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4)))/(4*(-a)^(1/4)*b^(1/4)*sqrt(b*c - a*d)) - atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4)))/(4*(-a)^(1/4)*b^(1/4)*sqrt((-b)*c + a*d)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(-a)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*sqrt(-a)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [1/(x^2*(a + b*x^4)*sqrt(c + d*x^4)), x, 13, -(sqrt(c + d*x^4)/(a*c*x)) + (sqrt(d)*x*sqrt(c + d*x^4))/(a*c*(sqrt(c) + sqrt(d)*x^2)) - (b*sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*atan((sqrt(-((b*c - a*d)/(sqrt(-a)*sqrt(b))))*x)/sqrt(c + d*x^4)))/(4*a*(b*c - a*d)) - (b*sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*atan((sqrt((b*c - a*d)/(sqrt(-a)*sqrt(b)))*x)/sqrt(c + d*x^4)))/(4*a*(b*c - a*d)) - (d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(a*c^(3/4)*sqrt(c + d*x^4)) + (d^(1/4)*(2*b*c + a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*a*c^(3/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (sqrt(b)*((sqrt(b)*c^(1/4))/d^(1/4) - (sqrt(-a)*d^(1/4))/c^(1/4))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*(sqrt(-a)*sqrt(b)*sqrt(c) - a*sqrt(d))*sqrt(c + d*x^4)) - (sqrt(b)*((sqrt(b)*c^(1/4))/d^(1/4) + (sqrt(-a)*d^(1/4))/c^(1/4))*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(c)*(sqrt(b) - (sqrt(-a)*sqrt(d))/sqrt(c))^2)/(4*sqrt(-a)*sqrt(b)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*sqrt(c + d*x^4)), If(13>=8, -(sqrt(c + d*x^4)/(a*c*x)) + (sqrt(d)*x*sqrt(c + d*x^4))/(a*c*(sqrt(c) + sqrt(d)*x^2)) + (b^(3/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(5/4)*sqrt(b*c - a*d)) - (b^(3/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(5/4)*sqrt((-b)*c + a*d)) - (d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(a*c^(3/4)*sqrt(c + d*x^4)) + (d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*a*c^(3/4)*sqrt(c + d*x^4)) + (b*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (b*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (sqrt(b)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(b)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)), -(sqrt(c + d*x^4)/(a*c*x)) + (sqrt(d)*x*sqrt(c + d*x^4))/(a*c*(sqrt(c) + sqrt(d)*x^2)) + (b^(3/4)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(5/4)*sqrt(b*c - a*d)) - (b^(3/4)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(4*(-a)^(5/4)*sqrt((-b)*c + a*d)) - (d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(a*c^(3/4)*sqrt(c + d*x^4)) + (d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(2*a*c^(3/4)*sqrt(c + d*x^4)) + (b*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (b*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) + (sqrt(b)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(b)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^4)))]

    @test_int [x^15/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 5, (a*x^8*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(a + b*x^4)) - (sqrt(c + d*x^4)*(4*b^2*c^2 + 8*a*b*c*d - 15*a^2*d^2 - b*d*(2*b*c - 5*a*d)*x^4))/(12*b^3*d^2*(b*c - a*d)) - (a^2*(6*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(4*b^(7/2)*(b*c - a*d)^(3/2))]
    @test_int [x^11/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 5, sqrt(c + d*x^4)/(2*b^2*d) - (a^2*sqrt(c + d*x^4))/(4*b^2*(b*c - a*d)*(a + b*x^4)) + (a*(4*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(4*b^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [x^7/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 4, (a*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(a + b*x^4)) - ((2*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(4*b^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [x^3/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 4, -(sqrt(c + d*x^4)/(4*(b*c - a*d)*(a + b*x^4))) + (d*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(4*sqrt(b)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^1*(a + b*x^4)^2*sqrt(c + d*x^4)), x, 7, (b*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*(a + b*x^4)) - atanh(sqrt(c + d*x^4)/sqrt(c))/(2*a^2*sqrt(c)) + (sqrt(b)*(2*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(4*a^2*(b*c - a*d)^(3/2))]
    @test_int [1/(x^5*(a + b*x^4)^2*sqrt(c + d*x^4)), x, 8, -((b*(2*b*c - a*d)*sqrt(c + d*x^4))/(4*a^2*c*(b*c - a*d)*(a + b*x^4))) - sqrt(c + d*x^4)/(4*a*c*x^4*(a + b*x^4)) + ((4*b*c + a*d)*atanh(sqrt(c + d*x^4)/sqrt(c)))/(4*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^4))/sqrt(b*c - a*d)))/(4*a^3*(b*c - a*d)^(3/2))]

    @test_int [x^13/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 8, ((b*c - 2*a*d)*x^2*sqrt(c + d*x^4))/(4*b^2*d*(b*c - a*d)) + (a*x^6*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(a + b*x^4)) + (a^(3/2)*(5*b*c - 4*a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(4*b^3*(b*c - a*d)^(3/2)) - ((b*c + 4*a*d)*atanh((sqrt(d)*x^2)/sqrt(c + d*x^4)))/(4*b^3*d^(3/2))]
    @test_int [x^9/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 7, (a*x^2*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(a + b*x^4)) - (sqrt(a)*(3*b*c - 2*a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(4*b^2*(b*c - a*d)^(3/2)) + atanh((sqrt(d)*x^2)/sqrt(c + d*x^4))/(2*b^2*sqrt(d))]
    @test_int [x^5/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 5, -((x^2*sqrt(c + d*x^4))/(4*(b*c - a*d)*(a + b*x^4))) + (c*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(4*sqrt(a)*(b*c - a*d)^(3/2))]
    @test_int [x^1/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 4, (b*x^2*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*(a + b*x^4)) + ((b*c - 2*a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(4*a^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^3*(a + b*x^4)^2*sqrt(c + d*x^4)), x, 6, -(((3*b*c - 2*a*d)*sqrt(c + d*x^4))/(4*a^2*c*(b*c - a*d)*x^2)) + (b*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*x^2*(a + b*x^4)) - (b*(3*b*c - 4*a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(4*a^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^7*(a + b*x^4)^2*sqrt(c + d*x^4)), x, 7, -(((5*b*c - 2*a*d)*sqrt(c + d*x^4))/(12*a^2*c*(b*c - a*d)*x^6)) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*sqrt(c + d*x^4))/(12*a^3*c^2*(b*c - a*d)*x^2) + (b*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*x^6*(a + b*x^4)) + (b^2*(5*b*c - 6*a*d)*atan((sqrt(b*c - a*d)*x^2)/(sqrt(a)*sqrt(c + d*x^4))))/(4*a^(7/2)*(b*c - a*d)^(3/2))]

    @test_int [x^8/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 10, If(13>=8, (a*x*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(a + b*x^4)) - ((-a)^(1/4)*(5*b*c - 3*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*b^(7/4)*(b*c - a*d)^(3/2)) + ((-a)^(1/4)*(5*b*c - 3*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*b^(7/4)*((-b)*c + a*d)^(3/2)) + ((4*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) - (a*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(-a)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)), (a*x*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(a + b*x^4)) - ((-a)^(1/4)*(5*b*c - 3*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*b^(7/4)*(b*c - a*d)^(3/2)) + ((-a)^(1/4)*(5*b*c - 3*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*b^(7/4)*((-b)*c + a*d)^(3/2)) + ((4*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) - (a*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(-a)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b^2*c^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*b^2*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(5*b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*b^2*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)))]
    @test_int [x^4/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 10, -((x*sqrt(c + d*x^4))/(4*(b*c - a*d)*(a + b*x^4))) - ((b*c + a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(3/4)*b^(3/4)*(b*c - a*d)^(3/2)) + ((b*c + a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(3/4)*b^(3/4)*((-b)*c + a*d)^(3/2)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) + ((sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a*b*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) - (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*sqrt(c + d*x^4))]
    @test_int [x^0/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 10, If(13>=8, (b*x*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*(a + b*x^4)) + (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(7/4)*(b*c - a*d)^(3/2)) - (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(7/4)*((-b)*c + a*d)^(3/2)) + (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*(-a)^(3/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)), (b*x*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*(a + b*x^4)) + (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(7/4)*(b*c - a*d)^(3/2)) - (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(7/4)*((-b)*c + a*d)^(3/2)) + (d^(3/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^4)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*(-a)^(3/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^2*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^2*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)))]
    @test_int [1/(x^4*(a + b*x^4)^2*sqrt(c + d*x^4)), x, 11, If(13>=8, -(((7*b*c - 4*a*d)*sqrt(c + d*x^4))/(12*a^2*c*(b*c - a*d)*x^3)) + (b*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*x^3*(a + b*x^4)) + (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(11/4)*(b*c - a*d)^(3/2)) - (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(11/4)*((-b)*c + a*d)^(3/2)) - (d^(3/4)*(7*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(24*a^2*c^(5/4)*(b*c - a*d)*sqrt(c + d*x^4)) + (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)), -(((7*b*c - 4*a*d)*sqrt(c + d*x^4))/(12*a^2*c*(b*c - a*d)*x^3)) + (b*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*x^3*(a + b*x^4)) + (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(11/4)*(b*c - a*d)^(3/2)) - (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(11/4)*((-b)*c + a*d)^(3/2)) - (d^(3/4)*(7*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(24*a^2*c^(5/4)*(b*c - a*d)*sqrt(c + d*x^4)) + (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^3*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*a^3*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)))]

    @test_int [x^6/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 13, If(13>=8, (sqrt(d)*x*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)) - (x^3*sqrt(c + d*x^4))/(4*(b*c - a*d)*(a + b*x^4)) + ((3*b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(1/4)*b^(5/4)*(b*c - a*d)^(3/2)) + ((3*b*c - a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(1/4)*b^(5/4)*((-b)*c + a*d)^(3/2)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*(b*c - a*d)*sqrt(c + d*x^4)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*(b*c - a*d)*sqrt(c + d*x^4)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)), (sqrt(d)*x*sqrt(c + d*x^4))/(4*b*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)) - (x^3*sqrt(c + d*x^4))/(4*(b*c - a*d)*(a + b*x^4)) + ((3*b*c - a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(1/4)*b^(5/4)*(b*c - a*d)^(3/2)) + ((3*b*c - a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(1/4)*b^(5/4)*((-b)*c + a*d)^(3/2)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*b*(b*c - a*d)*sqrt(c + d*x^4)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*b*(b*c - a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b^(3/2)*c^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*b^(3/2)*c^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)))]
    @test_int [x^2/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 13, -((sqrt(d)*x*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2))) + (b*x^3*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*(a + b*x^4)) - ((b*c - 3*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(5/4)*b^(1/4)*(b*c - a*d)^(3/2)) - ((b*c - 3*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(5/4)*b^(1/4)*((-b)*c + a*d)^(3/2)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a*(b*c - a*d)*sqrt(c + d*x^4)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a*(b*c - a*d)*sqrt(c + d*x^4)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*(-a)^(3/2)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*(-a)^(3/2)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4))]
    @test_int [1/(x^2*(a + b*x^4)^2*sqrt(c + d*x^4)), x, 14, -(((5*b*c - 4*a*d)*sqrt(c + d*x^4))/(4*a^2*c*(b*c - a*d)*x)) + (sqrt(d)*(5*b*c - 4*a*d)*x*sqrt(c + d*x^4))/(4*a^2*c*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^2)) + (b*sqrt(c + d*x^4))/(4*a*(b*c - a*d)*x*(a + b*x^4)) - (b^(3/4)*(5*b*c - 7*a*d)*atan((sqrt(b*c - a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(9/4)*(b*c - a*d)^(3/2)) - (b^(3/4)*(5*b*c - 7*a*d)*atan((sqrt((-b)*c + a*d)*x)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^4))))/(16*(-a)^(9/4)*((-b)*c + a*d)^(3/2)) - (d^(1/4)*(5*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.E(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(4*a^2*c^(3/4)*(b*c - a*d)*sqrt(c + d*x^4)) + (d^(1/4)*(5*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(8*a^2*c^(3/4)*(b*c - a*d)*sqrt(c + d*x^4)) + (b*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + (b*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.F(2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(16*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) - (sqrt(b)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4)) + (sqrt(b)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^2)*sqrt((c + d*x^4)/(sqrt(c) + sqrt(d)*x^2)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x)/c^(1/4)), 1/2))/(32*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^4))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^4)^p*(c+d*x^4)^(q/2)*with*m*symbolic=#

    #= ::Subsubsection:: =#
    #=q>0=#

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [(e*x)^m*(a + b*x^4)^2/sqrt(c + d*x^4), x, 4, -((b*(b*c*(5 + m) - 2*a*d*(7 + m))*(e*x)^(1 + m)*sqrt(c + d*x^4))/(d^2*e*(3 + m)*(7 + m))) + (b^2*(e*x)^(5 + m)*sqrt(c + d*x^4))/(d*e^5*(7 + m)) + ((a^2*d^2*(3 + m)*(7 + m) + b*c*(1 + m)*(b*c*(5 + m) - 2*a*d*(7 + m)))*(e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)))/(d^2*e*(1 + m)*(3 + m)*(7 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m*(a + b*x^4)^1/sqrt(c + d*x^4), x, 3, (b*(e*x)^(1 + m)*sqrt(c + d*x^4))/(d*e*(3 + m)) - ((b*c*(1 + m) - a*d*(3 + m))*(e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)))/(d*e*(1 + m)*(3 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m*(a + b*x^4)^0/sqrt(c + d*x^4), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)))/(e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m/((a + b*x^4)^1*sqrt(c + d*x^4)), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*AppellF1((1 + m)/4, 1, 1/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)))/(a*e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m/((a + b*x^4)^2*sqrt(c + d*x^4)), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*AppellF1((1 + m)/4, 2, 1/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)))/(a^2*e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m/((a + b*x^4)^3*sqrt(c + d*x^4)), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*AppellF1((1 + m)/4, 3, 1/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)))/(a^3*e*(1 + m)*sqrt(c + d*x^4))]

    @test_int [(e*x)^m*(a + b*x^4)^2/(c + d*x^4)^(3/2), x, 4, ((b*c - a*d)^2*(e*x)^(1 + m))/(2*c*d^2*e*sqrt(c + d*x^4)) + (b^2*(e*x)^(1 + m)*sqrt(c + d*x^4))/(d^2*e*(3 + m)) - ((2*b^2*c^2*(1 + m) - (3 + m)*(2*a^2*d^2 - (b*c - a*d)^2*(1 + m)))*(e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)))/(2*c*d^2*e*(1 + m)*(3 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m*(a + b*x^4)^1/(c + d*x^4)^(3/2), x, 3, -(((b*c - a*d)*(e*x)^(1 + m))/(2*c*d*e*sqrt(c + d*x^4))) + ((a*d*(1 - m) + b*c*(1 + m))*(e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)))/(2*c*d*e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m*(a + b*x^4)^0/(c + d*x^4)^(3/2), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*HypergeometricFunctions._₂F₁(3/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)))/(c*e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m/((a + b*x^4)^1*(c + d*x^4)^(3/2)), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*AppellF1((1 + m)/4, 1, 3/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)))/(a*c*e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m/((a + b*x^4)^2*(c + d*x^4)^(3/2)), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*AppellF1((1 + m)/4, 2, 3/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)))/(a^2*c*e*(1 + m)*sqrt(c + d*x^4))]
    @test_int [(e*x)^m/((a + b*x^4)^3*(c + d*x^4)^(3/2)), x, 2, ((e*x)^(1 + m)*sqrt(1 + (d*x^4)/c)*AppellF1((1 + m)/4, 3, 3/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)))/(a^3*c*e*(1 + m)*sqrt(c + d*x^4))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^6)^p*(c+d*x^6)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^6)^p*(c+d*x^6)^(q/2)=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^6)^p*(c+d*x^6)^(1/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^6)^p / (c+d*x^6)^(1/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^17/((a + b*x^6)*sqrt(c + d*x^6)), x, 5, -(((b*c + a*d)*sqrt(c + d*x^6))/(3*b^2*d^2)) + (c + d*x^6)^(3/2)/(9*b*d^2) - (a^2*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(3*b^(5/2)*sqrt(b*c - a*d))]
    @test_int [x^11/((a + b*x^6)*sqrt(c + d*x^6)), x, 4, sqrt(c + d*x^6)/(3*b*d) + (a*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(3*b^(3/2)*sqrt(b*c - a*d))]
    @test_int [x^5/((a + b*x^6)*sqrt(c + d*x^6)), x, 3, -(atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d))/(3*sqrt(b)*sqrt(b*c - a*d)))]
    @test_int [1/(x^1*(a + b*x^6)*sqrt(c + d*x^6)), x, 6, -(atanh(sqrt(c + d*x^6)/sqrt(c))/(3*a*sqrt(c))) + (sqrt(b)*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(3*a*sqrt(b*c - a*d))]
    @test_int [1/(x^7*(a + b*x^6)*sqrt(c + d*x^6)), x, 7, -(sqrt(c + d*x^6)/(6*a*c*x^6)) + ((2*b*c + a*d)*atanh(sqrt(c + d*x^6)/sqrt(c)))/(6*a^2*c^(3/2)) - (b^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(3*a^2*sqrt(b*c - a*d))]

    @test_int [x^14/((a + b*x^6)*sqrt(c + d*x^6)), x, 7, (x^3*sqrt(c + d*x^6))/(6*b*d) + (a^(3/2)*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(3*b^2*sqrt(b*c - a*d)) - ((b*c + 2*a*d)*atanh((sqrt(d)*x^3)/sqrt(c + d*x^6)))/(6*b^2*d^(3/2))]
    @test_int [x^8/((a + b*x^6)*sqrt(c + d*x^6)), x, 6, -((sqrt(a)*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(3*b*sqrt(b*c - a*d))) + atanh((sqrt(d)*x^3)/sqrt(c + d*x^6))/(3*b*sqrt(d))]
    @test_int [x^2/((a + b*x^6)*sqrt(c + d*x^6)), x, 3, atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6)))/(3*sqrt(a)*sqrt(b*c - a*d))]
    @test_int [1/(x^4*(a + b*x^6)*sqrt(c + d*x^6)), x, 5, -(sqrt(c + d*x^6)/(3*a*c*x^3)) - (b*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(3*a^(3/2)*sqrt(b*c - a*d))]
    @test_int [1/(x^10*(a + b*x^6)*sqrt(c + d*x^6)), x, 6, -(sqrt(c + d*x^6)/(9*a*c*x^9)) + ((3*b*c + 2*a*d)*sqrt(c + d*x^6))/(9*a^2*c^2*x^3) + (b^2*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(3*a^(5/2)*sqrt(b*c - a*d))]

    @test_int [x^4/((a + b*x^6)*sqrt(c + d*x^6)), x, 2, (x^5*sqrt(1 + (d*x^6)/c)*AppellF1(5/6, 1, 1/2, 11/6, -((b*x^6)/a), -((d*x^6)/c)))/(5*a*sqrt(c + d*x^6))]
    @test_int [x^3/((a + b*x^6)*sqrt(c + d*x^6)), x, 3, (x^4*sqrt(1 + (d*x^6)/c)*AppellF1(2/3, 1, 1/2, 5/3, -((b*x^6)/a), -((d*x^6)/c)))/(4*a*sqrt(c + d*x^6))]
    @test_int [x^1/((a + b*x^6)*sqrt(c + d*x^6)), x, 3, (x^2*sqrt(1 + (d*x^6)/c)*AppellF1(1/3, 1, 1/2, 4/3, -((b*x^6)/a), -((d*x^6)/c)))/(2*a*sqrt(c + d*x^6))]
    @test_int [x^0/((a + b*x^6)*sqrt(c + d*x^6)), x, 2, (x*sqrt(1 + (d*x^6)/c)*AppellF1(1/6, 1, 1/2, 7/6, -((b*x^6)/a), -((d*x^6)/c)))/(a*sqrt(c + d*x^6))]
    @test_int [1/(x^2*(a + b*x^6)*sqrt(c + d*x^6)), x, 2, -((sqrt(1 + (d*x^6)/c)*AppellF1(-(1/6), 1, 1/2, 5/6, -((b*x^6)/a), -((d*x^6)/c)))/(a*x*sqrt(c + d*x^6)))]
    @test_int [1/(x^3*(a + b*x^6)*sqrt(c + d*x^6)), x, 3, -((sqrt(1 + (d*x^6)/c)*AppellF1(-(1/3), 1, 1/2, 2/3, -((b*x^6)/a), -((d*x^6)/c)))/(2*a*x^2*sqrt(c + d*x^6)))]
    @test_int [1/(x^5*(a + b*x^6)*sqrt(c + d*x^6)), x, 3, -((sqrt(1 + (d*x^6)/c)*AppellF1(-(2/3), 1, 1/2, 1/3, -((b*x^6)/a), -((d*x^6)/c)))/(4*a*x^4*sqrt(c + d*x^6)))]

    @test_int [x^17/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 5, sqrt(c + d*x^6)/(3*b^2*d) - (a^2*sqrt(c + d*x^6))/(6*b^2*(b*c - a*d)*(a + b*x^6)) + (a*(4*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(6*b^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [x^11/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 4, (a*sqrt(c + d*x^6))/(6*b*(b*c - a*d)*(a + b*x^6)) - ((2*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(6*b^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [x^5/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 4, -(sqrt(c + d*x^6)/(6*(b*c - a*d)*(a + b*x^6))) + (d*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(6*sqrt(b)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^1*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 7, (b*sqrt(c + d*x^6))/(6*a*(b*c - a*d)*(a + b*x^6)) - atanh(sqrt(c + d*x^6)/sqrt(c))/(3*a^2*sqrt(c)) + (sqrt(b)*(2*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(6*a^2*(b*c - a*d)^(3/2))]
    @test_int [1/(x^7*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 8, -((b*(2*b*c - a*d)*sqrt(c + d*x^6))/(6*a^2*c*(b*c - a*d)*(a + b*x^6))) - sqrt(c + d*x^6)/(6*a*c*x^6*(a + b*x^6)) + ((4*b*c + a*d)*atanh(sqrt(c + d*x^6)/sqrt(c)))/(6*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^6))/sqrt(b*c - a*d)))/(6*a^3*(b*c - a*d)^(3/2))]

    @test_int [x^14/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 7, (a*x^3*sqrt(c + d*x^6))/(6*b*(b*c - a*d)*(a + b*x^6)) - (sqrt(a)*(3*b*c - 2*a*d)*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(6*b^2*(b*c - a*d)^(3/2)) + atanh((sqrt(d)*x^3)/sqrt(c + d*x^6))/(3*b^2*sqrt(d))]
    @test_int [x^8/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 5, -((x^3*sqrt(c + d*x^6))/(6*(b*c - a*d)*(a + b*x^6))) + (c*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(6*sqrt(a)*(b*c - a*d)^(3/2))]
    @test_int [x^2/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 4, (b*x^3*sqrt(c + d*x^6))/(6*a*(b*c - a*d)*(a + b*x^6)) + ((b*c - 2*a*d)*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(6*a^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^4*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 6, -(((3*b*c - 2*a*d)*sqrt(c + d*x^6))/(6*a^2*c*(b*c - a*d)*x^3)) + (b*sqrt(c + d*x^6))/(6*a*(b*c - a*d)*x^3*(a + b*x^6)) - (b*(3*b*c - 4*a*d)*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(6*a^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^10*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 7, -(((5*b*c - 2*a*d)*sqrt(c + d*x^6))/(18*a^2*c*(b*c - a*d)*x^9)) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*sqrt(c + d*x^6))/(18*a^3*c^2*(b*c - a*d)*x^3) + (b*sqrt(c + d*x^6))/(6*a*(b*c - a*d)*x^9*(a + b*x^6)) + (b^2*(5*b*c - 6*a*d)*atan((sqrt(b*c - a*d)*x^3)/(sqrt(a)*sqrt(c + d*x^6))))/(6*a^(7/2)*(b*c - a*d)^(3/2))]

    @test_int [x^4/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 2, (x^5*sqrt(1 + (d*x^6)/c)*AppellF1(5/6, 2, 1/2, 11/6, -((b*x^6)/a), -((d*x^6)/c)))/(5*a^2*sqrt(c + d*x^6))]
    @test_int [x^3/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 3, (x^4*sqrt(1 + (d*x^6)/c)*AppellF1(2/3, 2, 1/2, 5/3, -((b*x^6)/a), -((d*x^6)/c)))/(4*a^2*sqrt(c + d*x^6))]
    @test_int [x^1/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 3, (x^2*sqrt(1 + (d*x^6)/c)*AppellF1(1/3, 2, 1/2, 4/3, -((b*x^6)/a), -((d*x^6)/c)))/(2*a^2*sqrt(c + d*x^6))]
    @test_int [x^0/((a + b*x^6)^2*sqrt(c + d*x^6)), x, 2, (x*sqrt(1 + (d*x^6)/c)*AppellF1(1/6, 2, 1/2, 7/6, -((b*x^6)/a), -((d*x^6)/c)))/(a^2*sqrt(c + d*x^6))]
    @test_int [1/(x^2*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 2, -((sqrt(1 + (d*x^6)/c)*AppellF1(-(1/6), 2, 1/2, 5/6, -((b*x^6)/a), -((d*x^6)/c)))/(a^2*x*sqrt(c + d*x^6)))]
    @test_int [1/(x^3*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 3, -((sqrt(1 + (d*x^6)/c)*AppellF1(-(1/3), 2, 1/2, 2/3, -((b*x^6)/a), -((d*x^6)/c)))/(2*a^2*x^2*sqrt(c + d*x^6)))]
    @test_int [1/(x^5*(a + b*x^6)^2*sqrt(c + d*x^6)), x, 3, -((sqrt(1 + (d*x^6)/c)*AppellF1(-(2/3), 2, 1/2, 1/3, -((b*x^6)/a), -((d*x^6)/c)))/(4*a^2*x^4*sqrt(c + d*x^6)))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^8)^p*(c+d*x^8)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^8)^p*(c+d*x^8)^(q/2)=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^8)^p*(c+d*x^8)^(1/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^8)^p / (c+d*x^8)^(1/2)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^23/((a + b*x^8)*sqrt(c + d*x^8)), x, 5, -(((b*c + a*d)*sqrt(c + d*x^8))/(4*b^2*d^2)) + (c + d*x^8)^(3/2)/(12*b*d^2) - (a^2*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(4*b^(5/2)*sqrt(b*c - a*d))]
    @test_int [x^15/((a + b*x^8)*sqrt(c + d*x^8)), x, 4, sqrt(c + d*x^8)/(4*b*d) + (a*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(4*b^(3/2)*sqrt(b*c - a*d))]
    @test_int [x^7/((a + b*x^8)*sqrt(c + d*x^8)), x, 3, -(atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d))/(4*sqrt(b)*sqrt(b*c - a*d)))]
    @test_int [1/(x^1*(a + b*x^8)*sqrt(c + d*x^8)), x, 6, -(atanh(sqrt(c + d*x^8)/sqrt(c))/(4*a*sqrt(c))) + (sqrt(b)*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(4*a*sqrt(b*c - a*d))]
    @test_int [1/(x^9*(a + b*x^8)*sqrt(c + d*x^8)), x, 7, -(sqrt(c + d*x^8)/(8*a*c*x^8)) + ((2*b*c + a*d)*atanh(sqrt(c + d*x^8)/sqrt(c)))/(8*a^2*c^(3/2)) - (b^(3/2)*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(4*a^2*sqrt(b*c - a*d))]

    @test_int [x^19/((a + b*x^8)*sqrt(c + d*x^8)), x, 7, (x^4*sqrt(c + d*x^8))/(8*b*d) + (a^(3/2)*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(4*b^2*sqrt(b*c - a*d)) - ((b*c + 2*a*d)*atanh((sqrt(d)*x^4)/sqrt(c + d*x^8)))/(8*b^2*d^(3/2))]
    @test_int [x^11/((a + b*x^8)*sqrt(c + d*x^8)), x, 6, -((sqrt(a)*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(4*b*sqrt(b*c - a*d))) + atanh((sqrt(d)*x^4)/sqrt(c + d*x^8))/(4*b*sqrt(d))]
    @test_int [x^3/((a + b*x^8)*sqrt(c + d*x^8)), x, 3, atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8)))/(4*sqrt(a)*sqrt(b*c - a*d))]
    @test_int [1/(x^5*(a + b*x^8)*sqrt(c + d*x^8)), x, 5, -(sqrt(c + d*x^8)/(4*a*c*x^4)) - (b*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(4*a^(3/2)*sqrt(b*c - a*d))]
    @test_int [1/(x^13*(a + b*x^8)*sqrt(c + d*x^8)), x, 6, -(sqrt(c + d*x^8)/(12*a*c*x^12)) + ((3*b*c + 2*a*d)*sqrt(c + d*x^8))/(12*a^2*c^2*x^4) + (b^2*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(4*a^(5/2)*sqrt(b*c - a*d))]

    @test_int [x^9/((a + b*x^8)*sqrt(c + d*x^8)), x, 10, -(((-a)^(1/4)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*b^(3/4)*sqrt(b*c - a*d))) - ((-a)^(1/4)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*b^(3/4)*sqrt((-b)*c + a*d)) + ((sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(4*b*c^(1/4)*d^(1/4)*sqrt(c + d*x^8)) - (a*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8))]
    @test_int [x^1/((a + b*x^8)*sqrt(c + d*x^8)), x, 8, -((b^(1/4)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(3/4)*sqrt(b*c - a*d))) - (b^(1/4)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(3/4)*sqrt((-b)*c + a*d)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8))]
    @test_int [1/(x^7*(a + b*x^8)*sqrt(c + d*x^8)), x, 11, -(sqrt(c + d*x^8)/(6*a*c*x^6)) - (b^(5/4)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(7/4)*sqrt(b*c - a*d)) - (b^(5/4)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(7/4)*sqrt((-b)*c + a*d)) - (d^(3/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(12*a*c^(5/4)*sqrt(c + d*x^8)) - (b*((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a^2*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8))]

    @test_int [x^13/((a + b*x^8)*sqrt(c + d*x^8)), x, 12, (x^2*sqrt(c + d*x^8))/(2*b*sqrt(d)*(sqrt(c) + sqrt(d)*x^4)) + ((-a)^(3/4)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*b^(5/4)*sqrt(b*c - a*d)) - ((-a)^(3/4)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*b^(5/4)*sqrt((-b)*c + a*d)) - (c^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(2*b*d^(3/4)*sqrt(c + d*x^8)) + (c^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(4*b*d^(3/4)*sqrt(c + d*x^8)) + (a*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + (a*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*b*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + (sqrt(-a)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - (sqrt(-a)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8))]
    @test_int [x^5/((a + b*x^8)*sqrt(c + d*x^8)), x, 8, atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8)))/(8*(-a)^(1/4)*b^(1/4)*sqrt(b*c - a*d)) - atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8)))/(8*(-a)^(1/4)*b^(1/4)*sqrt((-b)*c + a*d)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*sqrt(-a)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*sqrt(-a)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8))]
    @test_int [1/(x^3*(a + b*x^8)*sqrt(c + d*x^8)), x, 14, If(13>=8, -(sqrt(c + d*x^8)/(2*a*c*x^2)) + (sqrt(d)*x^2*sqrt(c + d*x^8))/(2*a*c*(sqrt(c) + sqrt(d)*x^4)) + (b^(3/4)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(5/4)*sqrt(b*c - a*d)) - (b^(3/4)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(5/4)*sqrt((-b)*c + a*d)) - (d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(2*a*c^(3/4)*sqrt(c + d*x^8)) + (d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(4*a*c^(3/4)*sqrt(c + d*x^8)) + (b*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + (b*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + (sqrt(b)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - (sqrt(b)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)), -(sqrt(c + d*x^8)/(2*a*c*x^2)) + (sqrt(d)*x^2*sqrt(c + d*x^8))/(2*a*c*(sqrt(c) + sqrt(d)*x^4)) + (b^(3/4)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(5/4)*sqrt(b*c - a*d)) - (b^(3/4)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(8*(-a)^(5/4)*sqrt((-b)*c + a*d)) - (d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(2*a*c^(3/4)*sqrt(c + d*x^8)) + (d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(4*a*c^(3/4)*sqrt(c + d*x^8)) + (b*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + (b*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*c^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) + (sqrt(b)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)) - (sqrt(b)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*sqrt(c + d*x^8)))]

    @test_int [x^4/((a + b*x^8)*sqrt(c + d*x^8)), x, 2, (x^5*sqrt(1 + (d*x^8)/c)*AppellF1(5/8, 1, 1/2, 13/8, -((b*x^8)/a), -((d*x^8)/c)))/(5*a*sqrt(c + d*x^8))]
    @test_int [x^2/((a + b*x^8)*sqrt(c + d*x^8)), x, 2, (x^3*sqrt(1 + (d*x^8)/c)*AppellF1(3/8, 1, 1/2, 11/8, -((b*x^8)/a), -((d*x^8)/c)))/(3*a*sqrt(c + d*x^8))]
    @test_int [x^0/((a + b*x^8)*sqrt(c + d*x^8)), x, 2, (x*sqrt(1 + (d*x^8)/c)*AppellF1(1/8, 1, 1/2, 9/8, -((b*x^8)/a), -((d*x^8)/c)))/(a*sqrt(c + d*x^8))]
    @test_int [1/(x^2*(a + b*x^8)*sqrt(c + d*x^8)), x, 2, -((sqrt(1 + (d*x^8)/c)*AppellF1(-(1/8), 1, 1/2, 7/8, -((b*x^8)/a), -((d*x^8)/c)))/(a*x*sqrt(c + d*x^8)))]
    @test_int [1/(x^4*(a + b*x^8)*sqrt(c + d*x^8)), x, 2, -((sqrt(1 + (d*x^8)/c)*AppellF1(-(3/8), 1, 1/2, 5/8, -((b*x^8)/a), -((d*x^8)/c)))/(3*a*x^3*sqrt(c + d*x^8)))]

    @test_int [x^23/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 5, sqrt(c + d*x^8)/(4*b^2*d) - (a^2*sqrt(c + d*x^8))/(8*b^2*(b*c - a*d)*(a + b*x^8)) + (a*(4*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(8*b^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [x^15/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 4, (a*sqrt(c + d*x^8))/(8*b*(b*c - a*d)*(a + b*x^8)) - ((2*b*c - a*d)*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(8*b^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [x^7/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 4, -(sqrt(c + d*x^8)/(8*(b*c - a*d)*(a + b*x^8))) + (d*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(8*sqrt(b)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^1*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 7, (b*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*(a + b*x^8)) - atanh(sqrt(c + d*x^8)/sqrt(c))/(4*a^2*sqrt(c)) + (sqrt(b)*(2*b*c - 3*a*d)*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(8*a^2*(b*c - a*d)^(3/2))]
    @test_int [1/(x^9*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 8, -((b*(2*b*c - a*d)*sqrt(c + d*x^8))/(8*a^2*c*(b*c - a*d)*(a + b*x^8))) - sqrt(c + d*x^8)/(8*a*c*x^8*(a + b*x^8)) + ((4*b*c + a*d)*atanh(sqrt(c + d*x^8)/sqrt(c)))/(8*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*atanh((sqrt(b)*sqrt(c + d*x^8))/sqrt(b*c - a*d)))/(8*a^3*(b*c - a*d)^(3/2))]

    @test_int [x^19/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 7, (a*x^4*sqrt(c + d*x^8))/(8*b*(b*c - a*d)*(a + b*x^8)) - (sqrt(a)*(3*b*c - 2*a*d)*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(8*b^2*(b*c - a*d)^(3/2)) + atanh((sqrt(d)*x^4)/sqrt(c + d*x^8))/(4*b^2*sqrt(d))]
    @test_int [x^11/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 5, -((x^4*sqrt(c + d*x^8))/(8*(b*c - a*d)*(a + b*x^8))) + (c*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(8*sqrt(a)*(b*c - a*d)^(3/2))]
    @test_int [x^3/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 4, (b*x^4*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*(a + b*x^8)) + ((b*c - 2*a*d)*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(8*a^(3/2)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^5*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 6, -(((3*b*c - 2*a*d)*sqrt(c + d*x^8))/(8*a^2*c*(b*c - a*d)*x^4)) + (b*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*x^4*(a + b*x^8)) - (b*(3*b*c - 4*a*d)*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(8*a^(5/2)*(b*c - a*d)^(3/2))]
    @test_int [1/(x^13*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 7, -(((5*b*c - 2*a*d)*sqrt(c + d*x^8))/(24*a^2*c*(b*c - a*d)*x^12)) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*sqrt(c + d*x^8))/(24*a^3*c^2*(b*c - a*d)*x^4) + (b*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*x^12*(a + b*x^8)) + (b^2*(5*b*c - 6*a*d)*atan((sqrt(b*c - a*d)*x^4)/(sqrt(a)*sqrt(c + d*x^8))))/(8*a^(7/2)*(b*c - a*d)^(3/2))]

    @test_int [x^9/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 11, -((x^2*sqrt(c + d*x^8))/(8*(b*c - a*d)*(a + b*x^8))) - ((b*c + a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(3/4)*b^(3/4)*(b*c - a*d)^(3/2)) + ((b*c + a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(3/4)*b^(3/4)*((-b)*c + a*d)^(3/2)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*b*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^8)) + ((sqrt(-a)*sqrt(b)*sqrt(c) + a*sqrt(d))*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a*b*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^8)) - (d^(3/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*sqrt(c + d*x^8))]
    @test_int [x^1/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 11, If(13>=8, (b*x^2*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*(a + b*x^8)) + (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(7/4)*(b*c - a*d)^(3/2)) - (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(7/4)*((-b)*c + a*d)^(3/2)) + (d^(3/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^8)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*(-a)^(3/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)), (b*x^2*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*(a + b*x^8)) + (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(7/4)*(b*c - a*d)^(3/2)) - (b^(1/4)*(3*b*c - 5*a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(7/4)*((-b)*c + a*d)^(3/2)) + (d^(3/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a*c^(1/4)*(b*c - a*d)*sqrt(c + d*x^8)) + (((sqrt(b)*sqrt(c))/sqrt(-a) + sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*(-a)^(3/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^2*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - 5*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^2*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^8)))]
    @test_int [1/(x^7*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 12, If(13>=8, -(((7*b*c - 4*a*d)*sqrt(c + d*x^8))/(24*a^2*c*(b*c - a*d)*x^6)) + (b*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*x^6*(a + b*x^8)) + (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(11/4)*(b*c - a*d)^(3/2)) - (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(11/4)*((-b)*c + a*d)^(3/2)) - (d^(3/4)*(7*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(48*a^2*c^(5/4)*(b*c - a*d)*sqrt(c + d*x^8)) + (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)), -(((7*b*c - 4*a*d)*sqrt(c + d*x^8))/(24*a^2*c*(b*c - a*d)*x^6)) + (b*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*x^6*(a + b*x^8)) + (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(11/4)*(b*c - a*d)^(3/2)) - (b^(5/4)*(7*b*c - 9*a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(11/4)*((-b)*c + a*d)^(3/2)) - (d^(3/4)*(7*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(48*a^2*c^(5/4)*(b*c - a*d)*sqrt(c + d*x^8)) + (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^3*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^8)) - (b*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(7*b*c - 9*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*a^3*c^(1/4)*d^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^8)))]

    @test_int [x^13/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 14, If(13>=8, (sqrt(d)*x^2*sqrt(c + d*x^8))/(8*b*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)) - (x^6*sqrt(c + d*x^8))/(8*(b*c - a*d)*(a + b*x^8)) + ((3*b*c - a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(1/4)*b^(5/4)*(b*c - a*d)^(3/2)) + ((3*b*c - a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(1/4)*b^(5/4)*((-b)*c + a*d)^(3/2)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*b*(b*c - a*d)*sqrt(c + d*x^8)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b*(b*c - a*d)*sqrt(c + d*x^8)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)), (sqrt(d)*x^2*sqrt(c + d*x^8))/(8*b*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)) - (x^6*sqrt(c + d*x^8))/(8*(b*c - a*d)*(a + b*x^8)) + ((3*b*c - a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(1/4)*b^(5/4)*(b*c - a*d)^(3/2)) + ((3*b*c - a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(1/4)*b^(5/4)*((-b)*c + a*d)^(3/2)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*b*(b*c - a*d)*sqrt(c + d*x^8)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*b*(b*c - a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*b^(3/2)*c^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))*d^(1/4)*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*b^(3/2)*c^(1/4)*(b^2*c^2 - a^2*d^2)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(3*b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*sqrt(-a)*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)))]
    @test_int [x^5/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 14, -((sqrt(d)*x^2*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^4))) + (b*x^6*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*(a + b*x^8)) - ((b*c - 3*a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(5/4)*b^(1/4)*(b*c - a*d)^(3/2)) - ((b*c - 3*a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(5/4)*b^(1/4)*((-b)*c + a*d)^(3/2)) + (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a*(b*c - a*d)*sqrt(c + d*x^8)) - (c^(1/4)*d^(1/4)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a*(b*c - a*d)*sqrt(c + d*x^8)) - ((sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - ((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*(-a)^(3/2)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + ((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(b*c - 3*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*(-a)^(3/2)*sqrt(b)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8))]
    @test_int [1/(x^3*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 15, -(((5*b*c - 4*a*d)*sqrt(c + d*x^8))/(8*a^2*c*(b*c - a*d)*x^2)) + (sqrt(d)*(5*b*c - 4*a*d)*x^2*sqrt(c + d*x^8))/(8*a^2*c*(b*c - a*d)*(sqrt(c) + sqrt(d)*x^4)) + (b*sqrt(c + d*x^8))/(8*a*(b*c - a*d)*x^2*(a + b*x^8)) - (b^(3/4)*(5*b*c - 7*a*d)*atan((sqrt(b*c - a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(9/4)*(b*c - a*d)^(3/2)) - (b^(3/4)*(5*b*c - 7*a*d)*atan((sqrt((-b)*c + a*d)*x^2)/((-a)^(1/4)*b^(1/4)*sqrt(c + d*x^8))))/(32*(-a)^(9/4)*((-b)*c + a*d)^(3/2)) - (d^(1/4)*(5*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.E(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(8*a^2*c^(3/4)*(b*c - a*d)*sqrt(c + d*x^8)) + (d^(1/4)*(5*b*c - 4*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(16*a^2*c^(3/4)*(b*c - a*d)*sqrt(c + d*x^8)) + (b*(sqrt(c) - (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + (b*(sqrt(c) + (sqrt(-a)*sqrt(d))/sqrt(b))*d^(1/4)*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.F(2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(32*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) - (sqrt(b)*(sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi(-((sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d))), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8)) + (sqrt(b)*(sqrt(b)*sqrt(c) - sqrt(-a)*sqrt(d))^2*(5*b*c - 7*a*d)*(sqrt(c) + sqrt(d)*x^4)*sqrt((c + d*x^8)/(sqrt(c) + sqrt(d)*x^4)^2)*Elliptic.Pi((sqrt(b)*sqrt(c) + sqrt(-a)*sqrt(d))^2/(4*sqrt(-a)*sqrt(b)*sqrt(c)*sqrt(d)), 2*atan((d^(1/4)*x^2)/c^(1/4)), 1/2))/(64*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*sqrt(c + d*x^8))]

    @test_int [x^4/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 2, (x^5*sqrt(1 + (d*x^8)/c)*AppellF1(5/8, 2, 1/2, 13/8, -((b*x^8)/a), -((d*x^8)/c)))/(5*a^2*sqrt(c + d*x^8))]
    @test_int [x^2/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 2, (x^3*sqrt(1 + (d*x^8)/c)*AppellF1(3/8, 2, 1/2, 11/8, -((b*x^8)/a), -((d*x^8)/c)))/(3*a^2*sqrt(c + d*x^8))]
    @test_int [x^0/((a + b*x^8)^2*sqrt(c + d*x^8)), x, 2, (x*sqrt(1 + (d*x^8)/c)*AppellF1(1/8, 2, 1/2, 9/8, -((b*x^8)/a), -((d*x^8)/c)))/(a^2*sqrt(c + d*x^8))]
    @test_int [1/(x^2*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 2, -((sqrt(1 + (d*x^8)/c)*AppellF1(-(1/8), 2, 1/2, 7/8, -((b*x^8)/a), -((d*x^8)/c)))/(a^2*x*sqrt(c + d*x^8)))]
    @test_int [1/(x^4*(a + b*x^8)^2*sqrt(c + d*x^8)), x, 2, -((sqrt(1 + (d*x^8)/c)*AppellF1(-(3/8), 2, 1/2, 5/8, -((b*x^8)/a), -((d*x^8)/c)))/(3*a^2*x^3*sqrt(c + d*x^8)))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b/x^2)^p*(c+d/x^2)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b/x^2)^p*(c+d/x^2)^(q/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b/x^2)^1*(c+d/x^2)^(q/2)=#

    #= ::Subsubsection::Closed:: =#
    #=q>0=#

    @test_int [x^5*(a + b/x^2)*sqrt(c + d/x^2), x, 6, (d*(2*b*c - a*d)*sqrt(c + d/x^2)*x^2)/(16*c^2) + ((2*b*c - a*d)*sqrt(c + d/x^2)*x^4)/(8*c) + (a*(c + d/x^2)^(3/2)*x^6)/(6*c) - (d^2*(2*b*c - a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(16*c^(5/2))]
    @test_int [x^3*(a + b/x^2)*sqrt(c + d/x^2), x, 5, ((4*b*c - a*d)*sqrt(c + d/x^2)*x^2)/(8*c) + (a*(c + d/x^2)^(3/2)*x^4)/(4*c) + (d*(4*b*c - a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(8*c^(3/2))]
    @test_int [x^1*(a + b/x^2)*sqrt(c + d/x^2), x, 5, -(((2*b*c + a*d)*sqrt(c + d/x^2))/(2*c)) + (a*(c + d/x^2)^(3/2)*x^2)/(2*c) + ((2*b*c + a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(2*sqrt(c))]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^1, x, 5, (-a)*sqrt(c + d/x^2) - (b*(c + d/x^2)^(3/2))/(3*d) + a*sqrt(c)*atanh(sqrt(c + d/x^2)/sqrt(c))]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^3, x, 3, ((b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^2) - (b*(c + d/x^2)^(5/2))/(5*d^2)]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^5, x, 3, -((c*(b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^3)) + ((2*b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^3) - (b*(c + d/x^2)^(7/2))/(7*d^3)]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^7, x, 3, (c^2*(b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^4) - (c*(3*b*c - 2*a*d)*(c + d/x^2)^(5/2))/(5*d^4) + ((3*b*c - a*d)*(c + d/x^2)^(7/2))/(7*d^4) - (b*(c + d/x^2)^(9/2))/(9*d^4)]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^9, x, 3, -((c^3*(b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^5)) + (c^2*(4*b*c - 3*a*d)*(c + d/x^2)^(5/2))/(5*d^5) - (3*c*(2*b*c - a*d)*(c + d/x^2)^(7/2))/(7*d^5) + ((4*b*c - a*d)*(c + d/x^2)^(9/2))/(9*d^5) - (b*(c + d/x^2)^(11/2))/(11*d^5)]

    @test_int [x^10*(a + b/x^2)*sqrt(c + d/x^2), x, 5, -((16*d^3*(11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^3)/(3465*c^5)) + (8*d^2*(11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^5)/(1155*c^4) - (2*d*(11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^7)/(231*c^3) + ((11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^9)/(99*c^2) + (a*(c + d/x^2)^(3/2)*x^11)/(11*c)]
    @test_int [x^8*(a + b/x^2)*sqrt(c + d/x^2), x, 4, (8*d^2*(3*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^3)/(315*c^4) - (4*d*(3*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^5)/(105*c^3) + ((3*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^7)/(21*c^2) + (a*(c + d/x^2)^(3/2)*x^9)/(9*c)]
    @test_int [x^6*(a + b/x^2)*sqrt(c + d/x^2), x, 3, -((2*d*(7*b*c - 4*a*d)*(c + d/x^2)^(3/2)*x^3)/(105*c^3)) + ((7*b*c - 4*a*d)*(c + d/x^2)^(3/2)*x^5)/(35*c^2) + (a*(c + d/x^2)^(3/2)*x^7)/(7*c)]
    @test_int [x^4*(a + b/x^2)*sqrt(c + d/x^2), x, 2, ((5*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^3)/(15*c^2) + (a*(c + d/x^2)^(3/2)*x^5)/(5*c)]
    @test_int [x^2*(a + b/x^2)*sqrt(c + d/x^2), x, 5, b*sqrt(c + d/x^2)*x + (a*(c + d/x^2)^(3/2)*x^3)/(3*c) - b*sqrt(d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x))]
    @test_int [x^0*(a + b/x^2)*sqrt(c + d/x^2), x, 5, -(((b*c + 2*a*d)*sqrt(c + d/x^2))/(2*c*x)) + (a*(c + d/x^2)^(3/2)*x)/c - ((b*c + 2*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(2*sqrt(d))]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^2, x, 5, ((b*c - 4*a*d)*sqrt(c + d/x^2))/(8*d*x) - (b*(c + d/x^2)^(3/2))/(4*d*x) + (c*(b*c - 4*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(8*d^(3/2))]
    @test_int [(a + b/x^2)*sqrt(c + d/x^2)/x^4, x, 6, ((b*c - 2*a*d)*sqrt(c + d/x^2))/(8*d*x^3) - (b*(c + d/x^2)^(3/2))/(6*d*x^3) + (c*(b*c - 2*a*d)*sqrt(c + d/x^2))/(16*d^2*x) - (c^2*(b*c - 2*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(16*d^(5/2))]

    @test_int [x^5*(a + b/x^2)*(c + d/x^2)^(3/2), x, 6, (d*(6*b*c - a*d)*sqrt(c + d/x^2)*x^2)/(16*c) + ((6*b*c - a*d)*(c + d/x^2)^(3/2)*x^4)/(24*c) + (a*(c + d/x^2)^(5/2)*x^6)/(6*c) + (d^2*(6*b*c - a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(16*c^(3/2))]
    @test_int [x^3*(a + b/x^2)*(c + d/x^2)^(3/2), x, 6, -((3*d*(4*b*c + a*d)*sqrt(c + d/x^2))/(8*c)) + ((4*b*c + a*d)*(c + d/x^2)^(3/2)*x^2)/(8*c) + (a*(c + d/x^2)^(5/2)*x^4)/(4*c) + (3*d*(4*b*c + a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(8*sqrt(c))]
    @test_int [x^1*(a + b/x^2)*(c + d/x^2)^(3/2), x, 6, (-(1/2))*(2*b*c + 3*a*d)*sqrt(c + d/x^2) - ((2*b*c + 3*a*d)*(c + d/x^2)^(3/2))/(6*c) + (a*(c + d/x^2)^(5/2)*x^2)/(2*c) + (1/2)*sqrt(c)*(2*b*c + 3*a*d)*atanh(sqrt(c + d/x^2)/sqrt(c))]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^1, x, 6, (-a)*c*sqrt(c + d/x^2) - (1/3)*a*(c + d/x^2)^(3/2) - (b*(c + d/x^2)^(5/2))/(5*d) + a*c^(3/2)*atanh(sqrt(c + d/x^2)/sqrt(c))]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^3, x, 3, ((b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^2) - (b*(c + d/x^2)^(7/2))/(7*d^2)]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^5, x, 3, -((c*(b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^3)) + ((2*b*c - a*d)*(c + d/x^2)^(7/2))/(7*d^3) - (b*(c + d/x^2)^(9/2))/(9*d^3)]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^7, x, 3, (c^2*(b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^4) - (c*(3*b*c - 2*a*d)*(c + d/x^2)^(7/2))/(7*d^4) + ((3*b*c - a*d)*(c + d/x^2)^(9/2))/(9*d^4) - (b*(c + d/x^2)^(11/2))/(11*d^4)]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^9, x, 3, -((c^3*(b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^5)) + (c^2*(4*b*c - 3*a*d)*(c + d/x^2)^(7/2))/(7*d^5) - (c*(2*b*c - a*d)*(c + d/x^2)^(9/2))/(3*d^5) + ((4*b*c - a*d)*(c + d/x^2)^(11/2))/(11*d^5) - (b*(c + d/x^2)^(13/2))/(13*d^5)]

    @test_int [x^12*(a + b/x^2)*(c + d/x^2)^(3/2), x, 5, -((16*d^3*(13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^5)/(15015*c^5)) + (8*d^2*(13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^7)/(3003*c^4) - (2*d*(13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^9)/(429*c^3) + ((13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^11)/(143*c^2) + (a*(c + d/x^2)^(5/2)*x^13)/(13*c)]
    @test_int [x^10*(a + b/x^2)*(c + d/x^2)^(3/2), x, 4, (8*d^2*(11*b*c - 6*a*d)*(c + d/x^2)^(5/2)*x^5)/(3465*c^4) - (4*d*(11*b*c - 6*a*d)*(c + d/x^2)^(5/2)*x^7)/(693*c^3) + ((11*b*c - 6*a*d)*(c + d/x^2)^(5/2)*x^9)/(99*c^2) + (a*(c + d/x^2)^(5/2)*x^11)/(11*c)]
    @test_int [x^8*(a + b/x^2)*(c + d/x^2)^(3/2), x, 3, -((2*d*(9*b*c - 4*a*d)*(c + d/x^2)^(5/2)*x^5)/(315*c^3)) + ((9*b*c - 4*a*d)*(c + d/x^2)^(5/2)*x^7)/(63*c^2) + (a*(c + d/x^2)^(5/2)*x^9)/(9*c)]
    @test_int [x^6*(a + b/x^2)*(c + d/x^2)^(3/2), x, 2, ((7*b*c - 2*a*d)*(c + d/x^2)^(5/2)*x^5)/(35*c^2) + (a*(c + d/x^2)^(5/2)*x^7)/(7*c)]
    @test_int [x^4*(a + b/x^2)*(c + d/x^2)^(3/2), x, 6, b*d*sqrt(c + d/x^2)*x + (1/3)*b*(c + d/x^2)^(3/2)*x^3 + (a*(c + d/x^2)^(5/2)*x^5)/(5*c) - b*d^(3/2)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x))]
    @test_int [x^2*(a + b/x^2)*(c + d/x^2)^(3/2), x, 6, -((d*(3*b*c + 2*a*d)*sqrt(c + d/x^2))/(2*c*x)) + ((3*b*c + 2*a*d)*(c + d/x^2)^(3/2)*x)/(3*c) + (a*(c + d/x^2)^(5/2)*x^3)/(3*c) - (1/2)*sqrt(d)*(3*b*c + 2*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x))]
    @test_int [x^0*(a + b/x^2)*(c + d/x^2)^(3/2), x, 6, -((3*(b*c + 4*a*d)*sqrt(c + d/x^2))/(8*x)) - ((b*c + 4*a*d)*(c + d/x^2)^(3/2))/(4*c*x) + (a*(c + d/x^2)^(5/2)*x)/c - (3*c*(b*c + 4*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(8*sqrt(d))]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^2, x, 6, (c*(b*c - 6*a*d)*sqrt(c + d/x^2))/(16*d*x) + ((b*c - 6*a*d)*(c + d/x^2)^(3/2))/(24*d*x) - (b*(c + d/x^2)^(5/2))/(6*d*x) + (c^2*(b*c - 6*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(16*d^(3/2))]
    @test_int [(a + b/x^2)*(c + d/x^2)^(3/2)/x^4, x, 7, (c*(3*b*c - 8*a*d)*sqrt(c + d/x^2))/(64*d*x^3) + ((3*b*c - 8*a*d)*(c + d/x^2)^(3/2))/(48*d*x^3) - (b*(c + d/x^2)^(5/2))/(8*d*x^3) + (c^2*(3*b*c - 8*a*d)*sqrt(c + d/x^2))/(128*d^2*x) - (c^3*(3*b*c - 8*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(128*d^(5/2))]

    #= ::Subsubsection::Closed:: =#
    #=q<0=#

    @test_int [x^3*(a + b/x^2)/sqrt(c + d/x^2), x, 5, ((4*b*c - 3*a*d)*sqrt(c + d/x^2)*x^2)/(8*c^2) + (a*sqrt(c + d/x^2)*x^4)/(4*c) - (d*(4*b*c - 3*a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(8*c^(5/2))]
    @test_int [x^1*(a + b/x^2)/sqrt(c + d/x^2), x, 4, (a*sqrt(c + d/x^2)*x^2)/(2*c) + ((2*b*c - a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(2*c^(3/2))]
    @test_int [(a + b/x^2)/(x^1*sqrt(c + d/x^2)), x, 4, -((b*sqrt(c + d/x^2))/d) + (a*atanh(sqrt(c + d/x^2)/sqrt(c)))/sqrt(c)]
    @test_int [(a + b/x^2)/(x^3*sqrt(c + d/x^2)), x, 3, ((b*c - a*d)*sqrt(c + d/x^2))/d^2 - (b*(c + d/x^2)^(3/2))/(3*d^2)]
    @test_int [(a + b/x^2)/(x^5*sqrt(c + d/x^2)), x, 3, -((c*(b*c - a*d)*sqrt(c + d/x^2))/d^3) + ((2*b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^3) - (b*(c + d/x^2)^(5/2))/(5*d^3)]
    @test_int [(a + b/x^2)/(x^7*sqrt(c + d/x^2)), x, 3, (c^2*(b*c - a*d)*sqrt(c + d/x^2))/d^4 - (c*(3*b*c - 2*a*d)*(c + d/x^2)^(3/2))/(3*d^4) + ((3*b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^4) - (b*(c + d/x^2)^(7/2))/(7*d^4)]

    @test_int [x^4*(a + b/x^2)/sqrt(c + d/x^2), x, 3, -((2*d*(5*b*c - 4*a*d)*sqrt(c + d/x^2)*x)/(15*c^3)) + ((5*b*c - 4*a*d)*sqrt(c + d/x^2)*x^3)/(15*c^2) + (a*sqrt(c + d/x^2)*x^5)/(5*c)]
    @test_int [x^2*(a + b/x^2)/sqrt(c + d/x^2), x, 2, ((3*b*c - 2*a*d)*sqrt(c + d/x^2)*x)/(3*c^2) + (a*sqrt(c + d/x^2)*x^3)/(3*c)]
    @test_int [x^0*(a + b/x^2)/sqrt(c + d/x^2), x, 4, (a*sqrt(c + d/x^2)*x)/c - (b*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/sqrt(d)]
    @test_int [(a + b/x^2)/(x^2*sqrt(c + d/x^2)), x, 4, -((b*sqrt(c + d/x^2))/(2*d*x)) + ((b*c - 2*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(2*d^(3/2))]
    @test_int [(a + b/x^2)/(x^4*sqrt(c + d/x^2)), x, 5, -((b*sqrt(c + d/x^2))/(4*d*x^3)) + ((3*b*c - 4*a*d)*sqrt(c + d/x^2))/(8*d^2*x) - (c*(3*b*c - 4*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(8*d^(5/2))]

    @test_int [x^3*(a + b/x^2)/(c + d/x^2)^(3/2), x, 6, (3*d*(4*b*c - 5*a*d))/(8*c^3*sqrt(c + d/x^2)) + ((4*b*c - 5*a*d)*x^2)/(8*c^2*sqrt(c + d/x^2)) + (a*x^4)/(4*c*sqrt(c + d/x^2)) - (3*d*(4*b*c - 5*a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(8*c^(7/2))]
    @test_int [x^1*(a + b/x^2)/(c + d/x^2)^(3/2), x, 5, -((2*b*c - 3*a*d)/(2*c^2*sqrt(c + d/x^2))) + (a*x^2)/(2*c*sqrt(c + d/x^2)) + ((2*b*c - 3*a*d)*atanh(sqrt(c + d/x^2)/sqrt(c)))/(2*c^(5/2))]
    @test_int [(a + b/x^2)/(x^1*(c + d/x^2)^(3/2)), x, 4, (b*c - a*d)/(c*d*sqrt(c + d/x^2)) + (a*atanh(sqrt(c + d/x^2)/sqrt(c)))/c^(3/2)]
    @test_int [(a + b/x^2)/(x^3*(c + d/x^2)^(3/2)), x, 3, -((b*c - a*d)/(d^2*sqrt(c + d/x^2))) - (b*sqrt(c + d/x^2))/d^2]
    @test_int [(a + b/x^2)/(x^5*(c + d/x^2)^(3/2)), x, 3, (c*(b*c - a*d))/(d^3*sqrt(c + d/x^2)) + ((2*b*c - a*d)*sqrt(c + d/x^2))/d^3 - (b*(c + d/x^2)^(3/2))/(3*d^3)]
    @test_int [(a + b/x^2)/(x^7*(c + d/x^2)^(3/2)), x, 3, -((c^2*(b*c - a*d))/(d^4*sqrt(c + d/x^2))) - (c*(3*b*c - 2*a*d)*sqrt(c + d/x^2))/d^4 + ((3*b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^4) - (b*(c + d/x^2)^(5/2))/(5*d^4)]
    @test_int [(a + b/x^2)/(x^9*(c + d/x^2)^(3/2)), x, 3, (c^3*(b*c - a*d))/(d^5*sqrt(c + d/x^2)) + (c^2*(4*b*c - 3*a*d)*sqrt(c + d/x^2))/d^5 - (c*(2*b*c - a*d)*(c + d/x^2)^(3/2))/d^5 + ((4*b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^5) - (b*(c + d/x^2)^(7/2))/(7*d^5)]

    @test_int [x^4*(a + b/x^2)/(c + d/x^2)^(3/2), x, 4, (4*d*(5*b*c - 6*a*d)*x)/(15*c^3*sqrt(c + d/x^2)) - (8*d*(5*b*c - 6*a*d)*sqrt(c + d/x^2)*x)/(15*c^4) + ((5*b*c - 6*a*d)*x^3)/(15*c^2*sqrt(c + d/x^2)) + (a*x^5)/(5*c*sqrt(c + d/x^2))]
    @test_int [x^2*(a + b/x^2)/(c + d/x^2)^(3/2), x, 3, -(((3*b*c - 4*a*d)*x)/(3*c^2*sqrt(c + d/x^2))) + (2*(3*b*c - 4*a*d)*sqrt(c + d/x^2)*x)/(3*c^3) + (a*x^3)/(3*c*sqrt(c + d/x^2))]
    @test_int [x^0*(a + b/x^2)/(c + d/x^2)^(3/2), x, 3, -((b*c - 2*a*d)/(c^2*sqrt(c + d/x^2)*x)) + (a*x)/(c*sqrt(c + d/x^2))]
    @test_int [(a + b/x^2)/(x^2*(c + d/x^2)^(3/2)), x, 4, (b*c - a*d)/(c*d*sqrt(c + d/x^2)*x) - (b*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/d^(3/2)]
    @test_int [(a + b/x^2)/(x^4*(c + d/x^2)^(3/2)), x, 5, -(b/(2*d*sqrt(c + d/x^2)*x^3)) - (3*b*c - 2*a*d)/(2*d^2*sqrt(c + d/x^2)*x) + ((3*b*c - 2*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(2*d^(5/2))]
    @test_int [(a + b/x^2)/(x^6*(c + d/x^2)^(3/2)), x, 6, -(b/(4*d*sqrt(c + d/x^2)*x^5)) - (5*b*c - 4*a*d)/(4*d^2*sqrt(c + d/x^2)*x^3) + (3*(5*b*c - 4*a*d)*sqrt(c + d/x^2))/(8*d^3*x) - (3*c*(5*b*c - 4*a*d)*atanh(sqrt(d)/(sqrt(c + d/x^2)*x)))/(8*d^(7/2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b/x^2)^p*(c+d/x^2)^q*with*p*and/or*q*symbolic=#

    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^m, x, 4, ((a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(m + 1)*AppellF1((1/2)*(-1 - m), -p, -q, (1 - m)/2, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(e*(1 + m))), ((a + b/x^2)^p*(c + d/x^2)^q*x*(e*x)^m*AppellF1((1/2)*(-1 - m), -p, -q, (1 - m)/2, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(1 + m))]

    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*x^4, x, 4, ((1/5)*(a + b/x^2)^p*(c + d/x^2)^q*x^5*AppellF1(-(5/2), -p, -q, -(3/2), -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*x^3, x, 3, (b^2*(a + b/x^2)^(1 + p)*(c + d/x^2)^q*AppellF1(1 + p, -q, 3, 2 + p, -((d*(a + b/x^2))/(b*c - a*d)), (a + b/x^2)/a))/(((b*(c + d/x^2))/(b*c - a*d))^q*(2*a^3*(1 + p)))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*x^2, x, 4, ((1/3)*(a + b/x^2)^p*(c + d/x^2)^q*x^3*AppellF1(-(3/2), -p, -q, -(1/2), -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*x^1, x, 3, -((b*(a + b/x^2)^(1 + p)*(c + d/x^2)^q*AppellF1(1 + p, -q, 2, 2 + p, -((d*(a + b/x^2))/(b*c - a*d)), (a + b/x^2)/a))/(((b*(c + d/x^2))/(b*c - a*d))^q*(2*a^2*(1 + p))))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*x^0, x, 4, ((a + b/x^2)^p*(c + d/x^2)^q*x*AppellF1(-(1/2), -p, -q, 1/2, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/x^1, x, 3, ((a + b/x^2)^(1 + p)*(c + d/x^2)^q*AppellF1(1 + p, -q, 1, 2 + p, -((d*(a + b/x^2))/(b*c - a*d)), (a + b/x^2)/a))/(((b*(c + d/x^2))/(b*c - a*d))^q*(2*a*(1 + p)))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/x^2, x, 4, -(((a + b/x^2)^p*(c + d/x^2)^q*AppellF1(1/2, -p, -q, 3/2, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*x))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/x^3, x, 3, -(((a + b/x^2)^(1 + p)*(c + d/x^2)^q*HypergeometricFunctions._₂F₁(1 + p, -q, 2 + p, -((d*(a + b/x^2))/(b*c - a*d))))/(((b*(c + d/x^2))/(b*c - a*d))^q*(2*b*(1 + p))))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/x^4, x, 4, -(((a + b/x^2)^p*(c + d/x^2)^q*AppellF1(3/2, -p, -q, 5/2, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(3*x^3)))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b/x^2)^p*(c+d/x^2)^q*with*p*and/or*q*symbolic=#

    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(5/2), x, 4, (2*(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(7/2)*AppellF1(-(7/4), -p, -q, -(3/4), -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(7*e))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(3/2), x, 4, (2*(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(5/2)*AppellF1(-(5/4), -p, -q, -(1/4), -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(5*e))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(1/2), x, 4, (2*(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(3/2)*AppellF1(-(3/4), -p, -q, 1/4, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(3*e))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/(e*x)^(1/2), x, 4, (2*(a + b/x^2)^p*(c + d/x^2)^q*sqrt(e*x)*AppellF1(-(1/4), -p, -q, 3/4, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*e)]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/(e*x)^(3/2), x, 4, -((2*(a + b/x^2)^p*(c + d/x^2)^q*AppellF1(1/4, -p, -q, 5/4, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(e*sqrt(e*x))))]
    @test_int [(a + b/x^2)^p*(c + d/x^2)^q/(e*x)^(5/2), x, 4, -((2*(a + b/x^2)^p*(c + d/x^2)^q*AppellF1(3/4, -p, -q, 7/4, -(b/(a*x^2)), -(d/(c*x^2))))/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(3*e*(e*x)^(3/2))))]

    #= ::Title::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^n)^p*(c+d*x^n)^q=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^n)^p*(c+d*x^n)^p*with*p=q*and*b*c+a*d=0=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^(m/2)*(a+b*x^(n/2))^(p/2)*(c+d*x^(n/2))^(q/2)*with*p=q*and*b*c+a*d=0=#

    #= ::Subsubsection::Closed:: =#
    #=p>0=#

    @test_int [x^(5/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)), x, 6, (-(5/64))*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) - (5/96)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) - (1/24)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(5/2) + (1/4)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(7/2) - (5*acosh(sqrt(x)))/64]
    @test_int [x^(3/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)), x, 5, (-(1/8))*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) - (1/12)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) + (1/3)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(5/2) - acosh(sqrt(x))/8]
    @test_int [x^(1/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)), x, 4, (-(1/4))*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) + (1/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) - acosh(sqrt(x))/4]
    @test_int [sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))/x^(1/2), x, 3, sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) - acosh(sqrt(x))]
    @test_int [sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))/x^(3/2), x, 4, (2*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/sqrt(x) - 2*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) + 2*acosh(sqrt(x))]
    @test_int [sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))/x^(5/2), x, 1, (2*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(3*x^(3/2))]
    @test_int [sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))/x^(7/2), x, 2, (2*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(5*x^(5/2)) + (4*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(15*x^(3/2))]
    @test_int [sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))/x^(9/2), x, 3, (2*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(7*x^(7/2)) + (8*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(35*x^(5/2)) + (16*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(105*x^(3/2))]
    @test_int [sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))/x^(11/2), x, 4, (2*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(9*x^(9/2)) + (4*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(21*x^(7/2)) + (16*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(105*x^(5/2)) + (32*(-1 + sqrt(x))^(3/2)*(1 + sqrt(x))^(3/2))/(315*x^(3/2))]

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [x^(5/2)/(sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 5, (5/8)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) + (5/12)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) + (1/3)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(5/2) + (5*acosh(sqrt(x)))/8]
    @test_int [x^(3/2)/(sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 4, (3/4)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) + (1/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*x^(3/2) + (3*acosh(sqrt(x)))/4]
    @test_int [x^(1/2)/(sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 3, sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))*sqrt(x) + acosh(sqrt(x))]
    @test_int [1/(x^(1/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 2, 2*acosh(sqrt(x))]
    @test_int [1/(x^(3/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 1, (2*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/sqrt(x)]
    @test_int [1/(x^(5/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 2, (2*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(3*x^(3/2)) + (4*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(3*sqrt(x))]
    @test_int [1/(x^(7/2)*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x))), x, 3, (2*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(5*x^(5/2)) + (8*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(15*x^(3/2)) + (16*sqrt(-1 + sqrt(x))*sqrt(1 + sqrt(x)))/(15*sqrt(x))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^n)^p*(c+d*x^n)^q*with*p=q, b*c+a*d=0*and*p*symbolic=#

    @test_int [(-a + b*x^n)^p*(a + b*x^n)^p*x^2, x, 3, ((1/3)*x^3*(-a + b*x^n)^p*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(3/(2*n), -p, 1 + 3/(2*n), (b^2*x^(2*n))/a^2))/(1 - (b^2*x^(2*n))/a^2)^p]
    @test_int [(-a + b*x^n)^p*(a + b*x^n)^p*x^1, x, 3, ((1/2)*x^2*(-a + b*x^n)^p*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(1/n, -p, 1 + 1/n, (b^2*x^(2*n))/a^2))/(1 - (b^2*x^(2*n))/a^2)^p]
    @test_int [(-a + b*x^n)^p*(a + b*x^n)^p*x^0, x, 3, (x*(-a + b*x^n)^p*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(1/(2*n), -p, (1/2)*(2 + 1/n), (b^2*x^(2*n))/a^2))/(1 - (b^2*x^(2*n))/a^2)^p]
    @test_int [(-a + b*x^n)^p*(a + b*x^n)^p/x^1, x, 4, -(((-a + b*x^n)^p*(a + b*x^n)^p*(a^2 - b^2*x^(2*n))*HypergeometricFunctions._₂F₁(1, 1 + p, 2 + p, 1 - (b^2*x^(2*n))/a^2))/(2*a^2*n*(1 + p)))]
    @test_int [(-a + b*x^n)^p*(a + b*x^n)^p/x^2, x, 3, -(((-a + b*x^n)^p*(a + b*x^n)^p*HypergeometricFunctions._₂F₁(-(1/(2*n)), -p, 1 - 1/(2*n), (b^2*x^(2*n))/a^2))/((1 - (b^2*x^(2*n))/a^2)^p*x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^n)^p*(c+d*x^n)^q=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^n)^p*(c+d*x^n)=#

    @test_int [(1 + x^6)/(x*(1 - x^6)), x, 3, log(x) - log(1 - x^6)/3]

    @test_int [(e*x)^m*(a + b*x^n)^p*(a*(1 + m) + b*(1 + m + n + n*p)*x^n), x, 1, ((e*x)^(1 + m)*(a + b*x^n)^(1 + p))/e]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(e*x)^m*(a+b*x^n)^p / (c+d*x^n)=#

    #= ::Subsubsection:: =#
    #=p>0=#

    #= ::Subsubsection::Closed:: =#
    #=p<0=#

    @test_int [(e*x)^m/((a + b*x^n)*(c + d*x^n)), x, 3, (b*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a*(b*c - a*d)*e*(1 + m)) - (d*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)))/(c*(b*c - a*d)*e*(1 + m))]

    @test_int [x^2/((a + b*x^n)*(c + d*x^n)), x, 3, (b*x^3*HypergeometricFunctions._₂F₁(1, 3/n, (3 + n)/n, -((b*x^n)/a)))/(3*a*(b*c - a*d)) - (d*x^3*HypergeometricFunctions._₂F₁(1, 3/n, (3 + n)/n, -((d*x^n)/c)))/(3*c*(b*c - a*d))]
    @test_int [x^1/((a + b*x^n)*(c + d*x^n)), x, 3, (b*x^2*HypergeometricFunctions._₂F₁(1, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a*(b*c - a*d)) - (d*x^2*HypergeometricFunctions._₂F₁(1, 2/n, (2 + n)/n, -((d*x^n)/c)))/(2*c*(b*c - a*d))]
    @test_int [x^0/((a + b*x^n)*(c + d*x^n)), x, 3, (b*x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a*(b*c - a*d)) - (d*x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((d*x^n)/c)))/(c*(b*c - a*d))]
    @test_int [1/(x^1*(a + b*x^n)*(c + d*x^n)), x, 3, log(x)/(a*c) - (b*log(a + b*x^n))/(a*(b*c - a*d)*n) + (d*log(c + d*x^n))/(c*(b*c - a*d)*n)]
    @test_int [1/(x^2*(a + b*x^n)*(c + d*x^n)), x, 3, -((b*HypergeometricFunctions._₂F₁(1, -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(a*(b*c - a*d)*x)) + (d*HypergeometricFunctions._₂F₁(1, -(1/n), -((1 - n)/n), -((d*x^n)/c)))/(c*(b*c - a*d)*x)]
    @test_int [1/(x^3*(a + b*x^n)*(c + d*x^n)), x, 3, -((b*HypergeometricFunctions._₂F₁(1, -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*a*(b*c - a*d)*x^2)) + (d*HypergeometricFunctions._₂F₁(1, -(2/n), -((2 - n)/n), -((d*x^n)/c)))/(2*c*(b*c - a*d)*x^2)]

    @test_int [(e*x)^m/((a + b*x^n)^2*(c + d*x^n)), x, 5, (b*(e*x)^(1 + m))/(a*(b*c - a*d)*e*n*(a + b*x^n)) + (b*(a*d*(1 + m - 2*n) - b*c*(1 + m - n))*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)))/(a^2*(b*c - a*d)^2*e*(1 + m)*n) + (d^2*(e*x)^(1 + m)*HypergeometricFunctions._₂F₁(1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)))/(c*(b*c - a*d)^2*e*(1 + m))]

    @test_int [x^2/((a + b*x^n)^2*(c + d*x^n)), x, 5, (b*x^3)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(a*d*(3 - 2*n) - b*c*(3 - n))*x^3*HypergeometricFunctions._₂F₁(1, 3/n, (3 + n)/n, -((b*x^n)/a)))/(3*a^2*(b*c - a*d)^2*n) + (d^2*x^3*HypergeometricFunctions._₂F₁(1, 3/n, (3 + n)/n, -((d*x^n)/c)))/(3*c*(b*c - a*d)^2)]
    @test_int [x^1/((a + b*x^n)^2*(c + d*x^n)), x, 5, (b*x^2)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(2*a*d*(1 - n) - b*c*(2 - n))*x^2*HypergeometricFunctions._₂F₁(1, 2/n, (2 + n)/n, -((b*x^n)/a)))/(2*a^2*(b*c - a*d)^2*n) + (d^2*x^2*HypergeometricFunctions._₂F₁(1, 2/n, (2 + n)/n, -((d*x^n)/c)))/(2*c*(b*c - a*d)^2)]
    @test_int [x^0/((a + b*x^n)^2*(c + d*x^n)), x, 4, (b*x)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(a*d*(1 - 2*n) - b*c*(1 - n))*x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((b*x^n)/a)))/(a^2*(b*c - a*d)^2*n) + (d^2*x*HypergeometricFunctions._₂F₁(1, 1/n, 1 + 1/n, -((d*x^n)/c)))/(c*(b*c - a*d)^2)]
    @test_int [1/(x^1*(a + b*x^n)^2*(c + d*x^n)), x, 3, b/(a*(b*c - a*d)*n*(a + b*x^n)) + log(x)/(a^2*c) - (b*(b*c - 2*a*d)*log(a + b*x^n))/(a^2*(b*c - a*d)^2*n) - (d^2*log(c + d*x^n))/(c*(b*c - a*d)^2*n)]
    @test_int [1/(x^2*(a + b*x^n)^2*(c + d*x^n)), x, 5, b/(a*(b*c - a*d)*n*x*(a + b*x^n)) - (b*(b*c*(1 + n) - a*d*(1 + 2*n))*HypergeometricFunctions._₂F₁(1, -(1/n), -((1 - n)/n), -((b*x^n)/a)))/(a^2*(b*c - a*d)^2*n*x) - (d^2*HypergeometricFunctions._₂F₁(1, -(1/n), -((1 - n)/n), -((d*x^n)/c)))/(c*(b*c - a*d)^2*x)]
    @test_int [1/(x^3*(a + b*x^n)^2*(c + d*x^n)), x, 5, b/(a*(b*c - a*d)*n*x^2*(a + b*x^n)) + (b*(2*a*d*(1 + n) - b*c*(2 + n))*HypergeometricFunctions._₂F₁(1, -(2/n), -((2 - n)/n), -((b*x^n)/a)))/(2*a^2*(b*c - a*d)^2*n*x^2) - (d^2*HypergeometricFunctions._₂F₁(1, -(2/n), -((2 - n)/n), -((d*x^n)/c)))/(2*c*(b*c - a*d)^2*x^2)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^(k*n-1)*(a+b*x^n)^p / (c+d*x^n)=#

    @test_int [(x^(-1 + 2*n)*(a + b*x^n)^3)/(c + d*x^n), x, 3, -(((b*c - a*d)^3*x^n)/(d^4*n)) + (b*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*x^(2*n))/(2*d^3*n) - (b^2*(b*c - 3*a*d)*x^(3*n))/(3*d^2*n) + (b^3*x^(4*n))/(4*d*n) + (c*(b*c - a*d)^3*log(c + d*x^n))/(d^5*n)]
    @test_int [(x^(-1 + 2*n)*(a + b*x^n)^2)/(c + d*x^n), x, 3, ((b*c - a*d)^2*x^n)/(d^3*n) - (b*(b*c - 2*a*d)*x^(2*n))/(2*d^2*n) + (b^2*x^(3*n))/(3*d*n) - (c*(b*c - a*d)^2*log(c + d*x^n))/(d^4*n)]
    @test_int [(x^(-1 + 2*n)*(a + b*x^n))/(c + d*x^n), x, 3, -(((b*c - a*d)*x^n)/(d^2*n)) + (b*x^(2*n))/(2*d*n) + (c*(b*c - a*d)*log(c + d*x^n))/(d^3*n)]
    @test_int [x^(-1 + 2*n)/((a + b*x^n)*(c + d*x^n)), x, 3, -((a*log(a + b*x^n))/(b*(b*c - a*d)*n)) + (c*log(c + d*x^n))/(d*(b*c - a*d)*n)]
    @test_int [x^(-1 + 2*n)/((a + b*x^n)^2*(c + d*x^n)), x, 3, a/(b*(b*c - a*d)*n*(a + b*x^n)) + (c*log(a + b*x^n))/((b*c - a*d)^2*n) - (c*log(c + d*x^n))/((b*c - a*d)^2*n)]
    @test_int [x^(-1 + 2*n)/((a + b*x^n)^3*(c + d*x^n)), x, 3, a/(2*b*(b*c - a*d)*n*(a + b*x^n)^2) - c/((b*c - a*d)^2*n*(a + b*x^n)) - (c*d*log(a + b*x^n))/((b*c - a*d)^3*n) + (c*d*log(c + d*x^n))/((b*c - a*d)^3*n)]

    @test_int [(x^(-1 + 3*n)*(a + b*x^n)^3)/(c + d*x^n), x, 3, (c*(b*c - a*d)^3*x^n)/(d^5*n) - ((b*c - a*d)^3*x^(2*n))/(2*d^4*n) + (b*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*x^(3*n))/(3*d^3*n) - (b^2*(b*c - 3*a*d)*x^(4*n))/(4*d^2*n) + (b^3*x^(5*n))/(5*d*n) - (c^2*(b*c - a*d)^3*log(c + d*x^n))/(d^6*n)]
    @test_int [(x^(-1 + 3*n)*(a + b*x^n)^2)/(c + d*x^n), x, 3, -((c*(b*c - a*d)^2*x^n)/(d^4*n)) + ((b*c - a*d)^2*x^(2*n))/(2*d^3*n) - (b*(b*c - 2*a*d)*x^(3*n))/(3*d^2*n) + (b^2*x^(4*n))/(4*d*n) + (c^2*(b*c - a*d)^2*log(c + d*x^n))/(d^5*n)]
    @test_int [(x^(-1 + 3*n)*(a + b*x^n))/(c + d*x^n), x, 3, (c*(b*c - a*d)*x^n)/(d^3*n) - ((b*c - a*d)*x^(2*n))/(2*d^2*n) + (b*x^(3*n))/(3*d*n) - (c^2*(b*c - a*d)*log(c + d*x^n))/(d^4*n)]
    @test_int [x^(-1 + 3*n)/((a + b*x^n)*(c + d*x^n)), x, 3, x^n/(b*d*n) + (a^2*log(a + b*x^n))/(b^2*(b*c - a*d)*n) - (c^2*log(c + d*x^n))/(d^2*(b*c - a*d)*n)]
    @test_int [x^(-1 + 3*n)/((a + b*x^n)^2*(c + d*x^n)), x, 3, -(a^2/(b^2*(b*c - a*d)*n*(a + b*x^n))) - (a*(2*b*c - a*d)*log(a + b*x^n))/(b^2*(b*c - a*d)^2*n) + (c^2*log(c + d*x^n))/(d*(b*c - a*d)^2*n)]
    @test_int [x^(-1 + 3*n)/((a + b*x^n)^3*(c + d*x^n)), x, 3, -a^2/(2*b^2*(b*c - a*d)*n*(a + b*x^n)^2) + (a*(2*b*c - a*d))/(b^2*(b*c - a*d)^2*n*(a + b*x^n)) + (c^2*log(a + b*x^n))/((b*c - a*d)^3*n) - (c^2*log(c + d*x^n))/((b*c - a*d)^3*n)]

    @test_int [x^13*(b + 2*c*x^1)*(b + c*x^1)^13, x, 1, (1/14)*x^14*(b + c*x)^14]
    @test_int [x^27*(b + 2*c*x^2)*(b + c*x^2)^13, x, 2, (1/28)*x^28*(b + c*x^2)^14]
    @test_int [x^41*(b + 2*c*x^3)*(b + c*x^3)^13, x, 2, (1/42)*x^42*(b + c*x^3)^14]
    @test_int [x^(14*n - 1)*(b + 2*c*x^n)*(b + c*x^n)^13, x, 2, (x^(14*n)*(b + c*x^n)^14)/(14*n)]

    @test_int [x^(m - 1)*(a*m + b*(m + n*p)*x^n)*(a + b*x^n)^(p - 1), x, 1, x^m*(a + b*x^n)^p]

    @test_int [x^(-1)*(b + 2*c*x^1)/(b + c*x^1), x, 2, log(x*(b + c*x)), log(x) + log(b + c*x)]
    @test_int [x^(-1)*(b + 2*c*x^2)/(b + c*x^2), x, 3, log(x) + (1/2)*log(b + c*x^2)]
    @test_int [x^(-1)*(b + 2*c*x^3)/(b + c*x^3), x, 3, log(x) + (1/3)*log(b + c*x^3)]
    @test_int [x^(-1)*(b + 2*c*x^n)/(b + c*x^n), x, 3, log(x) + log(b + c*x^n)/n]

    @test_int [x^(-8)*(b + 2*c*x^1)/(b + c*x^1)^8, x, 1, -(1/(7*x^7*(b + c*x)^7))]
    @test_int [x^(-15)*(b + 2*c*x^2)/(b + c*x^2)^8, x, 2, -(1/(14*x^14*(b + c*x^2)^7))]
    @test_int [x^(-22)*(b + 2*c*x^3)/(b + c*x^3)^8, x, 2, -(1/(21*x^21*(b + c*x^3)^7))]
    @test_int [x^(-7*n - 1)*(b + 2*c*x^n)/(b + c*x^n)^8, x, 2, -(1/(x^(7*n)*(7*n*(b + c*x^n)^7)))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^p*(c+d*x^n)^(q/2)=#

    @test_int [(x^31*sqrt(1 + x^16))/(1 - x^16), x, 5, (-(1/8))*sqrt(1 + x^16) - (1/24)*(1 + x^16)^(3/2) + atanh(sqrt(1 + x^16)/sqrt(2))/(4*sqrt(2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^(p/2)*(c+d*x^n)^(q/2)=#

    @test_int [sqrt(c + d/x)/(sqrt(a + b/x)*x), x, 8, (2*sqrt(c)*atanh((sqrt(c)*sqrt(a + b/x))/(sqrt(a)*sqrt(c + d/x))))/sqrt(a) - (2*sqrt(d)*atanh((sqrt(d)*sqrt(a + b/x))/(sqrt(b)*sqrt(c + d/x))))/sqrt(b)]

    @test_int [(x^(-1 + 2*n)*(a + b*x^n)^(5/2))/sqrt(c + d*x^n), x, 8, (-5*(b*c - a*d)^2*(7*b*c + a*d)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(64*b*d^4*n) + (5*(b*c - a*d)*(7*b*c + a*d)*(a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(96*b*d^3*n) - ((7*b*c + a*d)*(a + b*x^n)^(5/2)*sqrt(c + d*x^n))/(24*b*d^2*n) + ((a + b*x^n)^(7/2)*sqrt(c + d*x^n))/(4*b*d*n) + (5*(b*c - a*d)^3*(7*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(64*b^(3/2)*d^(9/2)*n)]
    @test_int [(x^(-1 + 2*n)*(a + b*x^n)^(3/2))/sqrt(c + d*x^n), x, 7, ((b*c - a*d)*(5*b*c + a*d)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(8*b*d^3*n) - ((5*b*c + a*d)*(a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(12*b*d^2*n) + ((a + b*x^n)^(5/2)*sqrt(c + d*x^n))/(3*b*d*n) - ((b*c - a*d)^2*(5*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(8*b^(3/2)*d^(7/2)*n)]
    @test_int [(x^(-1 + 2*n)*sqrt(a + b*x^n))/sqrt(c + d*x^n), x, 6, -((3*b*c + a*d)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(4*b*d^2*n) + ((a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(2*b*d*n) + ((b*c - a*d)*(3*b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(4*b^(3/2)*d^(5/2)*n)]
    @test_int [x^(-1 + 2*n)/(sqrt(a + b*x^n)*sqrt(c + d*x^n)), x, 5, (sqrt(a + b*x^n)*sqrt(c + d*x^n))/(b*d*n) - ((b*c + a*d)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(b^(3/2)*d^(3/2)*n)]
    @test_int [x^(-1 + 2*n)/((a + b*x^n)^(3/2)*sqrt(c + d*x^n)), x, 5, (2*a*sqrt(c + d*x^n))/(b*(b*c - a*d)*n*sqrt(a + b*x^n)) + (2*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(b^(3/2)*sqrt(d)*n)]
    @test_int [x^(-1 + 2*n)/((a + b*x^n)^(5/2)*sqrt(c + d*x^n)), x, 3, (2*a*sqrt(c + d*x^n))/(3*b*(b*c - a*d)*n*(a + b*x^n)^(3/2)) - (2*(3*b*c - a*d)*sqrt(c + d*x^n))/(3*b*(b*c - a*d)^2*n*sqrt(a + b*x^n))]

    @test_int [(x^(-1 + 3*n)*(a + b*x^n)^(5/2))/sqrt(c + d*x^n), x, 9, ((b*c - a*d)^2*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(128*b^2*d^5*n) - ((b*c - a*d)*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(192*b^2*d^4*n) + ((63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x^n)^(5/2)*sqrt(c + d*x^n))/(240*b^2*d^3*n) - (3*(3*b*c + a*d)*(a + b*x^n)^(7/2)*sqrt(c + d*x^n))/(40*b^2*d^2*n) + (x^n*(a + b*x^n)^(7/2)*sqrt(c + d*x^n))/(5*b*d*n) - ((b*c - a*d)^3*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(128*b^(5/2)*d^(11/2)*n)]
    @test_int [(x^(-1 + 3*n)*(a + b*x^n)^(3/2))/sqrt(c + d*x^n), x, 8, -(((b*c - a*d)*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(64*b^2*d^4*n)) + ((35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*(a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(96*b^2*d^3*n) - ((7*b*c + 3*a*d)*(a + b*x^n)^(5/2)*sqrt(c + d*x^n))/(24*b^2*d^2*n) + (x^n*(a + b*x^n)^(5/2)*sqrt(c + d*x^n))/(4*b*d*n) + ((b*c - a*d)^2*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(64*b^(5/2)*d^(9/2)*n)]
    @test_int [(x^(-1 + 3*n)*sqrt(a + b*x^n))/sqrt(c + d*x^n), x, 7, ((5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(8*b^2*d^3*n) - ((5*b*c + 3*a*d)*(a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(12*b^2*d^2*n) + (x^n*(a + b*x^n)^(3/2)*sqrt(c + d*x^n))/(3*b*d*n) - ((b*c - a*d)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(8*b^(5/2)*d^(7/2)*n)]
    @test_int [x^(-1 + 3*n)/(sqrt(a + b*x^n)*sqrt(c + d*x^n)), x, 6, -((3*(b*c + a*d)*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(4*b^2*d^2*n)) + (x^n*sqrt(a + b*x^n)*sqrt(c + d*x^n))/(2*b*d*n) - ((4*a*b*c*d - 3*(b*c + a*d)^2)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(4*b^(5/2)*d^(5/2)*n)]
    @test_int [x^(-1 + 3*n)/((a + b*x^n)^(3/2)*sqrt(c + d*x^n)), x, 6, -((2*a^2*sqrt(c + d*x^n))/(b^2*(b*c - a*d)*n*sqrt(a + b*x^n))) + (sqrt(a + b*x^n)*sqrt(c + d*x^n))/(b^2*d*n) - ((b*c + 3*a*d)*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(b^(5/2)*d^(3/2)*n)]
    @test_int [x^(-1 + 3*n)/((a + b*x^n)^(5/2)*sqrt(c + d*x^n)), x, 6, -((2*a^2*sqrt(c + d*x^n))/(3*b^2*(b*c - a*d)*n*(a + b*x^n)^(3/2))) + (4*a*(3*b*c - 2*a*d)*sqrt(c + d*x^n))/(3*b^2*(b*c - a*d)^2*n*sqrt(a + b*x^n)) + (2*atanh((sqrt(d)*sqrt(a + b*x^n))/(sqrt(b)*sqrt(c + d*x^n))))/(b^(5/2)*sqrt(d)*n)]

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^(m/2)*(a+b*x^n)^(p/2)*(c+d*x^n)^(q/2)=#

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(a+b*x^n)^p*(c+d*x^n)^q*when*q*is*symbolic=#

    @test_int [x^(1*(p + 1) - 1)*(b + 2*c*x^1)*(b + c*x^1)^p, x, 1, (x^(1 + p)*(b + c*x)^(1 + p))/(1 + p)]
    @test_int [x^(2*(p + 1) - 1)*(b + 2*c*x^2)*(b + c*x^2)^p, x, 1, (x^(2*(1 + p))*(b + c*x^2)^(1 + p))/(2*(1 + p))]
    @test_int [x^(3*(p + 1) - 1)*(b + 2*c*x^3)*(b + c*x^3)^p, x, 1, (x^(3*(1 + p))*(b + c*x^3)^(1 + p))/(3*(1 + p))]
    @test_int [x^(n*(p + 1) - 1)*(b + 2*c*x^n)*(b + c*x^n)^p, x, 1, (x^(n*(1 + p))*(b + c*x^n)^(1 + p))/(n*(1 + p))]
    end

max_stars_repo_path: test/1 Algebraic functions/1.1 Binomial products/1.1.3 General/1.1.3.4 (e x)^m (a+b x^n)^p (c+d x^n)^q.jl