text:
@testset "7.2.4 (f x)^m (d+e x^2)^p (a+b arccosh(c x))^n" begin
    (a, b, c, d, d1, d2, e, f, m, n, x, ) = @variables a b c d d1 d2 e f m n x

    #= ::Package:: =#

    #= ::Title:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^n=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^1=#

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

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

    @test_int [x^4*(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 8, -((152*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3675*c^5)) - (76*b*d*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3675*c^3) - (19*b*d*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))/(1225*c) + (1/49)*b*c*d*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x) + (1/5)*d*x^5*(a + b*acosh(c*x)) - (1/7)*c^2*d*x^7*(a + b*acosh(c*x))]
    @test_int [x^3*(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 7, -((b*d*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(24*c^3)) - (b*d*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(36*c) + (1/36)*b*c*d*x^5*sqrt(-1 + c*x)*sqrt(1 + c*x) - (b*d*acosh(c*x))/(24*c^4) + (1/4)*d*x^4*(a + b*acosh(c*x)) - (1/6)*c^2*d*x^6*(a + b*acosh(c*x))]
    @test_int [x^2*(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 6, -((26*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(225*c^3)) - (13*b*d*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(225*c) + (1/25)*b*c*d*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x) + (1/3)*d*x^3*(a + b*acosh(c*x)) - (1/5)*c^2*d*x^5*(a + b*acosh(c*x))]
    @test_int [x^1*(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 4, -((3*b*d*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(32*c)) + (b*d*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(16*c) + (3*b*d*acosh(c*x))/(32*c^2) - (d*(1 - c^2*x^2)^2*(a + b*acosh(c*x)))/(4*c^2)]
    @test_int [x^0*(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 4, -((7*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c)) + (1/9)*b*c*d*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x) + d*x*(a + b*acosh(c*x)) - (1/3)*c^2*d*x^3*(a + b*acosh(c*x))]
    @test_int [((d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^1, x, 8, (1/4)*b*c*d*x*sqrt(-1 + c*x)*sqrt(1 + c*x) - (1/4)*b*d*acosh(c*x) + (1/2)*d*(1 - c^2*x^2)*(a + b*acosh(c*x)) + (d*(a + b*acosh(c*x))^2)/(2*b) + d*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))) - (1/2)*b*d*PolyLog(2, -ℯ^(-2*acosh(c*x)))]
    @test_int [((d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^2, x, 5, b*c*d*sqrt(-1 + c*x)*sqrt(1 + c*x) - (d*(a + b*acosh(c*x)))/x - c^2*d*x*(a + b*acosh(c*x)) + b*c*d*atan(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^3, x, 9, (b*c*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*x) - (1/2)*b*c^2*d*acosh(c*x) - (d*(1 - c^2*x^2)*(a + b*acosh(c*x)))/(2*x^2) - (c^2*d*(a + b*acosh(c*x))^2)/(2*b) - c^2*d*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))) + (1/2)*b*c^2*d*PolyLog(2, -ℯ^(-2*acosh(c*x)))]
    @test_int [((d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^4, x, 5, (b*c*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*x^2) - (d*(a + b*acosh(c*x)))/(3*x^3) + (c^2*d*(a + b*acosh(c*x)))/x - (5/6)*b*c^3*d*atan(sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^4*(d - c^2*d*x^2)^2*(a + b*acosh(c*x)), x, 7, -((8*b*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(315*c^5)) + (4*b*d^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(945*c^5) - (b*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(525*c^5) - (10*b*d^2*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(441*c^5) - (b*d^2*(-1 + c*x)^(9/2)*(1 + c*x)^(9/2))/(81*c^5) + (1/5)*d^2*x^5*(a + b*acosh(c*x)) - (2/7)*c^2*d^2*x^7*(a + b*acosh(c*x)) + (1/9)*c^4*d^2*x^9*(a + b*acosh(c*x)), (8*b*d^2*(1 - c^2*x^2))/(315*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*d^2*(1 - c^2*x^2)^2)/(945*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(1 - c^2*x^2)^3)/(525*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (10*b*d^2*(1 - c^2*x^2)^4)/(441*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(1 - c^2*x^2)^5)/(81*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/5)*d^2*x^5*(a + b*acosh(c*x)) - (2/7)*c^2*d^2*x^7*(a + b*acosh(c*x)) + (1/9)*c^4*d^2*x^9*(a + b*acosh(c*x))]
    @test_int [x^3*(d - c^2*d*x^2)^2*(a + b*acosh(c*x)), x, 9, -((73*b*d^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3072*c^3)) - (73*b*d^2*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4608*c) + (43*b*c*d^2*x^5*sqrt(-1 + c*x)*sqrt(1 + c*x))/1152 - (1/64)*b*c^3*d^2*x^7*sqrt(-1 + c*x)*sqrt(1 + c*x) - (73*b*d^2*acosh(c*x))/(3072*c^4) + (1/4)*d^2*x^4*(a + b*acosh(c*x)) - (1/3)*c^2*d^2*x^6*(a + b*acosh(c*x)) + (1/8)*c^4*d^2*x^8*(a + b*acosh(c*x)), (73*b*d^2*x*(1 - c^2*x^2))/(3072*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (73*b*d^2*x^3*(1 - c^2*x^2))/(4608*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (43*b*c*d^2*x^5*(1 - c^2*x^2))/(1152*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d^2*x^7*(1 - c^2*x^2))/(64*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/4)*d^2*x^4*(a + b*acosh(c*x)) - (1/3)*c^2*d^2*x^6*(a + b*acosh(c*x)) + (1/8)*c^4*d^2*x^8*(a + b*acosh(c*x)) - (73*b*d^2*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(3072*c^4*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*(d - c^2*d*x^2)^2*(a + b*acosh(c*x)), x, 6, -((8*b*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(105*c^3)) + (4*b*d^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(315*c^3) - (b*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(175*c^3) - (b*d^2*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(49*c^3) + (1/3)*d^2*x^3*(a + b*acosh(c*x)) - (2/5)*c^2*d^2*x^5*(a + b*acosh(c*x)) + (1/7)*c^4*d^2*x^7*(a + b*acosh(c*x)), (8*b*d^2*(1 - c^2*x^2))/(105*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*d^2*(1 - c^2*x^2)^2)/(315*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(1 - c^2*x^2)^3)/(175*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d^2*(1 - c^2*x^2)^4)/(49*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/3)*d^2*x^3*(a + b*acosh(c*x)) - (2/5)*c^2*d^2*x^5*(a + b*acosh(c*x)) + (1/7)*c^4*d^2*x^7*(a + b*acosh(c*x))]
    @test_int [x^1*(d - c^2*d*x^2)^2*(a + b*acosh(c*x)), x, 5, -((5*b*d^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(96*c)) + (5*b*d^2*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(144*c) - (b*d^2*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(36*c) + (5*b*d^2*acosh(c*x))/(96*c^2) - (d^2*(1 - c^2*x^2)^3*(a + b*acosh(c*x)))/(6*c^2)]
    @test_int [x^0*(d - c^2*d*x^2)^2*(a + b*acosh(c*x)), x, 6, -((8*b*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(15*c)) + (4*b*d^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(45*c) - (b*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(25*c) + d^2*x*(a + b*acosh(c*x)) - (2/3)*c^2*d^2*x^3*(a + b*acosh(c*x)) + (1/5)*c^4*d^2*x^5*(a + b*acosh(c*x)), (8*b*d^2*(1 - c^2*x^2))/(15*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*d^2*(1 - c^2*x^2)^2)/(45*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(1 - c^2*x^2)^3)/(25*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^2*x*(a + b*acosh(c*x)) - (2/3)*c^2*d^2*x^3*(a + b*acosh(c*x)) + (1/5)*c^4*d^2*x^5*(a + b*acosh(c*x))]
    @test_int [((d - c^2*d*x^2)^2*(a + b*acosh(c*x)))/x^1, x, 12, (11/32)*b*c*d^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x) - (1/16)*b*c*d^2*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2) - (11/32)*b*d^2*acosh(c*x) + (1/2)*d^2*(1 - c^2*x^2)*(a + b*acosh(c*x)) + (1/4)*d^2*(1 - c^2*x^2)^2*(a + b*acosh(c*x)) + (d^2*(a + b*acosh(c*x))^2)/(2*b) + d^2*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))) - (1/2)*b*d^2*PolyLog(2, -ℯ^(-2*acosh(c*x)))]
    @test_int [((d - c^2*d*x^2)^2*(a + b*acosh(c*x)))/x^2, x, 8, (5/3)*b*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x) - (1/9)*b*c*d^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2) - (d^2*(a + b*acosh(c*x)))/x - 2*c^2*d^2*x*(a + b*acosh(c*x)) + (1/3)*c^4*d^2*x^3*(a + b*acosh(c*x)) + b*c*d^2*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)), -((5*b*c*d^2*(1 - c^2*x^2))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c*d^2*(1 - c^2*x^2)^2)/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^2*(a + b*acosh(c*x)))/x - 2*c^2*d^2*x*(a + b*acosh(c*x)) + (1/3)*c^4*d^2*x^3*(a + b*acosh(c*x)) + (b*c*d^2*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^2*(a + b*acosh(c*x)))/x^3, x, 13, (1/4)*b*c^3*d^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x) - (b*c*d^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(2*x) - (1/4)*b*c^2*d^2*acosh(c*x) - c^2*d^2*(1 - c^2*x^2)*(a + b*acosh(c*x)) - (d^2*(1 - c^2*x^2)^2*(a + b*acosh(c*x)))/(2*x^2) - (c^2*d^2*(a + b*acosh(c*x))^2)/b - 2*c^2*d^2*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))) + b*c^2*d^2*PolyLog(2, -ℯ^(-2*acosh(c*x)))]
    @test_int [((d - c^2*d*x^2)^2*(a + b*acosh(c*x)))/x^4, x, 8, (-b)*c^3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x) + (b*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*x^2) - (d^2*(a + b*acosh(c*x)))/(3*x^3) + (2*c^2*d^2*(a + b*acosh(c*x)))/x + c^4*d^2*x*(a + b*acosh(c*x)) - (11/6)*b*c^3*d^2*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)), (b*c^3*d^2*(1 - c^2*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*(1 - c^2*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^2*(a + b*acosh(c*x)))/(3*x^3) + (2*c^2*d^2*(a + b*acosh(c*x)))/x + c^4*d^2*x*(a + b*acosh(c*x)) - (11*b*c^3*d^2*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(6*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^4*(d - c^2*d*x^2)^3*(a + b*acosh(c*x)), x, 6, -((16*b*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(1155*c^5)) + (8*b*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(3465*c^5) - (2*b*d^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(1925*c^5) + (b*d^3*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(1617*c^5) + (4*b*d^3*(-1 + c*x)^(9/2)*(1 + c*x)^(9/2))/(297*c^5) + (b*d^3*(-1 + c*x)^(11/2)*(1 + c*x)^(11/2))/(121*c^5) + (1/5)*d^3*x^5*(a + b*acosh(c*x)) - (3/7)*c^2*d^3*x^7*(a + b*acosh(c*x)) + (1/3)*c^4*d^3*x^9*(a + b*acosh(c*x)) - (1/11)*c^6*d^3*x^11*(a + b*acosh(c*x)), (16*b*d^3*(1 - c^2*x^2))/(1155*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (8*b*d^3*(1 - c^2*x^2)^2)/(3465*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d^3*(1 - c^2*x^2)^3)/(1925*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^3*(1 - c^2*x^2)^4)/(1617*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*d^3*(1 - c^2*x^2)^5)/(297*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^3*(1 - c^2*x^2)^6)/(121*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/5)*d^3*x^5*(a + b*acosh(c*x)) - (3/7)*c^2*d^3*x^7*(a + b*acosh(c*x)) + (1/3)*c^4*d^3*x^9*(a + b*acosh(c*x)) - (1/11)*c^6*d^3*x^11*(a + b*acosh(c*x))]
    @test_int [x^3*(d - c^2*d*x^2)^3*(a + b*acosh(c*x)), x, 11, -((49*b*d^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(5120*c^3)) + (49*b*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(7680*c^3) - (49*b*d^3*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(9600*c^3) + (7*b*d^3*x*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(1600*c^3) + (b*d^3*x*(-1 + c*x)^(9/2)*(1 + c*x)^(9/2))/(100*c^3) + (49*b*d^3*acosh(c*x))/(5120*c^4) - (d^3*(-1 + c*x)^4*(1 + c*x)^4*(a + b*acosh(c*x)))/(8*c^4) - (d^3*(-1 + c*x)^5*(1 + c*x)^5*(a + b*acosh(c*x)))/(10*c^4), (49*b*d^3*x*(1 - c^2*x^2))/(5120*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (49*b*d^3*x*(1 - c^2*x^2)^2)/(7680*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (49*b*d^3*x*(1 - c^2*x^2)^3)/(9600*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (7*b*d^3*x*(1 - c^2*x^2)^4)/(1600*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d^3*x*(1 - c^2*x^2)^5)/(100*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^3*(1 - c^2*x^2)^4*(a + b*acosh(c*x)))/(8*c^4) + (d^3*(1 - c^2*x^2)^5*(a + b*acosh(c*x)))/(10*c^4) + (49*b*d^3*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(5120*c^4*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*(d - c^2*d*x^2)^3*(a + b*acosh(c*x)), x, 6, -((16*b*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(315*c^3)) + (8*b*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(945*c^3) - (2*b*d^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(525*c^3) + (b*d^3*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(441*c^3) + (b*d^3*(-1 + c*x)^(9/2)*(1 + c*x)^(9/2))/(81*c^3) + (1/3)*d^3*x^3*(a + b*acosh(c*x)) - (3/5)*c^2*d^3*x^5*(a + b*acosh(c*x)) + (3/7)*c^4*d^3*x^7*(a + b*acosh(c*x)) - (1/9)*c^6*d^3*x^9*(a + b*acosh(c*x)), (16*b*d^3*(1 - c^2*x^2))/(315*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (8*b*d^3*(1 - c^2*x^2)^2)/(945*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d^3*(1 - c^2*x^2)^3)/(525*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^3*(1 - c^2*x^2)^4)/(441*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*d^3*(1 - c^2*x^2)^5)/(81*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^3*x^3*(a + b*acosh(c*x)))/3 - (3*c^2*d^3*x^5*(a + b*acosh(c*x)))/5 + (3*c^4*d^3*x^7*(a + b*acosh(c*x)))/7 - (c^6*d^3*x^9*(a + b*acosh(c*x)))/9]
    @test_int [x^1*(d - c^2*d*x^2)^3*(a + b*acosh(c*x)), x, 6, -((35*b*d^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(1024*c)) + (35*b*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(1536*c) - (7*b*d^3*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(384*c) + (b*d^3*x*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(64*c) + (35*b*d^3*acosh(c*x))/(1024*c^2) - (d^3*(1 - c^2*x^2)^4*(a + b*acosh(c*x)))/(8*c^2)]
    @test_int [x^0*(d - c^2*d*x^2)^3*(a + b*acosh(c*x)), x, 6, -((16*b*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(35*c)) + (8*b*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(105*c) - (6*b*d^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(175*c) + (b*d^3*(-1 + c*x)^(7/2)*(1 + c*x)^(7/2))/(49*c) + d^3*x*(a + b*acosh(c*x)) - c^2*d^3*x^3*(a + b*acosh(c*x)) + (3/5)*c^4*d^3*x^5*(a + b*acosh(c*x)) - (1/7)*c^6*d^3*x^7*(a + b*acosh(c*x)), (16*b*d^3*(1 - c^2*x^2))/(35*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (8*b*d^3*(1 - c^2*x^2)^2)/(105*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (6*b*d^3*(1 - c^2*x^2)^3)/(175*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^3*(1 - c^2*x^2)^4)/(49*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^3*x*(a + b*acosh(c*x)) - c^2*d^3*x^3*(a + b*acosh(c*x)) + (3*c^4*d^3*x^5*(a + b*acosh(c*x)))/5 - (c^6*d^3*x^7*(a + b*acosh(c*x)))/7]
    @test_int [((d - c^2*d*x^2)^3*(a + b*acosh(c*x)))/x^1, x, 17, (19/48)*b*c*d^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x) - (7/72)*b*c*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2) + (1/36)*b*c*d^3*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2) - (19/48)*b*d^3*acosh(c*x) + (1/2)*d^3*(1 - c^2*x^2)*(a + b*acosh(c*x)) + (1/4)*d^3*(1 - c^2*x^2)^2*(a + b*acosh(c*x)) + (1/6)*d^3*(1 - c^2*x^2)^3*(a + b*acosh(c*x)) + (d^3*(a + b*acosh(c*x))^2)/(2*b) + d^3*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))) - (1/2)*b*d^3*PolyLog(2, -ℯ^(-2*acosh(c*x)))]
    @test_int [((d - c^2*d*x^2)^3*(a + b*acosh(c*x)))/x^2, x, 8, (11/5)*b*c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x) - (1/5)*b*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2) + (1/25)*b*c*d^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2) - (d^3*(a + b*acosh(c*x)))/x - 3*c^2*d^3*x*(a + b*acosh(c*x)) + c^4*d^3*x^3*(a + b*acosh(c*x)) - (1/5)*c^6*d^3*x^5*(a + b*acosh(c*x)) + b*c*d^3*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)), -((11*b*c*d^3*(1 - c^2*x^2))/(5*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c*d^3*(1 - c^2*x^2)^2)/(5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^3*(1 - c^2*x^2)^3)/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^3*(a + b*acosh(c*x)))/x - 3*c^2*d^3*x*(a + b*acosh(c*x)) + c^4*d^3*x^3*(a + b*acosh(c*x)) - (1/5)*c^6*d^3*x^5*(a + b*acosh(c*x)) + (b*c*d^3*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^3*(a + b*acosh(c*x)))/x^3, x, 18, (-(3/32))*b*c^3*d^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x) - (7/16)*b*c^3*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2) + (b*c*d^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(2*x) + (3/32)*b*c^2*d^3*acosh(c*x) - (3/2)*c^2*d^3*(1 - c^2*x^2)*(a + b*acosh(c*x)) - (3/4)*c^2*d^3*(1 - c^2*x^2)^2*(a + b*acosh(c*x)) - (d^3*(1 - c^2*x^2)^3*(a + b*acosh(c*x)))/(2*x^2) - (3*c^2*d^3*(a + b*acosh(c*x))^2)/(2*b) - 3*c^2*d^3*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))) + (3/2)*b*c^2*d^3*PolyLog(2, -ℯ^(-2*acosh(c*x)))]
    @test_int [((d - c^2*d*x^2)^3*(a + b*acosh(c*x)))/x^4, x, 9, (-(8/3))*b*c^3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x) + (b*c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*x^2) + (1/9)*b*c^3*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2) - (d^3*(a + b*acosh(c*x)))/(3*x^3) + (3*c^2*d^3*(a + b*acosh(c*x)))/x + 3*c^4*d^3*x*(a + b*acosh(c*x)) - (1/3)*c^6*d^3*x^3*(a + b*acosh(c*x)) - (17/6)*b*c^3*d^3*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)), (8*b*c^3*d^3*(1 - c^2*x^2))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^3*(1 - c^2*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d^3*(1 - c^2*x^2)^2)/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^3*(a + b*acosh(c*x)))/(3*x^3) + (3*c^2*d^3*(a + b*acosh(c*x)))/x + 3*c^4*d^3*x*(a + b*acosh(c*x)) - (1/3)*c^6*d^3*x^3*(a + b*acosh(c*x)) - (17*b*c^3*d^3*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(6*sqrt(-1 + c*x)*sqrt(1 + c*x))]

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

    @test_int [x^4*(a + b*acosh(c*x))/(d - c^2*d*x^2), x, 12, (11*b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c^5*d) + (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c^3*d) - (x*(a + b*acosh(c*x)))/(c^4*d) - (x^3*(a + b*acosh(c*x)))/(3*c^2*d) + (2*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^5*d) + (b*PolyLog(2, -ℯ^acosh(c*x)))/(c^5*d) - (b*PolyLog(2, ℯ^acosh(c*x)))/(c^5*d)]
    @test_int [x^3*(a + b*acosh(c*x))/(d - c^2*d*x^2), x, 8, (b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c^3*d) + (b*acosh(c*x))/(4*c^4*d) - (x^2*(a + b*acosh(c*x)))/(2*c^2*d) + (a + b*acosh(c*x))^2/(2*b*c^4*d) - ((a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(c^4*d) - (b*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*c^4*d)]
    @test_int [x^2*(a + b*acosh(c*x))/(d - c^2*d*x^2), x, 8, (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c^3*d) - (x*(a + b*acosh(c*x)))/(c^2*d) + (2*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^3*d) + (b*PolyLog(2, -ℯ^acosh(c*x)))/(c^3*d) - (b*PolyLog(2, ℯ^acosh(c*x)))/(c^3*d)]
    @test_int [x^1*(a + b*acosh(c*x))/(d - c^2*d*x^2), x, 5, (a + b*acosh(c*x))^2/(2*b*c^2*d) - ((a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(c^2*d) - (b*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*c^2*d)]
    @test_int [x^0*(a + b*acosh(c*x))/(d - c^2*d*x^2), x, 6, (2*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c*d) + (b*PolyLog(2, -ℯ^acosh(c*x)))/(c*d) - (b*PolyLog(2, ℯ^acosh(c*x)))/(c*d)]
    @test_int [(a + b*acosh(c*x))/(x^1*(d - c^2*d*x^2)), x, 7, (2*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/d + (b*PolyLog(2, -ℯ^(2*acosh(c*x))))/(2*d) - (b*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*d)]
    @test_int [(a + b*acosh(c*x))/(x^2*(d - c^2*d*x^2)), x, 9, -((a + b*acosh(c*x))/(d*x)) + (b*c*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/d + (2*c*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/d + (b*c*PolyLog(2, -ℯ^acosh(c*x)))/d - (b*c*PolyLog(2, ℯ^acosh(c*x)))/d]
    @test_int [(a + b*acosh(c*x))/(x^3*(d - c^2*d*x^2)), x, 9, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*d*x) - (a + b*acosh(c*x))/(2*d*x^2) + (2*c^2*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/d + (b*c^2*PolyLog(2, -ℯ^(2*acosh(c*x))))/(2*d) - (b*c^2*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*d)]
    @test_int [(a + b*acosh(c*x))/(x^4*(d - c^2*d*x^2)), x, 14, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*d*x^2) - (a + b*acosh(c*x))/(3*d*x^3) - (c^2*(a + b*acosh(c*x)))/(d*x) + (7*b*c^3*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(6*d) + (2*c^3*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/d + (b*c^3*PolyLog(2, -ℯ^acosh(c*x)))/d - (b*c^3*PolyLog(2, ℯ^acosh(c*x)))/d]

    @test_int [x^4*(a + b*acosh(c*x))/(d - c^2*d*x^2)^2, x, 12, -((b*x^2)/(2*c^3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*c^5*d^2) + (3*x*(a + b*acosh(c*x)))/(2*c^4*d^2) + (x^3*(a + b*acosh(c*x)))/(2*c^2*d^2*(1 - c^2*x^2)) - (3*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^5*d^2) - (3*b*PolyLog(2, -ℯ^acosh(c*x)))/(2*c^5*d^2) + (3*b*PolyLog(2, ℯ^acosh(c*x)))/(2*c^5*d^2)]
    @test_int [x^3*(a + b*acosh(c*x))/(d - c^2*d*x^2)^2, x, 10, -(b/(2*c^4*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*sqrt(-1 + c*x))/(2*c^4*d^2*sqrt(1 + c*x)) + (b*acosh(c*x))/(2*c^4*d^2) + (x^2*(a + b*acosh(c*x)))/(2*c^2*d^2*(1 - c^2*x^2)) - (a + b*acosh(c*x))^2/(2*b*c^4*d^2) + ((a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(c^4*d^2) + (b*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*c^4*d^2)]
    @test_int [x^2*(a + b*acosh(c*x))/(d - c^2*d*x^2)^2, x, 8, -(b/(2*c^3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (x*(a + b*acosh(c*x)))/(2*c^2*d^2*(1 - c^2*x^2)) - ((a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^3*d^2) - (b*PolyLog(2, -ℯ^acosh(c*x)))/(2*c^3*d^2) + (b*PolyLog(2, ℯ^acosh(c*x)))/(2*c^3*d^2)]
    @test_int [x^1*(a + b*acosh(c*x))/(d - c^2*d*x^2)^2, x, 2, -((b*x)/(2*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (a + b*acosh(c*x))/(2*c^2*d^2*(1 - c^2*x^2))]
    @test_int [x^0*(a + b*acosh(c*x))/(d - c^2*d*x^2)^2, x, 8, -(b/(2*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (x*(a + b*acosh(c*x)))/(2*d^2*(1 - c^2*x^2)) + ((a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c*d^2) + (b*PolyLog(2, -ℯ^acosh(c*x)))/(2*c*d^2) - (b*PolyLog(2, ℯ^acosh(c*x)))/(2*c*d^2)]
    @test_int [(a + b*acosh(c*x))/(x^1*(d - c^2*d*x^2)^2), x, 9, -((b*c*x)/(2*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (a + b*acosh(c*x))/(2*d^2*(1 - c^2*x^2)) + (2*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/d^2 + (b*PolyLog(2, -ℯ^(2*acosh(c*x))))/(2*d^2) - (b*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*d^2)]
    @test_int [(a + b*acosh(c*x))/(x^2*(d - c^2*d*x^2)^2), x, 13, -((b*c)/(2*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (a + b*acosh(c*x))/(d^2*x*(1 - c^2*x^2)) + (3*c^2*x*(a + b*acosh(c*x)))/(2*d^2*(1 - c^2*x^2)) + (b*c*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/d^2 + (3*c*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/d^2 + (3*b*c*PolyLog(2, -ℯ^acosh(c*x)))/(2*d^2) - (3*b*c*PolyLog(2, ℯ^acosh(c*x)))/(2*d^2)]
    @test_int [(a + b*acosh(c*x))/(x^3*(d - c^2*d*x^2)^2), x, 13, -((b*c)/(2*d^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (c^2*(a + b*acosh(c*x)))/(d^2*(1 - c^2*x^2)) - (a + b*acosh(c*x))/(2*d^2*x^2*(1 - c^2*x^2)) + (4*c^2*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/d^2 + (b*c^2*PolyLog(2, -ℯ^(2*acosh(c*x))))/d^2 - (b*c^2*PolyLog(2, ℯ^(2*acosh(c*x))))/d^2]
    @test_int [(a + b*acosh(c*x))/(x^4*(d - c^2*d*x^2)^2), x, 20, -((b*c^3)/(3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c)/(6*d^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (a + b*acosh(c*x))/(3*d^2*x^3*(1 - c^2*x^2)) - (5*c^2*(a + b*acosh(c*x)))/(3*d^2*x*(1 - c^2*x^2)) + (5*c^4*x*(a + b*acosh(c*x)))/(2*d^2*(1 - c^2*x^2)) + (13*b*c^3*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(6*d^2) + (5*c^3*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/d^2 + (5*b*c^3*PolyLog(2, -ℯ^acosh(c*x)))/(2*d^2) - (5*b*c^3*PolyLog(2, ℯ^acosh(c*x)))/(2*d^2)]

    @test_int [x^4*(a + b*acosh(c*x))/(d - c^2*d*x^2)^3, x, 13, (b*x^3)/(12*c^2*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + b/(4*c^5*d^3*sqrt(-1 + c*x)*(1 + c*x)^(3/2)) - (b*(-1 + c*x)^(3/2))/(12*c^5*d^3*(1 + c*x)^(3/2)) + (3*b)/(8*c^5*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (x^3*(a + b*acosh(c*x)))/(4*c^2*d^3*(1 - c^2*x^2)^2) - (3*x*(a + b*acosh(c*x)))/(8*c^4*d^3*(1 - c^2*x^2)) + (3*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(4*c^5*d^3) + (3*b*PolyLog(2, -ℯ^acosh(c*x)))/(8*c^5*d^3) - (3*b*PolyLog(2, ℯ^acosh(c*x)))/(8*c^5*d^3)]
    @test_int [x^3*(a + b*acosh(c*x))/(d - c^2*d*x^2)^3, x, 7, (b*x^3)/(12*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + b/(4*c^4*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*sqrt(-1 + c*x))/(4*c^4*d^3*sqrt(1 + c*x)) - (b*acosh(c*x))/(4*c^4*d^3) + (x^4*(a + b*acosh(c*x)))/(4*d^3*(1 - c^2*x^2)^2)]
    @test_int [x^2*(a + b*acosh(c*x))/(d - c^2*d*x^2)^3, x, 10, b/(12*c^3*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + b/(8*c^3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (x*(a + b*acosh(c*x)))/(4*c^2*d^3*(1 - c^2*x^2)^2) - (x*(a + b*acosh(c*x)))/(8*c^2*d^3*(1 - c^2*x^2)) - ((a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(4*c^3*d^3) - (b*PolyLog(2, -ℯ^acosh(c*x)))/(8*c^3*d^3) + (b*PolyLog(2, ℯ^acosh(c*x)))/(8*c^3*d^3)]
    @test_int [x^1*(a + b*acosh(c*x))/(d - c^2*d*x^2)^3, x, 3, (b*x)/(12*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (b*x)/(6*c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (a + b*acosh(c*x))/(4*c^2*d^3*(1 - c^2*x^2)^2)]
    @test_int [x^0*(a + b*acosh(c*x))/(d - c^2*d*x^2)^3, x, 10, b/(12*c*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (3*b)/(8*c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (x*(a + b*acosh(c*x)))/(4*d^3*(1 - c^2*x^2)^2) + (3*x*(a + b*acosh(c*x)))/(8*d^3*(1 - c^2*x^2)) + (3*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(4*c*d^3) + (3*b*PolyLog(2, -ℯ^acosh(c*x)))/(8*c*d^3) - (3*b*PolyLog(2, ℯ^acosh(c*x)))/(8*c*d^3)]
    @test_int [(a + b*acosh(c*x))/(x^1*(d - c^2*d*x^2)^3), x, 12, (b*c*x)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (2*b*c*x)/(3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (a + b*acosh(c*x))/(4*d^3*(1 - c^2*x^2)^2) + (a + b*acosh(c*x))/(2*d^3*(1 - c^2*x^2)) + (2*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/d^3 + (b*PolyLog(2, -ℯ^(2*acosh(c*x))))/(2*d^3) - (b*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*d^3)]
    @test_int [(a + b*acosh(c*x))/(x^2*(d - c^2*d*x^2)^3), x, 17, (b*c)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (7*b*c)/(8*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (a + b*acosh(c*x))/(d^3*x*(1 - c^2*x^2)^2) + (5*c^2*x*(a + b*acosh(c*x)))/(4*d^3*(1 - c^2*x^2)^2) + (15*c^2*x*(a + b*acosh(c*x)))/(8*d^3*(1 - c^2*x^2)) + (b*c*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/d^3 + (15*c*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(4*d^3) + (15*b*c*PolyLog(2, -ℯ^acosh(c*x)))/(8*d^3) - (15*b*c*PolyLog(2, ℯ^acosh(c*x)))/(8*d^3)]
    @test_int [(a + b*acosh(c*x))/(x^3*(d - c^2*d*x^2)^3), x, 17, (b*c)/(2*d^3*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (5*b*c^3*x)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (2*b*c^3*x)/(3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*c^2*(a + b*acosh(c*x)))/(4*d^3*(1 - c^2*x^2)^2) - (a + b*acosh(c*x))/(2*d^3*x^2*(1 - c^2*x^2)^2) + (3*c^2*(a + b*acosh(c*x)))/(2*d^3*(1 - c^2*x^2)) + (6*c^2*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/d^3 + (3*b*c^2*PolyLog(2, -ℯ^(2*acosh(c*x))))/(2*d^3) - (3*b*c^2*PolyLog(2, ℯ^(2*acosh(c*x))))/(2*d^3)]
    @test_int [(a + b*acosh(c*x))/(x^4*(d - c^2*d*x^2)^3), x, 26, -((b*c^3)/(12*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))) + (b*c)/(6*d^3*x^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) - (29*b*c^3)/(24*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (a + b*acosh(c*x))/(3*d^3*x^3*(1 - c^2*x^2)^2) - (7*c^2*(a + b*acosh(c*x)))/(3*d^3*x*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*acosh(c*x)))/(12*d^3*(1 - c^2*x^2)^2) + (35*c^4*x*(a + b*acosh(c*x)))/(8*d^3*(1 - c^2*x^2)) + (19*b*c^3*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(6*d^3) + (35*c^3*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(4*d^3) + (35*b*c^3*PolyLog(2, -ℯ^acosh(c*x)))/(8*d^3) - (35*b*c^3*PolyLog(2, ℯ^acosh(c*x)))/(8*d^3)]

    @test_int [acosh(a*x)/(c - a^2*c*x^2), x, 6, (2*acosh(a*x)*atanh(ℯ^acosh(a*x)))/(a*c) + PolyLog(2, -ℯ^acosh(a*x))/(a*c) - PolyLog(2, ℯ^acosh(a*x))/(a*c)]
    @test_int [acosh(a*x)/(c - a^2*c*x^2)^2, x, 8, -(1/(2*a*c^2*sqrt(-1 + a*x)*sqrt(1 + a*x))) + (x*acosh(a*x))/(2*c^2*(1 - a^2*x^2)) + (acosh(a*x)*atanh(ℯ^acosh(a*x)))/(a*c^2) + PolyLog(2, -ℯ^acosh(a*x))/(2*a*c^2) - PolyLog(2, ℯ^acosh(a*x))/(2*a*c^2)]
    @test_int [acosh(a*x)/(c - a^2*c*x^2)^3, x, 10, 1/(12*a*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)) - 3/(8*a*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (x*acosh(a*x))/(4*c^3*(1 - a^2*x^2)^2) + (3*x*acosh(a*x))/(8*c^3*(1 - a^2*x^2)) + (3*acosh(a*x)*atanh(ℯ^acosh(a*x)))/(4*a*c^3) + (3*PolyLog(2, -ℯ^acosh(a*x)))/(8*a*c^3) - (3*PolyLog(2, ℯ^acosh(a*x)))/(8*a*c^3)]

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

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

    @test_int [x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 7, (b*x^2*sqrt(d - c^2*d*x^2))/(32*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x^4*sqrt(d - c^2*d*x^2))/(96*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^6*sqrt(d - c^2*d*x^2))/(36*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(16*c^4) - (x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(24*c^2) + (1/6)*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 5, (b*x^2*sqrt(d - c^2*d*x^2))/(16*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*c^2) + (1/4)*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^0*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 3, -((b*c*x^2*sqrt(d - c^2*d*x^2))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (1/2)*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^2, x, 3, -((sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x) + (c*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*sqrt(d - c^2*d*x^2)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^4, x, 4, -((b*c*sqrt(d - c^2*d*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*d*x^3) - (b*c^3*sqrt(d - c^2*d*x^2)*log(x))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^6, x, 4, -((b*c*sqrt(d - c^2*d*x^2))/(20*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*sqrt(d - c^2*d*x^2))/(30*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(5*d*x^5) - (2*c^2*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(15*d*x^3) - (2*b*c^5*sqrt(d - c^2*d*x^2)*log(x))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^8, x, 4, -((b*c*sqrt(d - c^2*d*x^2))/(42*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*sqrt(d - c^2*d*x^2))/(140*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^5*sqrt(d - c^2*d*x^2))/(105*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(7*d*x^7) - (4*c^2*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(35*d*x^5) - (8*c^4*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(105*d*x^3) - (8*b*c^7*sqrt(d - c^2*d*x^2)*log(x))/(105*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 3, (8*b*x*sqrt(d - c^2*d*x^2))/(105*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*x^3*sqrt(d - c^2*d*x^2))/(315*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x^5*sqrt(d - c^2*d*x^2))/(175*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*c^6*d) + (2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*c^6*d^2) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^6*d^3)]
    @test_int [x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 3, (2*b*x*sqrt(d - c^2*d*x^2))/(15*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x^3*sqrt(d - c^2*d*x^2))/(45*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*c^4*d) + ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*c^4*d^2)]
    @test_int [x^1*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)), x, 3, (b*x*sqrt(d - c^2*d*x^2))/(3*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^3*sqrt(d - c^2*d*x^2))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*c^2*d)]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^1, x, 8, -((b*c*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x))) + sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^3, x, 8, -((b*c*sqrt(d - c^2*d*x^2))/(2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*x^2) + (c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*c^2*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b*c^2*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x^5, x, 10, -((b*c*sqrt(d - c^2*d*x^2))/(12*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*sqrt(d - c^2*d*x^2))/(8*x*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(4*x^4) + (c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*x^2) + (c^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*c^4*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b*c^4*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^4*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 11, (3*b*d*x^2*sqrt(d - c^2*d*x^2))/(256*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*x^4*sqrt(d - c^2*d*x^2))/(256*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d*x^6*sqrt(d - c^2*d*x^2))/(32*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^8*sqrt(d - c^2*d*x^2))/(64*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(128*c^4) - (d*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(64*c^2) + (1/16)*d*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/8)*x^5*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) - (3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(256*b*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 9, (b*d*x^2*sqrt(d - c^2*d*x^2))/(32*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (7*b*c*d*x^4*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^6*sqrt(d - c^2*d*x^2))/(36*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(16*c^2) + (1/8)*d*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/6)*x^3*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) - (d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^0*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 7, -((5*b*c*d*x^2*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3/8)*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/4)*x*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) - (3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^2, x, 7, (b*c^3*d*x^2*sqrt(d - c^2*d*x^2))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3/2)*c^2*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x + (3*c*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*d*sqrt(d - c^2*d*x^2)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^4, x, 7, -((b*c*d*sqrt(d - c^2*d*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*x^3) - (c^3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*c^3*d*sqrt(d - c^2*d*x^2)*log(x))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^6, x, 5, -((b*c*d*sqrt(d - c^2*d*x^2))/(20*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d*sqrt(d - c^2*d*x^2))/(5*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*d*x^5) + (b*c^5*d*sqrt(d - c^2*d*x^2)*log(x))/(5*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^8, x, 5, -((b*c*d*sqrt(d - c^2*d*x^2))/(42*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (2*b*c^3*d*sqrt(d - c^2*d*x^2))/(35*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d*sqrt(d - c^2*d*x^2))/(70*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(7*d*x^7) - (2*c^2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(35*d*x^5) + (2*b*c^7*d*sqrt(d - c^2*d*x^2)*log(x))/(35*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^10, x, 5, -((b*c*d*sqrt(d - c^2*d*x^2))/(72*x^8*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (5*b*c^3*d*sqrt(d - c^2*d*x^2))/(189*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d*sqrt(d - c^2*d*x^2))/(420*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^7*d*sqrt(d - c^2*d*x^2))/(315*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(9*d*x^9) - (4*c^2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(63*d*x^7) - (8*c^4*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(315*d*x^5) + (8*b*c^9*d*sqrt(d - c^2*d*x^2)*log(x))/(315*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^12, x, 5, -((b*c*d*sqrt(d - c^2*d*x^2))/(110*x^10*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d*sqrt(d - c^2*d*x^2))/(66*x^8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d*sqrt(d - c^2*d*x^2))/(1386*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^7*d*sqrt(d - c^2*d*x^2))/(770*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*c^9*d*sqrt(d - c^2*d*x^2))/(1155*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(11*d*x^11) - (2*c^2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(33*d*x^9) - (8*c^4*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(231*d*x^7) - (16*c^6*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(1155*d*x^5) + (16*b*c^11*d*sqrt(d - c^2*d*x^2)*log(x))/(1155*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^7*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 4, (16*b*d*x*sqrt(d - c^2*d*x^2))/(1155*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (8*b*d*x^3*sqrt(d - c^2*d*x^2))/(3465*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d*x^5*sqrt(d - c^2*d*x^2))/(1925*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*x^7*sqrt(d - c^2*d*x^2))/(1617*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*c*d*x^9*sqrt(d - c^2*d*x^2))/(297*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^11*sqrt(d - c^2*d*x^2))/(121*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*c^8*d) + (3*(d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^8*d^2) - ((d - c^2*d*x^2)^(9/2)*(a + b*acosh(c*x)))/(3*c^8*d^3) + ((d - c^2*d*x^2)^(11/2)*(a + b*acosh(c*x)))/(11*c^8*d^4)]
    @test_int [x^5*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 4, (8*b*d*x*sqrt(d - c^2*d*x^2))/(315*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*d*x^3*sqrt(d - c^2*d*x^2))/(945*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*x^5*sqrt(d - c^2*d*x^2))/(525*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (10*b*c*d*x^7*sqrt(d - c^2*d*x^2))/(441*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^9*sqrt(d - c^2*d*x^2))/(81*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*c^6*d) + (2*(d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^6*d^2) - ((d - c^2*d*x^2)^(9/2)*(a + b*acosh(c*x)))/(9*c^6*d^3)]
    @test_int [x^3*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 4, (2*b*d*x*sqrt(d - c^2*d*x^2))/(35*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*x^3*sqrt(d - c^2*d*x^2))/(105*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (8*b*c*d*x^5*sqrt(d - c^2*d*x^2))/(175*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*c^4*d) + ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^4*d^2)]
    @test_int [x^1*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 4, (b*d*x*sqrt(d - c^2*d*x^2))/(5*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d*x^3*sqrt(d - c^2*d*x^2))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*c^2*d)]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^1, x, 11, -((4*b*c*d*x*sqrt(d - c^2*d*x^2))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d*x^3*sqrt(d - c^2*d*x^2))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/3)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) - (2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b*d*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^3, x, 12, -((b*c*d*sqrt(d - c^2*d*x^2))/(2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3/2)*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(2*x^2) + (3*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*im*b*c^2*d*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*im*b*c^2*d*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/x^5, x, 12, -((b*c*d*sqrt(d - c^2*d*x^2))/(12*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (5*b*c^3*d*sqrt(d - c^2*d*x^2))/(8*x*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*x^2) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(4*x^4) - (3*c^4*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*im*b*c^4*d*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*im*b*c^4*d*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^4*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 16, (3*b*d^2*x^2*sqrt(d - c^2*d*x^2))/(512*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*x^4*sqrt(d - c^2*d*x^2))/(512*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (31*b*c*d^2*x^6*sqrt(d - c^2*d*x^2))/(960*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (21*b*c^3*d^2*x^8*sqrt(d - c^2*d*x^2))/(640*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^10*sqrt(d - c^2*d*x^2))/(100*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(256*c^4) - (d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(128*c^2) + (1/32)*d^2*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/16)*d*x^5*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) + (1/10)*x^5*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)) - (3*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(512*b*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 14, (5*b*d^2*x^2*sqrt(d - c^2*d*x^2))/(256*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (59*b*c*d^2*x^4*sqrt(d - c^2*d*x^2))/(768*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (17*b*c^3*d^2*x^6*sqrt(d - c^2*d*x^2))/(288*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^8*sqrt(d - c^2*d*x^2))/(64*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(128*c^2) + (5/64)*d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/48)*d*x^3*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) + (1/8)*x^3*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)) - (5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(256*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^0*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 10, -((25*b*c*d^2*x^2*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (5*b*c^3*d^2*x^4*sqrt(d - c^2*d*x^2))/(96*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(36*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/16)*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5/24)*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) + (1/6)*x*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)) - (5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(32*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^2, x, 12, (9*b*c^3*d^2*x^2*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^4*sqrt(d - c^2*d*x^2))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (15/8)*c^2*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (5/4)*c^2*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x + (15*c*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*d^2*sqrt(d - c^2*d*x^2)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^4, x, 12, -((b*c*d^2*sqrt(d - c^2*d*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c^5*d^2*x^2*sqrt(d - c^2*d*x^2))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/2)*c^4*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*x) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(3*x^3) - (5*c^3*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (7*b*c^3*d^2*sqrt(d - c^2*d*x^2)*log(x))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^6, x, 12, -((b*c*d^2*sqrt(d - c^2*d*x^2))/(20*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (11*b*c^3*d^2*sqrt(d - c^2*d*x^2))/(30*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (c^4*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/x + (c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*x^3) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(5*x^5) + (c^5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (23*b*c^5*d^2*sqrt(d - c^2*d*x^2)*log(x))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^8, x, 5, -((b*c*d^2*sqrt(d - c^2*d*x^2))/(42*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (3*b*c^3*d^2*sqrt(d - c^2*d*x^2))/(28*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*c^5*d^2*sqrt(d - c^2*d*x^2))/(14*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*d*x^7) - (b*c^7*d^2*sqrt(d - c^2*d*x^2)*log(x))/(7*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^10, x, 6, -((b*c^3*d^2*sqrt(d - c^2*d*x^2))/(189*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^5*d^2*sqrt(d - c^2*d*x^2))/(42*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^7*d^2*sqrt(d - c^2*d*x^2))/(21*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*(1 - c^2*x^2)^4*sqrt(d - c^2*d*x^2))/(72*x^8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(9*d*x^9) - (2*c^2*(d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(63*d*x^7) - (2*b*c^9*d^2*sqrt(d - c^2*d*x^2)*log(x))/(63*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^12, x, 5, -((b*c*d^2*sqrt(d - c^2*d*x^2))/(110*x^10*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (23*b*c^3*d^2*sqrt(d - c^2*d*x^2))/(792*x^8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (113*b*c^5*d^2*sqrt(d - c^2*d*x^2))/(4158*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^7*d^2*sqrt(d - c^2*d*x^2))/(924*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^9*d^2*sqrt(d - c^2*d*x^2))/(693*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(11*d*x^11) - (4*c^2*(d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(99*d*x^9) - (8*c^4*(d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(693*d*x^7) - (8*b*c^11*d^2*sqrt(d - c^2*d*x^2)*log(x))/(693*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^7*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 4, (16*b*d^2*x*sqrt(d - c^2*d*x^2))/(3003*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (8*b*d^2*x^3*sqrt(d - c^2*d*x^2))/(9009*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d^2*x^5*sqrt(d - c^2*d*x^2))/(5005*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*d^2*x^7*sqrt(d - c^2*d*x^2))/(21021*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (53*b*c*d^2*x^9*sqrt(d - c^2*d*x^2))/(3861*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (27*b*c^3*d^2*x^11*sqrt(d - c^2*d*x^2))/(1573*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^13*sqrt(d - c^2*d*x^2))/(169*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^8*d) + ((d - c^2*d*x^2)^(9/2)*(a + b*acosh(c*x)))/(3*c^8*d^2) - (3*(d - c^2*d*x^2)^(11/2)*(a + b*acosh(c*x)))/(11*c^8*d^3) + ((d - c^2*d*x^2)^(13/2)*(a + b*acosh(c*x)))/(13*c^8*d^4)]
    @test_int [x^5*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 4, (8*b*d^2*x*sqrt(d - c^2*d*x^2))/(693*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*d^2*x^3*sqrt(d - c^2*d*x^2))/(2079*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*x^5*sqrt(d - c^2*d*x^2))/(1155*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (113*b*c*d^2*x^7*sqrt(d - c^2*d*x^2))/(4851*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (23*b*c^3*d^2*x^9*sqrt(d - c^2*d*x^2))/(891*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^11*sqrt(d - c^2*d*x^2))/(121*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^6*d) + (2*(d - c^2*d*x^2)^(9/2)*(a + b*acosh(c*x)))/(9*c^6*d^2) - ((d - c^2*d*x^2)^(11/2)*(a + b*acosh(c*x)))/(11*c^6*d^3)]
    @test_int [x^3*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 4, (2*b*d^2*x*sqrt(d - c^2*d*x^2))/(63*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*x^3*sqrt(d - c^2*d*x^2))/(189*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*x^5*sqrt(d - c^2*d*x^2))/(21*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (19*b*c^3*d^2*x^7*sqrt(d - c^2*d*x^2))/(441*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^9*sqrt(d - c^2*d*x^2))/(81*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^4*d) + ((d - c^2*d*x^2)^(9/2)*(a + b*acosh(c*x)))/(9*c^4*d^2)]
    @test_int [x^1*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 4, (b*d^2*x*sqrt(d - c^2*d*x^2))/(7*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*x^3*sqrt(d - c^2*d*x^2))/(7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*c^3*d^2*x^5*sqrt(d - c^2*d*x^2))/(35*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^7*sqrt(d - c^2*d*x^2))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x)))/(7*c^2*d)]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^1, x, 15, -((23*b*c*d^2*x*sqrt(d - c^2*d*x^2))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (11*b*c^3*d^2*x^3*sqrt(d - c^2*d*x^2))/(45*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^5*sqrt(d - c^2*d*x^2))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (1/3)*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) + (1/5)*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)) - (2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^3, x, 15, -((b*c*d^2*sqrt(d - c^2*d*x^2))/(2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (7*b*c^3*d^2*x*sqrt(d - c^2*d*x^2))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^3*sqrt(d - c^2*d*x^2))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5/2)*c^2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) - (5/6)*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(2*x^2) + (5*c^2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*im*b*c^2*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*im*b*c^2*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/x^5, x, 16, -((b*c*d^2*sqrt(d - c^2*d*x^2))/(12*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (9*b*c^3*d^2*sqrt(d - c^2*d*x^2))/(8*x*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15/8)*c^4*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)) + (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(8*x^2) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(4*x^4) - (15*c^4*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*im*b*c^4*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (15*im*b*c^4*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, im*ℯ^acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x))]

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

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

    @test_int [x^5*(a + b*acosh(c*x))/sqrt(d - c^2*d*x^2), x, 6, -((8*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(15*c^5*sqrt(d - c^2*d*x^2))) - (4*b*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(45*c^3*sqrt(d - c^2*d*x^2)) - (b*x^5*sqrt(-1 + c*x)*sqrt(1 + c*x))/(25*c*sqrt(d - c^2*d*x^2)) - (8*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(15*c^6*d) - (4*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(15*c^4*d) - (x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*c^2*d)]
    @test_int [x^4*(a + b*acosh(c*x))/sqrt(d - c^2*d*x^2), x, 5, -((3*b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*c^3*sqrt(d - c^2*d*x^2))) - (b*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*c*sqrt(d - c^2*d*x^2)) - (3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*c^4*d) - (x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(4*c^2*d) + (3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(16*b*c^5*sqrt(d - c^2*d*x^2))]
    @test_int [x^3*(a + b*acosh(c*x))/sqrt(d - c^2*d*x^2), x, 4, -((2*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3*c^3*sqrt(d - c^2*d*x^2))) - (b*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c*sqrt(d - c^2*d*x^2)) - (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*c^4*d) - (x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*c^2*d)]
    @test_int [x^2*(a + b*acosh(c*x))/sqrt(d - c^2*d*x^2), x, 3, -((b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c*sqrt(d - c^2*d*x^2))) - (x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*c^2*d) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(4*b*c^3*sqrt(d - c^2*d*x^2))]
    @test_int [x^1*(a + b*acosh(c*x))/sqrt(d - c^2*d*x^2), x, 2, -((b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*sqrt(d - c^2*d*x^2))) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(c^2*d)]
    @test_int [x^0*(a + b*acosh(c*x))/sqrt(d - c^2*d*x^2), x, 1, (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^1*sqrt(d - c^2*d*x^2)), x, 6, (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) - (im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) + (im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, im*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2)]
    @test_int [(a + b*acosh(c*x))/(x^2*sqrt(d - c^2*d*x^2)), x, 2, -((sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(d*x)) - (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(x))/sqrt(d - c^2*d*x^2)]
    @test_int [(a + b*acosh(c*x))/(x^3*sqrt(d - c^2*d*x^2)), x, 8, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*x*sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*d*x^2) + (c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) - (im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(2*sqrt(d - c^2*d*x^2)) + (im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, im*ℯ^acosh(c*x)))/(2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^4*sqrt(d - c^2*d*x^2)), x, 4, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*x^2*sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*d*x^3) - (2*c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*d*x) - (2*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(x))/(3*sqrt(d - c^2*d*x^2))]

    @test_int [(x^5*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(3/2), x, 5, -((5*b*x*sqrt(d - c^2*d*x^2))/(3*c^5*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*x^3*sqrt(d - c^2*d*x^2))/(9*c^3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (a + b*acosh(c*x))/(c^6*d*sqrt(d - c^2*d*x^2)) + (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(c^6*d^2) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(3*c^6*d^3) - (b*sqrt(d - c^2*d*x^2)*atanh(c*x))/(c^6*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(x^4*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(3/2), x, 7, (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c^3*d*sqrt(d - c^2*d*x^2)) + (x^3*(a + b*acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2)) + (3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*c^4*d^2) - (3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(4*b*c^5*d*sqrt(d - c^2*d*x^2)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(2*c^5*d*sqrt(d - c^2*d*x^2))]
    @test_int [(x^3*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(3/2), x, 4, -((b*x*sqrt(d - c^2*d*x^2))/(c^3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (a + b*acosh(c*x))/(c^4*d*sqrt(d - c^2*d*x^2)) + (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(c^4*d^2) - (b*sqrt(d - c^2*d*x^2)*atanh(c*x))/(c^4*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(x^2*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(3/2), x, 4, (x*(a + b*acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c^3*d*sqrt(d - c^2*d*x^2)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(2*c^3*d*sqrt(d - c^2*d*x^2))]
    @test_int [(x^1*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(3/2), x, 3, (a + b*acosh(c*x))/(c^2*d*sqrt(d - c^2*d*x^2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(c^2*d*sqrt(d - c^2*d*x^2))]
    @test_int [x^0*(a + b*acosh(c*x))/(d - c^2*d*x^2)^(3/2), x, 2, (x*(a + b*acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(2*c*d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^1*(d - c^2*d*x^2)^(3/2)), x, 9, (a + b*acosh(c*x))/(d*sqrt(d - c^2*d*x^2)) + (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(d*sqrt(d - c^2*d*x^2)) - (im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, im*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^2*(d - c^2*d*x^2)^(3/2)), x, 5, -((a + b*acosh(c*x))/(d*x*sqrt(d - c^2*d*x^2))) + (2*c^2*x*(a + b*acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (b*c*sqrt(d - c^2*d*x^2)*log(x))/(d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*sqrt(d - c^2*d*x^2)*log(1 - c^2*x^2))/(2*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(a + b*acosh(c*x))/(x^3*(d - c^2*d*x^2)^(3/2)), x, 13, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*d*x*sqrt(d - c^2*d*x^2)) + (3*c^2*(a + b*acosh(c*x)))/(2*d*sqrt(d - c^2*d*x^2)) - (a + b*acosh(c*x))/(2*d*x^2*sqrt(d - c^2*d*x^2)) + (3*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(d*sqrt(d - c^2*d*x^2)) - (3*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(2*d*sqrt(d - c^2*d*x^2)) + (3*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, im*ℯ^acosh(c*x)))/(2*d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^4*(d - c^2*d*x^2)^(3/2)), x, 5, -((b*c*sqrt(d - c^2*d*x^2))/(6*d^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (a + b*acosh(c*x))/(3*d*x^3*sqrt(d - c^2*d*x^2)) - (4*c^2*(a + b*acosh(c*x)))/(3*d*x*sqrt(d - c^2*d*x^2)) + (8*c^4*x*(a + b*acosh(c*x)))/(3*d*sqrt(d - c^2*d*x^2)) + (5*b*c^3*sqrt(d - c^2*d*x^2)*log(x))/(3*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*sqrt(d - c^2*d*x^2)*log(1 - c^2*x^2))/(2*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [(x^5*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(5/2), x, 5, (b*x*sqrt(d - c^2*d*x^2))/(c^5*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*x*sqrt(d - c^2*d*x^2))/(6*c^5*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)) + (a + b*acosh(c*x))/(3*c^6*d*(d - c^2*d*x^2)^(3/2)) - (2*(a + b*acosh(c*x)))/(c^6*d^2*sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(c^6*d^3) + (11*b*sqrt(d - c^2*d*x^2)*atanh(c*x))/(6*c^6*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(x^4*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(5/2), x, 9, (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c^5*d*(d - c^2*d*x^2)^(3/2)) + (x^3*(a + b*acosh(c*x)))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (x*(a + b*acosh(c*x)))/(c^4*d^2*sqrt(d - c^2*d*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c^5*d^2*sqrt(d - c^2*d*x^2)) + (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)), (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c^5*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x^3*(a + b*acosh(c*x)))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (x*(a + b*acosh(c*x)))/(c^4*d^2*sqrt(d - c^2*d*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(2*b*c^5*d^2*sqrt(d - c^2*d*x^2)) + (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(3*c^5*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(x^3*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(5/2), x, 4, (b*x*sqrt(d - c^2*d*x^2))/(6*c^3*d^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2)) + (a + b*acosh(c*x))/(3*c^4*d*(d - c^2*d*x^2)^(3/2)) - (a + b*acosh(c*x))/(c^4*d^2*sqrt(d - c^2*d*x^2)) + (5*b*sqrt(d - c^2*d*x^2)*atanh(c*x))/(6*c^4*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*x*sqrt(d - c^2*d*x^2))/(6*c^3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2))) + (a + b*acosh(c*x))/(3*c^4*d*(d - c^2*d*x^2)^(3/2)) - (a + b*acosh(c*x))/(c^4*d^2*sqrt(d - c^2*d*x^2)) + (5*b*sqrt(d - c^2*d*x^2)*atanh(c*x))/(6*c^4*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(x^2*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(5/2), x, 5, (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c^3*d*(d - c^2*d*x^2)^(3/2)) + (x^3*(a + b*acosh(c*x)))/(3*d*(d - c^2*d*x^2)^(3/2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(6*c^3*d^2*sqrt(d - c^2*d*x^2)), (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c^3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x^3*(a + b*acosh(c*x)))/(3*d*(d - c^2*d*x^2)^(3/2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(6*c^3*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(x^1*(a + b*acosh(c*x)))/(d - c^2*d*x^2)^(5/2), x, 4, (b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c*d*(d - c^2*d*x^2)^(3/2)) + (a + b*acosh(c*x))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(6*c^2*d^2*sqrt(d - c^2*d*x^2)), (b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (a + b*acosh(c*x))/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(6*c^2*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [x^0*(a + b*acosh(c*x))/(d - c^2*d*x^2)^(5/2), x, 5, (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c*d*(d - c^2*d*x^2)^(3/2)) + (x*(a + b*acosh(c*x)))/(3*d*(d - c^2*d*x^2)^(3/2)) + (2*x*(a + b*acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(3*c*d^2*sqrt(d - c^2*d*x^2)), (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*c*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x*(a + b*acosh(c*x)))/(3*d*(d - c^2*d*x^2)^(3/2)) + (2*x*(a + b*acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) - (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*log(1 - c^2*x^2))/(3*c*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^1*(d - c^2*d*x^2)^(5/2)), x, 13, (b*c*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (a + b*acosh(c*x))/(3*d*(d - c^2*d*x^2)^(3/2)) + (a + b*acosh(c*x))/(d^2*sqrt(d - c^2*d*x^2)) + (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (7*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(6*d^2*sqrt(d - c^2*d*x^2)) - (im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, im*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^2*(d - c^2*d*x^2)^(5/2)), x, 5, -((b*c*sqrt(d - c^2*d*x^2))/(6*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2))) - (a + b*acosh(c*x))/(d*x*(d - c^2*d*x^2)^(3/2)) + (4*c^2*x*(a + b*acosh(c*x)))/(3*d*(d - c^2*d*x^2)^(3/2)) + (8*c^2*x*(a + b*acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) + (b*c*sqrt(d - c^2*d*x^2)*log(x))/(d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c*sqrt(d - c^2*d*x^2)*log(1 - c^2*x^2))/(6*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(a + b*acosh(c*x))/(x^3*(d - c^2*d*x^2)^(5/2)), x, 18, (3*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*d^2*x*sqrt(d - c^2*d*x^2)) - (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*d^2*x*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (5*b*c^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(12*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (5*c^2*(a + b*acosh(c*x)))/(6*d*(d - c^2*d*x^2)^(3/2)) - (a + b*acosh(c*x))/(2*d*x^2*(d - c^2*d*x^2)^(3/2)) + (5*c^2*(a + b*acosh(c*x)))/(2*d^2*sqrt(d - c^2*d*x^2)) + (5*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atan(ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (13*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*atanh(c*x))/(6*d^2*sqrt(d - c^2*d*x^2)) - (5*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(2*d^2*sqrt(d - c^2*d*x^2)) + (5*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, im*ℯ^acosh(c*x)))/(2*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))/(x^4*(d - c^2*d*x^2)^(5/2)), x, 5, -((b*c*sqrt(d - c^2*d*x^2))/(6*d^3*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c^3*sqrt(d - c^2*d*x^2))/(6*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)) - (a + b*acosh(c*x))/(3*d*x^3*(d - c^2*d*x^2)^(3/2)) - (2*c^2*(a + b*acosh(c*x)))/(d*x*(d - c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*acosh(c*x)))/(3*d*(d - c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) + (8*b*c^3*sqrt(d - c^2*d*x^2)*log(x))/(3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*c^3*sqrt(d - c^2*d*x^2)*log(1 - c^2*x^2))/(3*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [acosh(a*x)/(c - a^2*c*x^2)^(7/2), x, 8, (sqrt(-1 + a*x)*sqrt(1 + a*x))/(20*a*c^3*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)) + (2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(15*a*c^3*(1 - a^2*x^2)*sqrt(c - a^2*c*x^2)) + (x*acosh(a*x))/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*acosh(a*x))/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*acosh(a*x))/(15*c^3*sqrt(c - a^2*c*x^2)) - (4*sqrt(-1 + a*x)*sqrt(1 + a*x)*log(1 - a^2*x^2))/(15*a*c^3*sqrt(c - a^2*c*x^2))]

    @test_int [(x^4*acosh(a*x))/sqrt(1 - a^2*x^2), x, 5, -((3*x^2*sqrt(-1 + a*x))/(16*a^3*sqrt(1 - a*x))) - (x^4*sqrt(-1 + a*x))/(16*a*sqrt(1 - a*x)) - (3*x*sqrt(1 - a^2*x^2)*acosh(a*x))/(8*a^4) - (x^3*sqrt(1 - a^2*x^2)*acosh(a*x))/(4*a^2) + (3*sqrt(-1 + a*x)*acosh(a*x)^2)/(16*a^5*sqrt(1 - a*x))]
    @test_int [(x^3*acosh(a*x))/sqrt(1 - a^2*x^2), x, 4, -((2*x*sqrt(-1 + a*x))/(3*a^3*sqrt(1 - a*x))) - (x^3*sqrt(-1 + a*x))/(9*a*sqrt(1 - a*x)) - (2*sqrt(1 - a^2*x^2)*acosh(a*x))/(3*a^4) - (x^2*sqrt(1 - a^2*x^2)*acosh(a*x))/(3*a^2)]
    @test_int [(x^2*acosh(a*x))/sqrt(1 - a^2*x^2), x, 3, -((x^2*sqrt(-1 + a*x))/(4*a*sqrt(1 - a*x))) - (x*sqrt(1 - a^2*x^2)*acosh(a*x))/(2*a^2) + (sqrt(-1 + a*x)*acosh(a*x)^2)/(4*a^3*sqrt(1 - a*x))]
    @test_int [(x^1*acosh(a*x))/sqrt(1 - a^2*x^2), x, 2, -((x*sqrt(-1 + a*x))/(a*sqrt(1 - a*x))) - (sqrt(1 - a^2*x^2)*acosh(a*x))/a^2]
    @test_int [x^0*acosh(a*x)/sqrt(1 - a^2*x^2), x, 1, (sqrt(-1 + a*x)*acosh(a*x)^2)/(2*a*sqrt(1 - a*x))]
    @test_int [acosh(a*x)/(x^1*sqrt(1 - a^2*x^2)), x, 6, (2*sqrt(-1 + a*x)*acosh(a*x)*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) - (im*sqrt(-1 + a*x)*PolyLog(2, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (im*sqrt(-1 + a*x)*PolyLog(2, im*ℯ^acosh(a*x)))/sqrt(1 - a*x)]
    @test_int [acosh(a*x)/(x^2*sqrt(1 - a^2*x^2)), x, 2, -((sqrt(1 - a^2*x^2)*acosh(a*x))/x) - (a*sqrt(-1 + a*x)*log(x))/sqrt(1 - a*x)]
    @test_int [acosh(a*x)/(x^3*sqrt(1 - a^2*x^2)), x, 8, (a*sqrt(-1 + a*x))/(2*x*sqrt(1 - a*x)) - (sqrt(1 - a^2*x^2)*acosh(a*x))/(2*x^2) + (a^2*sqrt(-1 + a*x)*acosh(a*x)*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) - (im*a^2*sqrt(-1 + a*x)*PolyLog(2, (-im)*ℯ^acosh(a*x)))/(2*sqrt(1 - a*x)) + (im*a^2*sqrt(-1 + a*x)*PolyLog(2, im*ℯ^acosh(a*x)))/(2*sqrt(1 - a*x))]

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

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

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

    @test_int [((f*x)^(3/2)*(a + b*acosh(c*x)))/sqrt(1 - c^2*x^2), x, 1, (2*(f*x)^(5/2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, 5/4, 9/4, c^2*x^2))/(5*f) + (4*b*c*(f*x)^(7/2)*sqrt(-1 + c*x)*HypergeometricPFQ([1, 7/4, 7/4], [9/4, 11/4], c^2*x^2))/(35*f^2*sqrt(1 - c*x))]

    @test_int [((f*x)^(3/2)*(a + b*acosh(c*x)))/sqrt(d - c^2*d*x^2), x, 1, (2*(f*x)^(5/2)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, 5/4, 9/4, c^2*x^2))/(5*f*sqrt(d - c^2*d*x^2)) + (4*b*c*(f*x)^(7/2)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 7/4, 7/4], [9/4, 11/4], c^2*x^2))/(35*f^2*sqrt(d - c^2*d*x^2))]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))*with*m*symbolic=#

    @test_int [(f*x)^m*(d - c^2*d*x^2)^3*(a + b*acosh(c*x)), x, 8, If(13>=8, -((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*(f*x)^(2 + m)*(1 - c^2*x^2))/(f^2*(3 + m)^2*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d^3*(9 + m)*(13 + 2*m)*(f*x)^(4 + m)*(1 - c^2*x^2))/(f^4*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^3*(f*x)^(6 + m)*(1 - c^2*x^2))/(f^6*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^3*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) - (3*c^2*d^3*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (3*c^4*d^3*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) - (c^6*d^3*(f*x)^(7 + m)*(a + b*acosh(c*x)))/(f^7*(7 + m)) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(f^2*(1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*c*d^3*(2271 + 1329*m + 284*m^2 + 27*m^3 + m^4)*(f*x)^(2 + m)*(1 - c^2*x^2))/(f^2*(7 + m)^2*(15 + 8*m + m^2)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d^3*(9 + m)*(13 + 2*m)*(f*x)^(4 + m)*(1 - c^2*x^2))/(f^4*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^3*(f*x)^(6 + m)*(1 - c^2*x^2))/(f^6*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^3*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) - (3*c^2*d^3*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (3*c^4*d^3*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) - (c^6*d^3*(f*x)^(7 + m)*(a + b*acosh(c*x)))/(f^7*(7 + m)) - (3*b*c*d^3*(2161 + 1813*m + 455*m^2 + 35*m^3)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(f^2*(7 + m)^2*(2 + 3*m + m^2)*(15 + 8*m + m^2)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^2*(a + b*acosh(c*x)), x, 7, If(13>=8, -((b*c*d^2*(38 + 13*m + m^2)*(f*x)^(2 + m)*(1 - c^2*x^2))/(f^2*(3 + m)^2*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d^2*(f*x)^(4 + m)*(1 - c^2*x^2))/(f^4*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^2*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) - (2*c^2*d^2*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (c^4*d^2*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) - (b*c*d^2*(149 + 100*m + 15*m^2)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(f^2*(1 + m)*(2 + m)*(3 + m)^2*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*c*d^2*(38 + 13*m + m^2)*(f*x)^(2 + m)*(1 - c^2*x^2))/(f^2*(3 + m)^2*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (b*c^3*d^2*(f*x)^(4 + m)*(1 - c^2*x^2))/(f^4*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^2*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) - (2*c^2*d^2*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (c^4*d^2*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) - (b*c*d^2*(149 + 100*m + 15*m^2)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(f^2*(2 + 3*m + m^2)*(15 + 8*m + m^2)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^1*(a + b*acosh(c*x)), x, 6, If(13>=8, (b*c*d*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(f^2*(3 + m)^2) + (d*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) - (c^2*d*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) - (b*c*d*(7 + 3*m)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(f^2*(1 + m)*(2 + m)*(3 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)), (b*c*d*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(f^2*(3 + m)^2) + (d*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) - (c^2*d*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) - (b*c*d*(7 + 3*m)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(f^2*(3 + m)^2*(2 + 3*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d - c^2*d*x^2)^1, x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x)))/(d - c^2*d*x^2), x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d - c^2*d*x^2)^2, x, 4, ((f*x)^(1 + m)*(a + b*acosh(c*x)))/(2*d^2*f*(1 - c^2*x^2)) - (b*c*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(3/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(2*d^2*f^2*(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((1 - m)*Unintegrable(((f*x)^m*(a + b*acosh(c*x)))/(d - c^2*d*x^2), x))/(2*d)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d - c^2*d*x^2)^3, x, 8, ((f*x)^(1 + m)*(a + b*acosh(c*x)))/(4*d^3*f*(1 - c^2*x^2)^2) + ((3 - m)*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(8*d^3*f*(1 - c^2*x^2)) - (b*c*(3 - m)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(3/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(8*d^3*f^2*(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(5/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(4*d^3*f^2*(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((1 - m)*(3 - m)*Unintegrable(((f*x)^m*(a + b*acosh(c*x)))/(d - c^2*d*x^2), x))/(8*d^2)]

    @test_int [(f*x)^m*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)), x, 11, If(13>=8, -((b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (15*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2))/(f^4*(4 + m)^2*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2))/(f^4*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*(f*x)^(6 + m)*sqrt(d - c^2*d*x^2))/(f^6*(6 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*d^2*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d*(f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(f*(6 + m)) + (15*d^2*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(4 + m)*(6 + m)*(2 + 3*m + m^2)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (15*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (15*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(6 + m)*(8 + 6*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2))/(f^4*(4 + m)^2*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2))/(f^4*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*(f*x)^(6 + m)*sqrt(d - c^2*d*x^2))/(f^6*(6 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*d^2*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d*(f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x)))/(f*(6 + m)) + (15*d^2*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(6 + m)*(8 + 14*m + 7*m^2 + m^3)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (15*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(2 + m)^2*(6 + m)*(4 + 5*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)), x, 7, If(13>=8, -((3*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2))/(f^4*(4 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*d*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)) + (3*d*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(4 + m)*(2 + 3*m + m^2)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (3*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((3*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2))/(f^4*(4 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*d*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)) + (3*d*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(8 + 14*m + 7*m^2 + m^3)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (3*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(2 + m)^2*(4 + 5*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^(1/2)*(a + b*acosh(c*x)), x, 3, -((b*c*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2))/(f^2*(2 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + ((f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f*(2 + m)) + ((f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(2 + 3*m + m^2)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (b*c*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d - c^2*d*x^2)^(1/2), x, 1, ((f*x)^(1 + m)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(1 + m)*sqrt(d - c^2*d*x^2)) + (b*c*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)*sqrt(d - c^2*d*x^2))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d - c^2*d*x^2)^(3/2), x, 4, ((f*x)^(1 + m)*(a + b*acosh(c*x)))/(d*f*sqrt(d - c^2*d*x^2)) - (m*(f*x)^(1 + m)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(d*f*(1 + m)*sqrt(d - c^2*d*x^2)) + (b*c*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, c^2*x^2))/(d*f^2*(2 + m)*sqrt(d - c^2*d*x^2)) - (b*c*m*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(d*f^2*(1 + m)*(2 + m)*sqrt(d - c^2*d*x^2))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d - c^2*d*x^2)^(5/2), x, 7, ((f*x)^(1 + m)*(a + b*acosh(c*x)))/(3*d*f*(d - c^2*d*x^2)^(3/2)) + ((2 - m)*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(3*d^2*f*sqrt(d - c^2*d*x^2)) - ((2 - m)*m*(f*x)^(1 + m)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(3*d^2*f*(1 + m)*sqrt(d - c^2*d*x^2)) + (b*c*(2 - m)*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, c^2*x^2))/(3*d^2*f^2*(2 + m)*sqrt(d - c^2*d*x^2)) + (b*c*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricFunctions._₂F₁(2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(3*d^2*f^2*(2 + m)*sqrt(d - c^2*d*x^2)) - (b*c*(2 - m)*m*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(3*d^2*f^2*(1 + m)*(2 + m)*sqrt(d - c^2*d*x^2))]

    @test_int [(f*x)^m*(d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)*(a + b*acosh(c*x)), x, 11, If(13>=8, -((b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (15*b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d1^2*d2^2*(f*x)^(4 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^4*(4 + m)^2*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d1^2*d2^2*(f*x)^(4 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^4*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d1^2*d2^2*(f*x)^(6 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^6*(6 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*d1^2*d2^2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x)))/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d1*d2*(f*x)^(1 + m)*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)*(a + b*acosh(c*x)))/(f*(6 + m)) + (15*d1^2*d2^2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(4 + m)*(6 + m)*(2 + 3*m + m^2)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (15*b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (15*b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(6 + m)*(8 + 6*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*c^3*d1^2*d2^2*(f*x)^(4 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^4*(4 + m)^2*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d1^2*d2^2*(f*x)^(4 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^4*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d1^2*d2^2*(f*x)^(6 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^6*(6 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*d1^2*d2^2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x)))/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d1*d2*(f*x)^(1 + m)*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)*(a + b*acosh(c*x)))/(f*(6 + m)) + (15*d1^2*d2^2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(6 + m)*(8 + 14*m + 7*m^2 + m^3)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (15*b*c*d1^2*d2^2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(2 + m)^2*(6 + m)*(4 + 5*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*acosh(c*x)), x, 7, If(13>=8, -((3*b*c*d1*d2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c*d1*d2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d1*d2*(f*x)^(4 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^4*(4 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*d1*d2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x)))/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)) + (3*d1*d2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(4 + m)*(2 + 3*m + m^2)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (3*b*c*d1*d2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((3*b*c*d1*d2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*c*d1*d2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d1*d2*(f*x)^(4 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^4*(4 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*d1*d2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x)))/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)*(a + b*acosh(c*x)))/(f*(4 + m)) + (3*d1*d2*(f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(8 + 14*m + 7*m^2 + m^3)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (3*b*c*d1*d2*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(2 + m)^2*(4 + 5*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d1 + c*d1*x)^(1/2)*(d2 - c*d2*x)^(1/2)*(a + b*acosh(c*x)), x, 3, -((b*c*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))/(f^2*(2 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + ((f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x)))/(f*(2 + m)) + ((f*x)^(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(2 + 3*m + m^2)*sqrt(1 - c*x)*sqrt(1 + c*x)) - (b*c*(f*x)^(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/((d1 + c*d1*x)^(1/2)*(d2 - c*d2*x)^(1/2)), x, 1, ((f*x)^(1 + m)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(f*(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) + (b*c*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(f^2*(1 + m)*(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/((d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)), x, 4, ((f*x)^(1 + m)*(a + b*acosh(c*x)))/(d1*d2*f*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) - (m*(f*x)^(1 + m)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(d1*d2*f*(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) + (b*c*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, c^2*x^2))/(d1*d2*f^2*(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) - (b*c*m*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(d1*d2*f^2*(1 + m)*(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/((d1 + c*d1*x)^(5/2)*(d2 - c*d2*x)^(5/2)), x, 7, ((f*x)^(1 + m)*(a + b*acosh(c*x)))/(3*d1*d2*f*(d1 + c*d1*x)^(3/2)*(d2 - c*d2*x)^(3/2)) + ((2 - m)*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(3*d1^2*d2^2*f*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) - ((2 - m)*m*(f*x)^(1 + m)*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, c^2*x^2))/(3*d1^2*d2^2*f*(1 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) + (b*c*(2 - m)*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricFunctions._₂F₁(1, (2 + m)/2, (4 + m)/2, c^2*x^2))/(3*d1^2*d2^2*f^2*(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) + (b*c*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricFunctions._₂F₁(2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(3*d1^2*d2^2*f^2*(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x)) - (b*c*(2 - m)*m*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], c^2*x^2))/(3*d1^2*d2^2*f^2*(1 + m)*(2 + m)*sqrt(d1 + c*d1*x)*sqrt(d2 - c*d2*x))]

    @test_int [(f*x)^m*acosh(a*x)/sqrt(1 - a^2*x^2), x, 1, ((f*x)^(1 + m)*acosh(a*x)*HypergeometricFunctions._₂F₁(1/2, (1 + m)/2, (3 + m)/2, a^2*x^2))/(f*(1 + m)) + (a*(f*x)^(2 + m)*sqrt(-1 + a*x)*HypergeometricPFQ([1, 1 + m/2, 1 + m/2], [3/2 + m/2, 2 + m/2], a^2*x^2))/(f^2*(1 + m)*(2 + m)*sqrt(1 - a*x))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^2=#

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

    @test_int [(c - a^2*c*x^2)^3*acosh(a*x)^2, x, 17, (4322*c^3*x)/3675 - (1514*a^2*c^3*x^3)/11025 + (234*a^4*c^3*x^5)/6125 - (2/343)*a^6*c^3*x^7 - (32*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(35*a) + (16*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x))/(105*a) - (12*c^3*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*acosh(a*x))/(175*a) + (2*c^3*(-1 + a*x)^(7/2)*(1 + a*x)^(7/2)*acosh(a*x))/(49*a) + (16/35)*c^3*x*acosh(a*x)^2 + (8/35)*c^3*x*(1 - a^2*x^2)*acosh(a*x)^2 + (6/35)*c^3*x*(1 - a^2*x^2)^2*acosh(a*x)^2 + (1/7)*c^3*x*(1 - a^2*x^2)^3*acosh(a*x)^2]
    @test_int [(c - a^2*c*x^2)^2*acosh(a*x)^2, x, 12, (298*c^2*x)/225 - (76/675)*a^2*c^2*x^3 + (2/125)*a^4*c^2*x^5 - (16*c^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(15*a) + (8*c^2*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x))/(45*a) - (2*c^2*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*acosh(a*x))/(25*a) + (8/15)*c^2*x*acosh(a*x)^2 + (4/15)*c^2*x*(1 - a^2*x^2)*acosh(a*x)^2 + (1/5)*c^2*x*(1 - a^2*x^2)^2*acosh(a*x)^2]
    @test_int [(c - a^2*c*x^2)^1*acosh(a*x)^2, x, 7, (14*c*x)/9 - (2/27)*a^2*c*x^3 - (4*c*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(3*a) + (2*c*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x))/(9*a) + (2/3)*c*x*acosh(a*x)^2 + (1/3)*c*x*(1 - a^2*x^2)*acosh(a*x)^2]
    @test_int [acosh(a*x)^2/(c - a^2*c*x^2)^1, x, 8, (2*acosh(a*x)^2*atanh(ℯ^acosh(a*x)))/(a*c) + (2*acosh(a*x)*PolyLog(2, -ℯ^acosh(a*x)))/(a*c) - (2*acosh(a*x)*PolyLog(2, ℯ^acosh(a*x)))/(a*c) - (2*PolyLog(3, -ℯ^acosh(a*x)))/(a*c) + (2*PolyLog(3, ℯ^acosh(a*x)))/(a*c)]
    @test_int [acosh(a*x)^2/(c - a^2*c*x^2)^2, x, 12, -(acosh(a*x)/(a*c^2*sqrt(-1 + a*x)*sqrt(1 + a*x))) + (x*acosh(a*x)^2)/(2*c^2*(1 - a^2*x^2)) + (acosh(a*x)^2*atanh(ℯ^acosh(a*x)))/(a*c^2) - atanh(a*x)/(a*c^2) + (acosh(a*x)*PolyLog(2, -ℯ^acosh(a*x)))/(a*c^2) - (acosh(a*x)*PolyLog(2, ℯ^acosh(a*x)))/(a*c^2) - PolyLog(3, -ℯ^acosh(a*x))/(a*c^2) + PolyLog(3, ℯ^acosh(a*x))/(a*c^2)]
    @test_int [acosh(a*x)^2/(c - a^2*c*x^2)^3, x, 17, -(x/(12*c^3*(1 - a^2*x^2))) + acosh(a*x)/(6*a*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)) - (3*acosh(a*x))/(4*a*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (x*acosh(a*x)^2)/(4*c^3*(1 - a^2*x^2)^2) + (3*x*acosh(a*x)^2)/(8*c^3*(1 - a^2*x^2)) + (3*acosh(a*x)^2*atanh(ℯ^acosh(a*x)))/(4*a*c^3) - (5*atanh(a*x))/(6*a*c^3) + (3*acosh(a*x)*PolyLog(2, -ℯ^acosh(a*x)))/(4*a*c^3) - (3*acosh(a*x)*PolyLog(2, ℯ^acosh(a*x)))/(4*a*c^3) - (3*PolyLog(3, -ℯ^acosh(a*x)))/(4*a*c^3) + (3*PolyLog(3, ℯ^acosh(a*x)))/(4*a*c^3)]

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

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

    @test_int [x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2, x, 16, (-856*b^2*sqrt(d - c^2*d*x^2))/(3375*c^4) + (22*b^2*x^2*sqrt(d - c^2*d*x^2))/(3375*c^2) + (2*b^2*x^4*sqrt(d - c^2*d*x^2))/125 + (4*a*b*x*sqrt(d - c^2*d*x^2))/(15*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b^2*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(15*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(45*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(15*c^4) - (x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(15*c^2) + (x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/5]
    @test_int [x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2, x, 11, -(b^2*x*sqrt(d - c^2*d*x^2))/(64*c^2) + (b^2*x^3*sqrt(d - c^2*d*x^2))/32 - (b^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(64*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(8*c^2) + (x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/4 - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(24*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^1*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2, x, 6, -((14*b^2*sqrt(d - c^2*d*x^2))/(27*c^2)) + (2/27)*b^2*x^2*sqrt(d - c^2*d*x^2) + (2*b*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(3*c^2*d)]
    @test_int [x^0*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2, x, 5, (b^2*x*sqrt(d - c^2*d*x^2))/4 + (b^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(4*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/2 - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(6*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/x^1, x, 12, 2*b^2*sqrt(d - c^2*d*x^2) - (2*a*b*c*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b^2*c*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 - (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*im*b*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*im*b*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*im*b^2*sqrt(d - c^2*d*x^2)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*im*b^2*sqrt(d - c^2*d*x^2)*PolyLog(3, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/x^2, x, 7, -((sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/x) + (c*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (c*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(3*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b^2*c*sqrt(d - c^2*d*x^2)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/x^3, x, 12, -((b*c*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(x*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*x^2) + (c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b^2*c^2*sqrt(d - c^2*d*x^2)*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b*c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (im*b^2*c^2*sqrt(d - c^2*d*x^2)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b^2*c^2*sqrt(d - c^2*d*x^2)*PolyLog(3, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/x^4, x, 11, (b^2*c^2*sqrt(d - c^2*d*x^2))/(3*x) - (b^2*c^3*sqrt(d - c^2*d*x^2)*acosh(c*x))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (c^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(3*d*x^3) - (2*b*c^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b^2*c^3*sqrt(d - c^2*d*x^2)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^3*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2, x, 26, -((37384*b^2*d*sqrt(d - c^2*d*x^2))/(385875*c^4)) + (3358*b^2*d*x^2*sqrt(d - c^2*d*x^2))/(385875*c^2) + (484*b^2*d*x^4*sqrt(d - c^2*d*x^2))/42875 - (2/343)*b^2*c^2*d*x^6*sqrt(d - c^2*d*x^2) + (4*a*b*d*x*sqrt(d - c^2*d*x^2))/(35*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b^2*d*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(35*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(105*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (16*b*c*d*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(175*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d*x^7*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(35*c^4) - (d*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(35*c^2) + (3/35)*d*x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (1/7)*x^4*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2]
    @test_int [x^2*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2, x, 20, (7*b^2*d*x*sqrt(d - c^2*d*x^2))/(1152*c^2) + (43*b^2*d*x^3*sqrt(d - c^2*d*x^2))/1728 - (1/108)*b^2*c^2*d*x^5*sqrt(d - c^2*d*x^2) + (7*b^2*d*sqrt(d - c^2*d*x^2)*acosh(c*x))/(1152*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(16*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (7*b*c*d*x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(48*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c^3*d*x^6*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(18*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(16*c^2) + (1/8)*d*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (1/6)*x^3*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 - (d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(48*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^1*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2, x, 8, -((16*b^2*d*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(75*c^2*(1 - c*x)*(1 + c*x))) - (8*b^2*d*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2))/(225*c^2*(1 - c*x)*(1 + c*x)) - (2*b^2*d*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(125*c^2*(1 - c*x)*(1 + c*x)) + (2*b*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(5*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*c*d*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/(5*c^2*d)]
    @test_int [x^0*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2, x, 11, (15/64)*b^2*d*x*sqrt(d - c^2*d*x^2) + (1/32)*b^2*d*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2) + (9*b^2*d*sqrt(d - c^2*d*x^2)*acosh(c*x))/(64*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*c*d*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3/8)*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (1/4)*x*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 - (d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(8*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/x^1, x, 18, (68/27)*b^2*d*sqrt(d - c^2*d*x^2) - (2/27)*b^2*c^2*d*x^2*sqrt(d - c^2*d*x^2) - (2*a*b*c*d*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b^2*c*d*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (1/3)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 - (2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*im*b*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*im*b*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*im*b^2*d*sqrt(d - c^2*d*x^2)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*im*b^2*d*sqrt(d - c^2*d*x^2)*PolyLog(3, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/x^2, x, 15, (-(1/4))*b^2*c^2*d*x*sqrt(d - c^2*d*x^2) - (5*b^2*c*d*sqrt(d - c^2*d*x^2)*acosh(c*x))/(4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*c^3*d*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*d*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3/2)*c^2*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (c*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/x + (c*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b^2*c*d*sqrt(d - c^2*d*x^2)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/x^3, x, 18, -2*b^2*c^2*d*sqrt(d - c^2*d*x^2) + (3*a*b*c^3*d*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b^2*c^3*d*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(x*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^3*d*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3/2)*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(2*x^2) + (3*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b^2*c^2*d*sqrt(d - c^2*d*x^2)*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*im*b*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*im*b*c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*im*b^2*c^2*d*sqrt(d - c^2*d*x^2)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*im*b^2*c^2*d*sqrt(d - c^2*d*x^2)*PolyLog(3, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/x^4, x, 18, (b^2*c^2*d*sqrt(d - c^2*d*x^2))/(3*x) - (b^2*c^3*d*sqrt(d - c^2*d*x^2)*acosh(c*x))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (c^2*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/x - (4*c^3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(3*x^3) - (c^3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(3*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (8*b*c^3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b^2*c^3*d*sqrt(d - c^2*d*x^2)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^3*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2, x, 35, -((37384*b^2*d^2*sqrt(d - c^2*d*x^2))/(694575*c^4)) + (3358*b^2*d^2*x^2*sqrt(d - c^2*d*x^2))/(694575*c^2) + (484*b^2*d^2*x^4*sqrt(d - c^2*d*x^2))/77175 - (10*b^2*c^2*d^2*x^6*sqrt(d - c^2*d*x^2))/3087 + (4*a*b*d^2*x*sqrt(d - c^2*d*x^2))/(63*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (16*b^2*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(2835*c^4*(1 - c*x)*(1 + c*x)) + (8*b^2*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2))/(8505*c^4*(1 - c*x)*(1 + c*x)) + (2*b^2*d^2*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(4725*c^4*(1 - c*x)*(1 + c*x)) - (20*b^2*d^2*(1 - c^2*x^2)^4*sqrt(d - c^2*d*x^2))/(3969*c^4*(1 - c*x)*(1 + c*x)) + (2*b^2*d^2*(1 - c^2*x^2)^5*sqrt(d - c^2*d*x^2))/(729*c^4*(1 - c*x)*(1 + c*x)) + (4*b^2*d^2*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(63*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(189*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d^2*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(21*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (38*b*c^3*d^2*x^7*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(441*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*x^9*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(81*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(63*c^4) - (d^2*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(63*c^2) + (1/21)*d^2*x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (5/63)*d*x^4*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 + (1/9)*x^4*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2]
    @test_int [x^2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2, x, 31, (35*b^2*d^2*x*sqrt(d - c^2*d*x^2))/(9216*c^2) + (215*b^2*d^2*x^3*sqrt(d - c^2*d*x^2))/13824 - (5/864)*b^2*c^2*d^2*x^5*sqrt(d - c^2*d*x^2) + (73*b^2*d^2*x*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(12288*c^2*(1 - c*x)*(1 + c*x)) + (73*b^2*d^2*x^3*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(18432*(1 - c*x)*(1 + c*x)) - (43*b^2*c^2*d^2*x^5*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(4608*(1 - c*x)*(1 + c*x)) + (b^2*c^4*d^2*x^7*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(256*(1 - c*x)*(1 + c*x)) + (35*b^2*d^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(9216*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*d^2*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(128*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (59*b*c*d^2*x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(384*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (17*b*c^3*d^2*x^6*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(144*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^5*d^2*x^8*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(32*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(128*c^2) + (5/64)*d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (5/48)*d*x^3*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 + (1/8)*x^3*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2 - (5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(384*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (73*b^2*d^2*sqrt(-1 + c^2*x^2)*sqrt(d - c^2*d*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(12288*c^3*(1 - c*x)*(1 + c*x))]
    @test_int [x^1*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2, x, 8, -((32*b^2*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(245*c^2*(1 - c*x)*(1 + c*x))) - (16*b^2*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2))/(735*c^2*(1 - c*x)*(1 + c*x)) - (12*b^2*d^2*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(1225*c^2*(1 - c*x)*(1 + c*x)) - (2*b^2*d^2*(1 - c^2*x^2)^4*sqrt(d - c^2*d*x^2))/(343*c^2*(1 - c*x)*(1 + c*x)) + (2*b*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(7*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (6*b*c^3*d^2*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(35*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*x^7*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(49*sqrt(-1 + c*x)*sqrt(1 + c*x)) - ((d - c^2*d*x^2)^(7/2)*(a + b*acosh(c*x))^2)/(7*c^2*d)]
    @test_int [x^0*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2, x, 18, (245*b^2*d^2*x*sqrt(d - c^2*d*x^2))/1152 + (65*b^2*d^2*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2))/1728 + (1/108)*b^2*d^2*x*(1 - c*x)^2*(1 + c*x)^2*sqrt(d - c^2*d*x^2) + (115*b^2*d^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(1152*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c*d^2*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(16*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(48*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(18*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/16)*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (5/24)*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 + (1/6)*x*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2 - (5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(48*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/x^1, x, 26, (68/27)*b^2*d^2*sqrt(d - c^2*d*x^2) - (2/27)*b^2*c^2*d^2*x^2*sqrt(d - c^2*d*x^2) - (2*a*b*c*d^2*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (16*b^2*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(75*(1 - c*x)*(1 + c*x)) + (8*b^2*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2))/(225*(1 - c*x)*(1 + c*x)) + (2*b^2*d^2*(1 - c^2*x^2)^3*sqrt(d - c^2*d*x^2))/(125*(1 - c*x)*(1 + c*x)) - (2*b^2*c*d^2*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (16*b*c*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(15*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (22*b*c^3*d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(45*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*x^5*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(25*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (1/3)*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 + (1/5)*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2 - (2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*im*b*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*im*b*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*im*b^2*d^2*sqrt(d - c^2*d*x^2)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*im*b^2*d^2*sqrt(d - c^2*d*x^2)*PolyLog(3, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/x^2, x, 25, (-(31/64))*b^2*c^2*d^2*x*sqrt(d - c^2*d*x^2) - (1/32)*b^2*c^2*d^2*x*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2) - (89*b^2*c*d^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(64*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*b*c^3*d^2*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(8*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (15/8)*c^2*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 + (c*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5/4)*c^2*d*x*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/x + (5*c*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(8*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b^2*c*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/x^3, x, 28, (-(170/27))*b^2*c^2*d^2*sqrt(d - c^2*d*x^2) + (5/27)*b^2*c^4*d^2*x^2*sqrt(d - c^2*d*x^2) + (5*a*b*c^3*d^2*x*sqrt(d - c^2*d*x^2))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b^2*c^2*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(3*(1 - c*x)*(1 + c*x)) + (b^2*c^2*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2))/(9*(1 - c*x)*(1 + c*x)) + (5*b^2*c^3*d^2*x*sqrt(d - c^2*d*x^2)*acosh(c*x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(x*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c^3*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5/2)*c^2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 - (5/6)*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2 - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/(2*x^2) + (5*c^2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b^2*c^2*d^2*sqrt(-1 + c^2*x^2)*sqrt(d - c^2*d*x^2)*atan(sqrt(-1 + c^2*x^2)))/((1 - c*x)*(1 + c*x)) - (5*im*b*c^2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*im*b*c^2*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*im*b^2*c^2*d^2*sqrt(d - c^2*d*x^2)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*im*b^2*c^2*d^2*sqrt(d - c^2*d*x^2)*PolyLog(3, im*ℯ^acosh(c*x)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/x^4, x, 30, (7/12)*b^2*c^4*d^2*x*sqrt(d - c^2*d*x^2) + (b^2*c^2*d^2*(1 - c*x)*(1 + c*x)*sqrt(d - c^2*d*x^2))/(3*x) + (23*b^2*c^3*d^2*sqrt(d - c^2*d*x^2)*acosh(c*x))/(12*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (5*b*c^5*d^2*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (7*b*c^3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*(1 - c^2*x^2)^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(3*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5/2)*c^4*d^2*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2 - (7*c^3*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*c^2*d*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(3*x) - ((d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/(3*x^3) - (5*c^3*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^3)/(6*b*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (14*b*c^3*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (7*b^2*c^3*d^2*sqrt(d - c^2*d*x^2)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(3*sqrt(-1 + c*x)*sqrt(1 + c*x))]

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

    @test_int [(x^5*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x, 16, -((16*a*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(15*c^5*sqrt(d - c^2*d*x^2))) - (4144*b^2*(1 - c*x)*(1 + c*x))/(3375*c^6*sqrt(d - c^2*d*x^2)) - (272*b^2*x^2*(1 - c*x)*(1 + c*x))/(3375*c^4*sqrt(d - c^2*d*x^2)) - (2*b^2*x^4*(1 - c*x)*(1 + c*x))/(125*c^2*sqrt(d - c^2*d*x^2)) - (16*b^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(15*c^5*sqrt(d - c^2*d*x^2)) - (8*b*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(45*c^3*sqrt(d - c^2*d*x^2)) - (2*b*x^5*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(25*c*sqrt(d - c^2*d*x^2)) - (8*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(15*c^6*d) - (4*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(15*c^4*d) - (x^4*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(5*c^2*d)]
    @test_int [(x^4*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x, 11, -((15*b^2*x*(1 - c*x)*(1 + c*x))/(64*c^4*sqrt(d - c^2*d*x^2))) - (b^2*x^3*(1 - c*x)*(1 + c*x))/(32*c^2*sqrt(d - c^2*d*x^2)) + (15*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(64*c^5*sqrt(d - c^2*d*x^2)) - (3*b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(8*c^3*sqrt(d - c^2*d*x^2)) - (b*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(8*c*sqrt(d - c^2*d*x^2)) - (3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(8*c^4*d) - (x^3*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(4*c^2*d) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(8*b*c^5*sqrt(d - c^2*d*x^2))]
    @test_int [(x^3*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x, 9, -((4*a*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3*c^3*sqrt(d - c^2*d*x^2))) - (40*b^2*(1 - c*x)*(1 + c*x))/(27*c^4*sqrt(d - c^2*d*x^2)) - (2*b^2*x^2*(1 - c*x)*(1 + c*x))/(27*c^2*sqrt(d - c^2*d*x^2)) - (4*b^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c^3*sqrt(d - c^2*d*x^2)) - (2*b*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c*sqrt(d - c^2*d*x^2)) - (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*c^4*d) - (x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*c^2*d)]
    @test_int [(x^2*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x, 5, -((b^2*x*(1 - c*x)*(1 + c*x))/(4*c^2*sqrt(d - c^2*d*x^2))) + (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(4*c^3*sqrt(d - c^2*d*x^2)) - (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(2*c*sqrt(d - c^2*d*x^2)) - (x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*c^2*d) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(6*b*c^3*sqrt(d - c^2*d*x^2))]
    @test_int [(x^1*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x, 4, -((2*a*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*sqrt(d - c^2*d*x^2))) - (2*b^2*(1 - c*x)*(1 + c*x))/(c^2*sqrt(d - c^2*d*x^2)) - (2*b^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(c*sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(c^2*d)]
    @test_int [x^0*(a + b*acosh(c*x))^2/sqrt(d - c^2*d*x^2), x, 1, (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(3*b*c*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^1*sqrt(d - c^2*d*x^2)), x, 8, (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) - ((2*im)*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) + ((2*im)*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) + ((2*im)*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) - ((2*im)*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, im*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2)]
    @test_int [(a + b*acosh(c*x))^2/(x^2*sqrt(d - c^2*d*x^2)), x, 6, -((c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(d*x) - (2*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/sqrt(d - c^2*d*x^2) + (b^2*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/sqrt(d - c^2*d*x^2)]
    @test_int [(a + b*acosh(c*x))^2/(x^3*sqrt(d - c^2*d*x^2)), x, 12, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(x*sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*d*x^2) + (c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) - (b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/sqrt(d - c^2*d*x^2) - (im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) + (im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) + (im*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2) - (im*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, im*ℯ^acosh(c*x)))/sqrt(d - c^2*d*x^2)]
    @test_int [(a + b*acosh(c*x))^2/(x^4*sqrt(d - c^2*d*x^2)), x, 9, (b^2*c^2*(1 - c*x)*(1 + c*x))/(3*x*sqrt(d - c^2*d*x^2)) + (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*x^2*sqrt(d - c^2*d*x^2)) - (2*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*sqrt(d - c^2*d*x^2)) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*d*x^3) - (2*c^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*d*x) - (4*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/(3*sqrt(d - c^2*d*x^2)) + (2*b^2*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(3*sqrt(d - c^2*d*x^2))]

    @test_int [(x^5*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(3/2), x, 23, (16*a*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3*c^5*d*sqrt(d - c^2*d*x^2)) + (94*b^2*(1 - c*x)*(1 + c*x))/(27*c^6*d*sqrt(d - c^2*d*x^2)) + (2*b^2*x^2*(1 - c*x)*(1 + c*x))/(27*c^4*d*sqrt(d - c^2*d*x^2)) + (16*b^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c^5*d*sqrt(d - c^2*d*x^2)) - (2*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(c^5*d*sqrt(d - c^2*d*x^2)) + (2*b*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c^3*d*sqrt(d - c^2*d*x^2)) + (x^4*(a + b*acosh(c*x))^2)/(c^2*d*sqrt(d - c^2*d*x^2)) + (8*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*c^6*d^2) + (4*x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*c^4*d^2) + (4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^6*d*sqrt(d - c^2*d*x^2)) + (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(c^6*d*sqrt(d - c^2*d*x^2)) - (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(c^6*d*sqrt(d - c^2*d*x^2))]
    @test_int [(x^4*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(3/2), x, 15, (b^2*x*(1 - c*x)*(1 + c*x))/(4*c^4*d*sqrt(d - c^2*d*x^2)) - (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(4*c^5*d*sqrt(d - c^2*d*x^2)) + (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(2*c^3*d*sqrt(d - c^2*d*x^2)) + (x^3*(a + b*acosh(c*x))^2)/(c^2*d*sqrt(d - c^2*d*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(c^5*d*sqrt(d - c^2*d*x^2)) + (3*x*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(2*c^4*d^2) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(2*b*c^5*d*sqrt(d - c^2*d*x^2)) - (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(c^5*d*sqrt(d - c^2*d*x^2)) - (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(c^5*d*sqrt(d - c^2*d*x^2))]
    @test_int [(x^3*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(3/2), x, 14, (4*a*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c^3*d*sqrt(d - c^2*d*x^2)) + (2*b^2*(1 - c*x)*(1 + c*x))/(c^4*d*sqrt(d - c^2*d*x^2)) + (4*b^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(c^3*d*sqrt(d - c^2*d*x^2)) - (2*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(c^3*d*sqrt(d - c^2*d*x^2)) + (x^2*(a + b*acosh(c*x))^2)/(c^2*d*sqrt(d - c^2*d*x^2)) + (2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(c^4*d^2) + (4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^4*d*sqrt(d - c^2*d*x^2)) + (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(c^4*d*sqrt(d - c^2*d*x^2)) - (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(c^4*d*sqrt(d - c^2*d*x^2))]
    @test_int [(x^2*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(3/2), x, 8, (x*(a + b*acosh(c*x))^2)/(c^2*d*sqrt(d - c^2*d*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(c^3*d*sqrt(d - c^2*d*x^2)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(3*b*c^3*d*sqrt(d - c^2*d*x^2)) - (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(c^3*d*sqrt(d - c^2*d*x^2)) - (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(c^3*d*sqrt(d - c^2*d*x^2))]
    @test_int [(x^1*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(3/2), x, 8, (a + b*acosh(c*x))^2/(c^2*d*sqrt(d - c^2*d*x^2)) + (4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2)) + (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2)) - (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(c^2*d*sqrt(d - c^2*d*x^2))]
    @test_int [x^0*(a + b*acosh(c*x))^2/(d - c^2*d*x^2)^(3/2), x, 6, (x*(a + b*acosh(c*x))^2)/(d*sqrt(d - c^2*d*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(c*d*sqrt(d - c^2*d*x^2)) - (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(c*d*sqrt(d - c^2*d*x^2)) - (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(c*d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^1*(d - c^2*d*x^2)^(3/2)), x, 16, (a + b*acosh(c*x))^2/(d*sqrt(d - c^2*d*x^2)) + (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - ((2*im)*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + ((2*im)*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + ((2*im)*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - ((2*im)*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, im*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^2*(d - c^2*d*x^2)^(3/2)), x, 15, -((a + b*acosh(c*x))^2/(d*x*sqrt(d - c^2*d*x^2))) + (2*c^2*x*(a + b*acosh(c*x))^2)/(d*sqrt(d - c^2*d*x^2)) + (2*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(d*sqrt(d - c^2*d*x^2)) - (4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/(d*sqrt(d - c^2*d*x^2)) - (4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(d*sqrt(d - c^2*d*x^2)) - (b^2*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^(2*acosh(c*x))))/(d*sqrt(d - c^2*d*x^2)) - (b^2*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^3*(d - c^2*d*x^2)^(3/2)), x, 27, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(d*x*sqrt(d - c^2*d*x^2)) + (3*c^2*(a + b*acosh(c*x))^2)/(2*d*sqrt(d - c^2*d*x^2)) - (a + b*acosh(c*x))^2/(2*d*x^2*sqrt(d - c^2*d*x^2)) + (3*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - (b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(d*sqrt(d - c^2*d*x^2)) + (4*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (2*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - (3*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (3*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - (2*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) + (3*im*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2)) - (3*im*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, im*ℯ^acosh(c*x)))/(d*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^4*(d - c^2*d*x^2)^(3/2)), x, 26, (b^2*c^2*(1 - c*x)*(1 + c*x))/(3*d*x*sqrt(d - c^2*d*x^2)) + (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*d*x^2*sqrt(d - c^2*d*x^2)) - (a + b*acosh(c*x))^2/(3*d*x^3*sqrt(d - c^2*d*x^2)) - (4*c^2*(a + b*acosh(c*x))^2)/(3*d*x*sqrt(d - c^2*d*x^2)) + (8*c^4*x*(a + b*acosh(c*x))^2)/(3*d*sqrt(d - c^2*d*x^2)) + (8*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*d*sqrt(d - c^2*d*x^2)) - (20*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/(3*d*sqrt(d - c^2*d*x^2)) - (16*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(3*d*sqrt(d - c^2*d*x^2)) - (5*b^2*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^(2*acosh(c*x))))/(3*d*sqrt(d - c^2*d*x^2)) - (b^2*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(d*sqrt(d - c^2*d*x^2))]

    @test_int [(x^5*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(5/2), x, 28, -((b^2*x^2)/(3*c^4*d^2*sqrt(d - c^2*d*x^2))) - (16*a*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) - (7*b^2*(1 - c*x)*(1 + c*x))/(3*c^6*d^2*sqrt(d - c^2*d*x^2)) - (16*b^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) + (11*b*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) + (b*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c^3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x^4*(a + b*acosh(c*x))^2)/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (4*x^2*(a + b*acosh(c*x))^2)/(3*c^4*d^2*sqrt(d - c^2*d*x^2)) - (8*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(3*c^6*d^3) - (22*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(3*c^6*d^2*sqrt(d - c^2*d*x^2)) - (11*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(3*c^6*d^2*sqrt(d - c^2*d*x^2)) + (11*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(3*c^6*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(x^4*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(5/2), x, 20, -(b^2/(3*c^5*d^2*sqrt(d - c^2*d*x^2))) + (b^2*(1 - c*x))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) + (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) + (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c^3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x^3*(a + b*acosh(c*x))^2)/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (x*(a + b*acosh(c*x))^2)/(c^4*d^2*sqrt(d - c^2*d*x^2)) - (4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) + (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^3)/(3*b*c^5*d^2*sqrt(d - c^2*d*x^2)) + (8*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(3*c^5*d^2*sqrt(d - c^2*d*x^2)) + (4*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(3*c^5*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(x^3*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(5/2), x, 18, -(b^2/(3*c^4*d^2*sqrt(d - c^2*d*x^2))) + (b*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c^3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x^2*(a + b*acosh(c*x))^2)/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) - (2*(a + b*acosh(c*x))^2)/(3*c^4*d^2*sqrt(d - c^2*d*x^2)) - (10*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(3*c^4*d^2*sqrt(d - c^2*d*x^2)) - (5*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(3*c^4*d^2*sqrt(d - c^2*d*x^2)) + (5*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(3*c^4*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(x^2*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(5/2), x, 12, -(b^2/(3*c^3*d^2*sqrt(d - c^2*d*x^2))) + (b^2*(1 - c*x))/(3*c^3*d^2*sqrt(d - c^2*d*x^2)) + (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*acosh(c*x))/(3*c^3*d^2*sqrt(d - c^2*d*x^2)) + (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x^3*(a + b*acosh(c*x))^2)/(3*d*(d - c^2*d*x^2)^(3/2)) - (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*c^3*d^2*sqrt(d - c^2*d*x^2)) + (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(3*c^3*d^2*sqrt(d - c^2*d*x^2)) + (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(3*c^3*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(x^1*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(5/2), x, 10, -(b^2/(3*c^2*d^2*sqrt(d - c^2*d*x^2))) + (b*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (a + b*acosh(c*x))^2/(3*c^2*d*(d - c^2*d*x^2)^(3/2)) + (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(3*c^2*d^2*sqrt(d - c^2*d*x^2)) + (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(3*c^2*d^2*sqrt(d - c^2*d*x^2)) - (b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(3*c^2*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [x^0*(a + b*acosh(c*x))^2/(d - c^2*d*x^2)^(5/2), x, 10, -((b^2*x)/(3*d^2*sqrt(d - c^2*d*x^2))) + (b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (x*(a + b*acosh(c*x))^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + (2*x*(a + b*acosh(c*x))^2)/(3*d^2*sqrt(d - c^2*d*x^2)) + (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*c*d^2*sqrt(d - c^2*d*x^2)) - (4*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(3*c*d^2*sqrt(d - c^2*d*x^2)) - (2*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(3*c*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^1*(d - c^2*d*x^2)^(5/2)), x, 26, -(b^2/(3*d^2*sqrt(d - c^2*d*x^2))) + (b*c*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (a + b*acosh(c*x))^2/(3*d*(d - c^2*d*x^2)^(3/2)) + (a + b*acosh(c*x))^2/(d^2*sqrt(d - c^2*d*x^2)) + (2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (14*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) + (7*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) - (2*im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (2*im*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) - (7*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) + (2*im*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) - (2*im*b^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, im*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^2*(d - c^2*d*x^2)^(5/2)), x, 21, -((b^2*c^2*x)/(3*d^2*sqrt(d - c^2*d*x^2))) + (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) - (a + b*acosh(c*x))^2/(d*x*(d - c^2*d*x^2)^(3/2)) + (4*c^2*x*(a + b*acosh(c*x))^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + (8*c^2*x*(a + b*acosh(c*x))^2)/(3*d^2*sqrt(d - c^2*d*x^2)) + (8*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*d^2*sqrt(d - c^2*d*x^2)) - (4*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/(d^2*sqrt(d - c^2*d*x^2)) - (16*b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(3*d^2*sqrt(d - c^2*d*x^2)) - (b^2*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^(2*acosh(c*x))))/(d^2*sqrt(d - c^2*d*x^2)) - (5*b^2*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(3*d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^3*(d - c^2*d*x^2)^(5/2)), x, 41, -((b^2*c^2)/(3*d^2*sqrt(d - c^2*d*x^2))) + (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(d^2*x*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) - (2*b*c^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*d^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) + (5*c^2*(a + b*acosh(c*x))^2)/(6*d*(d - c^2*d*x^2)^(3/2)) - (a + b*acosh(c*x))^2/(2*d*x^2*(d - c^2*d*x^2)^(3/2)) + (5*c^2*(a + b*acosh(c*x))^2)/(2*d^2*sqrt(d - c^2*d*x^2)) + (5*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2*atan(ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) - (b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (26*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) + (13*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) - (5*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, (-im)*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) + (5*im*b*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*PolyLog(2, im*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) - (13*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^acosh(c*x)))/(3*d^2*sqrt(d - c^2*d*x^2)) + (5*im*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, (-im)*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2)) - (5*im*b^2*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(3, im*ℯ^acosh(c*x)))/(d^2*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^2/(x^4*(d - c^2*d*x^2)^(5/2)), x, 36, (b^2*c^2)/(3*d^2*x*sqrt(d - c^2*d*x^2)) - (2*b^2*c^4*x)/(3*d^2*sqrt(d - c^2*d*x^2)) + (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*d^2*x^2*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)) - (a + b*acosh(c*x))^2/(3*d*x^3*(d - c^2*d*x^2)^(3/2)) - (2*c^2*(a + b*acosh(c*x))^2)/(d*x*(d - c^2*d*x^2)^(3/2)) + (8*c^4*x*(a + b*acosh(c*x))^2)/(3*d*(d - c^2*d*x^2)^(3/2)) + (16*c^4*x*(a + b*acosh(c*x))^2)/(3*d^2*sqrt(d - c^2*d*x^2)) + (16*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^2)/(3*d^2*sqrt(d - c^2*d*x^2)) - (32*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*atanh(ℯ^(2*acosh(c*x))))/(3*d^2*sqrt(d - c^2*d*x^2)) - (32*b*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))*log(1 - ℯ^(2*acosh(c*x))))/(3*d^2*sqrt(d - c^2*d*x^2)) - (8*b^2*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, -ℯ^(2*acosh(c*x))))/(3*d^2*sqrt(d - c^2*d*x^2)) - (8*b^2*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*PolyLog(2, ℯ^(2*acosh(c*x))))/(3*d^2*sqrt(d - c^2*d*x^2))]

    @test_int [acosh(a*x)^2/(c - a^2*c*x^2)^(7/2), x, 15, -(x/(3*c^3*sqrt(c - a^2*c*x^2))) - x/(30*c^3*(1 - a*x)*(1 + a*x)*sqrt(c - a^2*c*x^2)) + (sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(10*a*c^3*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)) + (4*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x))/(15*a*c^3*(1 - a^2*x^2)*sqrt(c - a^2*c*x^2)) + (x*acosh(a*x)^2)/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*acosh(a*x)^2)/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*acosh(a*x)^2)/(15*c^3*sqrt(c - a^2*c*x^2)) + (8*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/(15*a*c^3*sqrt(c - a^2*c*x^2)) - (16*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*log(1 - ℯ^(2*acosh(a*x))))/(15*a*c^3*sqrt(c - a^2*c*x^2)) - (8*sqrt(-1 + a*x)*sqrt(1 + a*x)*PolyLog(2, ℯ^(2*acosh(a*x))))/(15*a*c^3*sqrt(c - a^2*c*x^2))]

    @test_int [x^4*acosh(a*x)^2/sqrt(1 - a^2*x^2), x, 11, -((15*x*sqrt(1 - a*x)*sqrt(1 + a*x))/(64*a^4)) - (x^3*sqrt(1 - a*x)*sqrt(1 + a*x))/(32*a^2) + (15*sqrt(-1 + a*x)*acosh(a*x))/(64*a^5*sqrt(1 - a*x)) - (3*x^2*sqrt(-1 + a*x)*acosh(a*x))/(8*a^3*sqrt(1 - a*x)) - (x^4*sqrt(-1 + a*x)*acosh(a*x))/(8*a*sqrt(1 - a*x)) - (3*x*sqrt(1 - a^2*x^2)*acosh(a*x)^2)/(8*a^4) - (x^3*sqrt(1 - a^2*x^2)*acosh(a*x)^2)/(4*a^2) + (sqrt(-1 + a*x)*acosh(a*x)^3)/(8*a^5*sqrt(1 - a*x))]
    @test_int [x^3*acosh(a*x)^2/sqrt(1 - a^2*x^2), x, 8, -((40*sqrt(1 - a*x)*sqrt(1 + a*x))/(27*a^4)) - (2*x^2*sqrt(1 - a*x)*sqrt(1 + a*x))/(27*a^2) - (4*x*sqrt(-1 + a*x)*acosh(a*x))/(3*a^3*sqrt(1 - a*x)) - (2*x^3*sqrt(-1 + a*x)*acosh(a*x))/(9*a*sqrt(1 - a*x)) - (2*sqrt(1 - a^2*x^2)*acosh(a*x)^2)/(3*a^4) - (x^2*sqrt(1 - a^2*x^2)*acosh(a*x)^2)/(3*a^2)]
    @test_int [x^2*acosh(a*x)^2/sqrt(1 - a^2*x^2), x, 5, -((x*sqrt(1 - a*x)*sqrt(1 + a*x))/(4*a^2)) + (sqrt(-1 + a*x)*acosh(a*x))/(4*a^3*sqrt(1 - a*x)) - (x^2*sqrt(-1 + a*x)*acosh(a*x))/(2*a*sqrt(1 - a*x)) - (x*sqrt(1 - a^2*x^2)*acosh(a*x)^2)/(2*a^2) + (sqrt(-1 + a*x)*acosh(a*x)^3)/(6*a^3*sqrt(1 - a*x))]
    @test_int [x^1*acosh(a*x)^2/sqrt(1 - a^2*x^2), x, 3, -((2*sqrt(1 - a*x)*sqrt(1 + a*x))/a^2) - (2*x*sqrt(-1 + a*x)*acosh(a*x))/(a*sqrt(1 - a*x)) - (sqrt(1 - a^2*x^2)*acosh(a*x)^2)/a^2]
    @test_int [x^0*acosh(a*x)^2/sqrt(1 - a^2*x^2), x, 1, (sqrt(-1 + a*x)*acosh(a*x)^3)/(3*a*sqrt(1 - a*x))]
    @test_int [acosh(a*x)^2/(x^1*sqrt(1 - a^2*x^2)), x, 8, (2*sqrt(-1 + a*x)*acosh(a*x)^2*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) - (2*im*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(2, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (2*im*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(2, im*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (2*im*sqrt(-1 + a*x)*PolyLog(3, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (2*im*sqrt(-1 + a*x)*PolyLog(3, im*ℯ^acosh(a*x)))/sqrt(1 - a*x)]
    @test_int [acosh(a*x)^2/(x^2*sqrt(1 - a^2*x^2)), x, 6, (a*sqrt(-1 + a*x)*acosh(a*x)^2)/sqrt(1 - a*x) - (sqrt(1 - a^2*x^2)*acosh(a*x)^2)/x - (2*a*sqrt(-1 + a*x)*acosh(a*x)*log(1 + ℯ^(2*acosh(a*x))))/sqrt(1 - a*x) - (a*sqrt(-1 + a*x)*PolyLog(2, -ℯ^(2*acosh(a*x))))/sqrt(1 - a*x)]
    @test_int [acosh(a*x)^2/(x^3*sqrt(1 - a^2*x^2)), x, 12, (a*sqrt(-1 + a*x)*acosh(a*x))/(x*sqrt(1 - a*x)) - (sqrt(1 - a^2*x^2)*acosh(a*x)^2)/(2*x^2) + (a^2*sqrt(-1 + a*x)*acosh(a*x)^2*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) - (a^2*sqrt(-1 + a*x)*atan(sqrt(-1 + a*x)*sqrt(1 + a*x)))/sqrt(1 - a*x) - (im*a^2*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(2, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (im*a^2*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(2, im*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (im*a^2*sqrt(-1 + a*x)*PolyLog(3, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (im*a^2*sqrt(-1 + a*x)*PolyLog(3, im*ℯ^acosh(a*x)))/sqrt(1 - a*x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^2*with*m*symbolic=#

    #= [(f*x)^m*(d - c^2*d*x^2)^2*(a + b*acosh(c*x))^2, x, 1, 0]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^1*(a + b*acosh(c*x))^2, x, 1, 0]
    @test_int [(f*x)^m/(d - c^2*d*x^2)^1*(a + b*acosh(c*x))^2, x, 1, 0]
    @test_int [(f*x)^m/(d - c^2*d*x^2)^2*(a + b*acosh(c*x))^2, x, 1, 0] =#

    @test_int [(f*x)^m*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2, x, 22, If(13>=8, -((10*b^2*c^2*d^2*(f*x)^(3 + m)*sqrt(d - c^2*d*x^2))/(f^3*(4 + m)^3*(6 + m))) - (2*b^2*c^2*d^2*(52 + 15*m + m^2)*(f*x)^(3 + m)*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(f^3*(4 + m)^2*(6 + m)^3*(1 - c*x)*(1 + c*x)) + (2*b^2*c^4*d^2*(f*x)^(5 + m)*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(f^5*(6 + m)^3*(1 - c*x)*(1 + c*x)) - (2*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (30*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (10*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (10*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^4*(4 + m)^2*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^4*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*(f*x)^(6 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^6*(6 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*d^2*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d*(f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/(f*(6 + m)) - (30*b^2*c^2*d^2*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)^2*(3 + m)*(4 + m)*(6 + m)*(1 - c*x)*(1 + c*x)) - (10*b^2*c^2*d^2*(10 + 3*m)*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)*(3 + m)*(4 + m)^3*(6 + m)*(1 - c*x)*(1 + c*x)) - (2*b^2*c^2*d^2*(264 + 130*m + 15*m^2)*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)*(3 + m)*(4 + m)^2*(6 + m)^3*(1 - c*x)*(1 + c*x)) + (15*d^3*Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x))/((6 + m)*(8 + 6*m + m^2)), -((10*b^2*c^2*d^2*(f*x)^(3 + m)*sqrt(d - c^2*d*x^2))/(f^3*(4 + m)^3*(6 + m))) - (2*b^2*c^2*d^2*(52 + 15*m + m^2)*(f*x)^(3 + m)*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(f^3*(4 + m)^2*(6 + m)^3*(1 - c*x)*(1 + c*x)) + (2*b^2*c^4*d^2*(f*x)^(5 + m)*(1 - c^2*x^2)*sqrt(d - c^2*d*x^2))/(f^5*(6 + m)^3*(1 - c*x)*(1 + c*x)) - (2*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (30*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)^2*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (10*b*c*d^2*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(6 + m)*(8 + 6*m + m^2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (10*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^4*(4 + m)^2*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (4*b*c^3*d^2*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^4*(4 + m)*(6 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c^5*d^2*(f*x)^(6 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^6*(6 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (15*d^2*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(f*(6 + m)*(8 + 6*m + m^2)) + (5*d*(f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(f*(4 + m)*(6 + m)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^2)/(f*(6 + m)) - (30*b^2*c^2*d^2*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)^2*(3 + m)*(4 + m)*(6 + m)*(1 - c*x)*(1 + c*x)) - (10*b^2*c^2*d^2*(10 + 3*m)*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(4 + m)^3*(6 + m)*(6 + 5*m + m^2)*(1 - c*x)*(1 + c*x)) - (2*b^2*c^2*d^2*(264 + 130*m + 15*m^2)*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(4 + m)^2*(6 + m)^3*(6 + 5*m + m^2)*(1 - c*x)*(1 + c*x)) + (15*d^3*Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x))/((6 + m)*(8 + 6*m + m^2)))]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2, x, 13, If(13>=8, -((2*b^2*c^2*d*(f*x)^(3 + m)*sqrt(d - c^2*d*x^2))/(f^3*(4 + m)^3)) - (6*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^4*(4 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*d*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(f*(4 + m)) - (6*b^2*c^2*d*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)^2*(3 + m)*(4 + m)*(1 - c*x)*(1 + c*x)) - (2*b^2*c^2*d*(10 + 3*m)*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)*(3 + m)*(4 + m)^3*(1 - c*x)*(1 + c*x)) + (3*d^2*Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x))/(8 + 6*m + m^2), -((2*b^2*c^2*d*(f*x)^(3 + m)*sqrt(d - c^2*d*x^2))/(f^3*(4 + m)^3)) - (6*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)^2*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*c*d*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)*(4 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*c^3*d*(f*x)^(4 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^4*(4 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*d*(f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(f*(8 + 6*m + m^2)) + ((f*x)^(1 + m)*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^2)/(f*(4 + m)) - (6*b^2*c^2*d*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)^2*(3 + m)*(4 + m)*(1 - c*x)*(1 + c*x)) - (2*b^2*c^2*d*(10 + 3*m)*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(4 + m)^3*(6 + 5*m + m^2)*(1 - c*x)*(1 + c*x)) + (3*d^2*Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x))/(8 + 6*m + m^2))]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^(1/2)*(a + b*acosh(c*x))^2, x, 5, -((2*b*c*(f*x)^(2 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x)))/(f^2*(2 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))) + ((f*x)^(1 + m)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^2)/(f*(2 + m)) - (2*b^2*c^2*(f*x)^(3 + m)*sqrt(1 - c^2*x^2)*sqrt(d - c^2*d*x^2)*HypergeometricFunctions._₂F₁(1/2, (3 + m)/2, (5 + m)/2, c^2*x^2))/(f^3*(2 + m)^2*(3 + m)*(1 - c*x)*(1 + c*x)) + (d*Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x))/(2 + m)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^2/(d - c^2*d*x^2)^(1/2), x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/sqrt(d - c^2*d*x^2), x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^2/(d - c^2*d*x^2)^(3/2), x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(3/2), x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^2/(d - c^2*d*x^2)^(5/2), x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^2)/(d - c^2*d*x^2)^(5/2), x)]

    @test_int [(f*x)^m*acosh(c*x)^2/sqrt(1 - c^2*x^2), x, 0, Unintegrable(((f*x)^m*acosh(c*x)^2)/sqrt(1 - c^2*x^2), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^3=#

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

    @test_int [(c - a^2*c*x^2)^3*acosh(a*x)^3, x, 29, -((976*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x))/(315*a)) + (16/315)*a*c^3*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x) + (7104*c^3*(1 - a^2*x^2))/(42875*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (1184*c^3*(1 - a^2*x^2)^2)/(42875*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (2664*c^3*(1 - a^2*x^2)^3)/(214375*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (6*c^3*(1 - a^2*x^2)^4)/(2401*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (4322*c^3*x*acosh(a*x))/1225 - (1514*a^2*c^3*x^3*acosh(a*x))/3675 + (702*a^4*c^3*x^5*acosh(a*x))/6125 - (6/343)*a^6*c^3*x^7*acosh(a*x) - (48*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/(35*a) + (8*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x)^2)/(35*a) - (18*c^3*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*acosh(a*x)^2)/(175*a) + (3*c^3*(-1 + a*x)^(7/2)*(1 + a*x)^(7/2)*acosh(a*x)^2)/(49*a) + (16/35)*c^3*x*acosh(a*x)^3 + (8/35)*c^3*x*(1 - a^2*x^2)*acosh(a*x)^3 + (6/35)*c^3*x*(1 - a^2*x^2)^2*acosh(a*x)^3 + (1/7)*c^3*x*(1 - a^2*x^2)^3*acosh(a*x)^3]
    @test_int [(c - a^2*c*x^2)^2*acosh(a*x)^3, x, 20, -((488*c^2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(135*a)) + (8/135)*a*c^2*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x) + (16*c^2*(1 - a^2*x^2))/(125*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (8*c^2*(1 - a^2*x^2)^2)/(375*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (6*c^2*(1 - a^2*x^2)^3)/(625*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (298/75)*c^2*x*acosh(a*x) - (76/225)*a^2*c^2*x^3*acosh(a*x) + (6/125)*a^4*c^2*x^5*acosh(a*x) - (8*c^2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/(5*a) + (4*c^2*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x)^2)/(15*a) - (3*c^2*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*acosh(a*x)^2)/(25*a) + (8/15)*c^2*x*acosh(a*x)^3 + (4/15)*c^2*x*(1 - a^2*x^2)*acosh(a*x)^3 + (1/5)*c^2*x*(1 - a^2*x^2)^2*acosh(a*x)^3]
    @test_int [(c - a^2*c*x^2)*acosh(a*x)^3, x, 11, -((122*c*sqrt(-1 + a*x)*sqrt(1 + a*x))/(27*a)) + (2/27)*a*c*x^2*sqrt(-1 + a*x)*sqrt(1 + a*x) + (14/3)*c*x*acosh(a*x) - (2/9)*a^2*c*x^3*acosh(a*x) - (2*c*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/a + (c*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x)^2)/(3*a) + (2/3)*c*x*acosh(a*x)^3 + (1/3)*c*x*(1 - a^2*x^2)*acosh(a*x)^3]
    @test_int [acosh(a*x)^3/(c - a^2*c*x^2), x, 10, (2*acosh(a*x)^3*atanh(ℯ^acosh(a*x)))/(a*c) + (3*acosh(a*x)^2*PolyLog(2, -ℯ^acosh(a*x)))/(a*c) - (3*acosh(a*x)^2*PolyLog(2, ℯ^acosh(a*x)))/(a*c) - (6*acosh(a*x)*PolyLog(3, -ℯ^acosh(a*x)))/(a*c) + (6*acosh(a*x)*PolyLog(3, ℯ^acosh(a*x)))/(a*c) + (6*PolyLog(4, -ℯ^acosh(a*x)))/(a*c) - (6*PolyLog(4, ℯ^acosh(a*x)))/(a*c)]
    @test_int [acosh(a*x)^3/(c - a^2*c*x^2)^2, x, 19, -((3*acosh(a*x)^2)/(2*a*c^2*sqrt(-1 + a*x)*sqrt(1 + a*x))) + (x*acosh(a*x)^3)/(2*c^2*(1 - a^2*x^2)) - (6*acosh(a*x)*atanh(ℯ^acosh(a*x)))/(a*c^2) + (acosh(a*x)^3*atanh(ℯ^acosh(a*x)))/(a*c^2) - (3*PolyLog(2, -ℯ^acosh(a*x)))/(a*c^2) + (3*acosh(a*x)^2*PolyLog(2, -ℯ^acosh(a*x)))/(2*a*c^2) + (3*PolyLog(2, ℯ^acosh(a*x)))/(a*c^2) - (3*acosh(a*x)^2*PolyLog(2, ℯ^acosh(a*x)))/(2*a*c^2) - (3*acosh(a*x)*PolyLog(3, -ℯ^acosh(a*x)))/(a*c^2) + (3*acosh(a*x)*PolyLog(3, ℯ^acosh(a*x)))/(a*c^2) + (3*PolyLog(4, -ℯ^acosh(a*x)))/(a*c^2) - (3*PolyLog(4, ℯ^acosh(a*x)))/(a*c^2)]
    @test_int [acosh(a*x)^3/(c - a^2*c*x^2)^3, x, 30, 1/(4*a*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (x*acosh(a*x))/(4*c^3*(1 - a^2*x^2)) + acosh(a*x)^2/(4*a*c^3*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)) - (9*acosh(a*x)^2)/(8*a*c^3*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (x*acosh(a*x)^3)/(4*c^3*(1 - a^2*x^2)^2) + (3*x*acosh(a*x)^3)/(8*c^3*(1 - a^2*x^2)) - (5*acosh(a*x)*atanh(ℯ^acosh(a*x)))/(a*c^3) + (3*acosh(a*x)^3*atanh(ℯ^acosh(a*x)))/(4*a*c^3) - (5*PolyLog(2, -ℯ^acosh(a*x)))/(2*a*c^3) + (9*acosh(a*x)^2*PolyLog(2, -ℯ^acosh(a*x)))/(8*a*c^3) + (5*PolyLog(2, ℯ^acosh(a*x)))/(2*a*c^3) - (9*acosh(a*x)^2*PolyLog(2, ℯ^acosh(a*x)))/(8*a*c^3) - (9*acosh(a*x)*PolyLog(3, -ℯ^acosh(a*x)))/(4*a*c^3) + (9*acosh(a*x)*PolyLog(3, ℯ^acosh(a*x)))/(4*a*c^3) + (9*PolyLog(4, -ℯ^acosh(a*x)))/(4*a*c^3) - (9*PolyLog(4, ℯ^acosh(a*x)))/(4*a*c^3)]

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

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

    @test_int [(c - a^2*c*x^2)^(5/2)*acosh(a*x)^3, x, 29, -((865*a*c^2*x^2*sqrt(c - a^2*c*x^2))/(2304*sqrt(-1 + a*x)*sqrt(1 + a*x))) + (65*a^3*c^2*x^4*sqrt(c - a^2*c*x^2))/(2304*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c^2*(1 - a^2*x^2)^3*sqrt(c - a^2*c*x^2))/(216*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (245/384)*c^2*x*sqrt(c - a^2*c*x^2)*acosh(a*x) + (65/576)*c^2*x*(1 - a*x)*(1 + a*x)*sqrt(c - a^2*c*x^2)*acosh(a*x) + (1/36)*c^2*x*(1 - a*x)^2*(1 + a*x)^2*sqrt(c - a^2*c*x^2)*acosh(a*x) + (115*c^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(768*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (15*a*c^2*x^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(32*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (5*c^2*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(32*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c^2*(1 - a^2*x^2)^3*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(12*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (5/16)*c^2*x*sqrt(c - a^2*c*x^2)*acosh(a*x)^3 + (5/24)*c*x*(c - a^2*c*x^2)^(3/2)*acosh(a*x)^3 + (1/6)*x*(c - a^2*c*x^2)^(5/2)*acosh(a*x)^3 - (5*c^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^4)/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [(c - a^2*c*x^2)^(3/2)*acosh(a*x)^3, x, 16, -((51*a*c*x^2*sqrt(c - a^2*c*x^2))/(128*sqrt(-1 + a*x)*sqrt(1 + a*x))) + (3*a^3*c*x^4*sqrt(c - a^2*c*x^2))/(128*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (45/64)*c*x*sqrt(c - a^2*c*x^2)*acosh(a*x) + (3/32)*c*x*(1 - a*x)*(1 + a*x)*sqrt(c - a^2*c*x^2)*acosh(a*x) + (27*c*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(128*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (9*a*c*x^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(16*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*c*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3/8)*c*x*sqrt(c - a^2*c*x^2)*acosh(a*x)^3 + (1/4)*x*(c - a^2*c*x^2)^(3/2)*acosh(a*x)^3 - (3*c*sqrt(c - a^2*c*x^2)*acosh(a*x)^4)/(32*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [sqrt(c - a^2*c*x^2)*acosh(a*x)^3, x, 6, (-3*a*x^2*sqrt(c - a^2*c*x^2))/(8*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*x*sqrt(c - a^2*c*x^2)*acosh(a*x))/4 + (3*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(8*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*a*x^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^2)/(4*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (x*sqrt(c - a^2*c*x^2)*acosh(a*x)^3)/2 - (sqrt(c - a^2*c*x^2)*acosh(a*x)^4)/(8*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]

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

    @test_int [acosh(a*x)^3/(c - a^2*c*x^2)^(1/2), x, 1, (sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^4)/(4*a*sqrt(c - a^2*c*x^2))]
    @test_int [acosh(a*x)^3/(c - a^2*c*x^2)^(3/2), x, 7, (x*acosh(a*x)^3)/(c*sqrt(c - a^2*c*x^2)) + (sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^3)/(a*c*sqrt(c - a^2*c*x^2)) - (3*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2*log(1 - ℯ^(2*acosh(a*x))))/(a*c*sqrt(c - a^2*c*x^2)) - (3*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*PolyLog(2, ℯ^(2*acosh(a*x))))/(a*c*sqrt(c - a^2*c*x^2)) + (3*sqrt(-1 + a*x)*sqrt(1 + a*x)*PolyLog(3, ℯ^(2*acosh(a*x))))/(2*a*c*sqrt(c - a^2*c*x^2))]
    @test_int [acosh(a*x)^3/(c - a^2*c*x^2)^(5/2), x, 12, -((x*acosh(a*x))/(c^2*sqrt(c - a^2*c*x^2))) + (sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/(2*a*c^2*(1 - a^2*x^2)*sqrt(c - a^2*c*x^2)) + (x*acosh(a*x)^3)/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*acosh(a*x)^3)/(3*c^2*sqrt(c - a^2*c*x^2)) + (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^3)/(3*a*c^2*sqrt(c - a^2*c*x^2)) - (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2*log(1 - ℯ^(2*acosh(a*x))))/(a*c^2*sqrt(c - a^2*c*x^2)) + (sqrt(-1 + a*x)*sqrt(1 + a*x)*log(1 - a^2*x^2))/(2*a*c^2*sqrt(c - a^2*c*x^2)) - (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*PolyLog(2, ℯ^(2*acosh(a*x))))/(a*c^2*sqrt(c - a^2*c*x^2)) + (sqrt(-1 + a*x)*sqrt(1 + a*x)*PolyLog(3, ℯ^(2*acosh(a*x))))/(a*c^2*sqrt(c - a^2*c*x^2))]
    @test_int [acosh(a*x)^3/(c - a^2*c*x^2)^(7/2), x, 20, -((sqrt(-1 + a*x)*sqrt(1 + a*x))/(20*a*c^3*(1 - a^2*x^2)*sqrt(c - a^2*c*x^2))) - (x*acosh(a*x))/(c^3*sqrt(c - a^2*c*x^2)) - (x*acosh(a*x))/(10*c^3*(1 - a*x)*(1 + a*x)*sqrt(c - a^2*c*x^2)) + (3*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/(20*a*c^3*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)) + (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2)/(5*a*c^3*(1 - a^2*x^2)*sqrt(c - a^2*c*x^2)) + (x*acosh(a*x)^3)/(5*c*(c - a^2*c*x^2)^(5/2)) + (4*x*acosh(a*x)^3)/(15*c^2*(c - a^2*c*x^2)^(3/2)) + (8*x*acosh(a*x)^3)/(15*c^3*sqrt(c - a^2*c*x^2)) + (8*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^3)/(15*a*c^3*sqrt(c - a^2*c*x^2)) - (8*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^2*log(1 - ℯ^(2*acosh(a*x))))/(5*a*c^3*sqrt(c - a^2*c*x^2)) + (sqrt(-1 + a*x)*sqrt(1 + a*x)*log(1 - a^2*x^2))/(2*a*c^3*sqrt(c - a^2*c*x^2)) - (8*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)*PolyLog(2, ℯ^(2*acosh(a*x))))/(5*a*c^3*sqrt(c - a^2*c*x^2)) + (4*sqrt(-1 + a*x)*sqrt(1 + a*x)*PolyLog(3, ℯ^(2*acosh(a*x))))/(5*a*c^3*sqrt(c - a^2*c*x^2))]

    @test_int [(x^4*acosh(a*x)^3)/sqrt(1 - a^2*x^2), x, 13, -((45*x^2*sqrt(-1 + a*x))/(128*a^3*sqrt(1 - a*x))) - (3*x^4*sqrt(-1 + a*x))/(128*a*sqrt(1 - a*x)) - (45*x*sqrt(1 - a*x)*sqrt(1 + a*x)*acosh(a*x))/(64*a^4) - (3*x^3*sqrt(1 - a*x)*sqrt(1 + a*x)*acosh(a*x))/(32*a^2) + (45*sqrt(-1 + a*x)*acosh(a*x)^2)/(128*a^5*sqrt(1 - a*x)) - (9*x^2*sqrt(-1 + a*x)*acosh(a*x)^2)/(16*a^3*sqrt(1 - a*x)) - (3*x^4*sqrt(-1 + a*x)*acosh(a*x)^2)/(16*a*sqrt(1 - a*x)) - (3*x*sqrt(1 - a^2*x^2)*acosh(a*x)^3)/(8*a^4) - (x^3*sqrt(1 - a^2*x^2)*acosh(a*x)^3)/(4*a^2) + (3*sqrt(-1 + a*x)*acosh(a*x)^4)/(32*a^5*sqrt(1 - a*x))]
    @test_int [(x^3*acosh(a*x)^3)/sqrt(1 - a^2*x^2), x, 10, -((40*x*sqrt(-1 + a*x))/(9*a^3*sqrt(1 - a*x))) - (2*x^3*sqrt(-1 + a*x))/(27*a*sqrt(1 - a*x)) - (40*sqrt(1 - a*x)*sqrt(1 + a*x)*acosh(a*x))/(9*a^4) - (2*x^2*sqrt(1 - a*x)*sqrt(1 + a*x)*acosh(a*x))/(9*a^2) - (2*x*sqrt(-1 + a*x)*acosh(a*x)^2)/(a^3*sqrt(1 - a*x)) - (x^3*sqrt(-1 + a*x)*acosh(a*x)^2)/(3*a*sqrt(1 - a*x)) - (2*sqrt(1 - a^2*x^2)*acosh(a*x)^3)/(3*a^4) - (x^2*sqrt(1 - a^2*x^2)*acosh(a*x)^3)/(3*a^2)]
    @test_int [(x^2*acosh(a*x)^3)/sqrt(1 - a^2*x^2), x, 6, -((3*x^2*sqrt(-1 + a*x))/(8*a*sqrt(1 - a*x))) - (3*x*sqrt(1 - a*x)*sqrt(1 + a*x)*acosh(a*x))/(4*a^2) + (3*sqrt(-1 + a*x)*acosh(a*x)^2)/(8*a^3*sqrt(1 - a*x)) - (3*x^2*sqrt(-1 + a*x)*acosh(a*x)^2)/(4*a*sqrt(1 - a*x)) - (x*sqrt(1 - a^2*x^2)*acosh(a*x)^3)/(2*a^2) + (sqrt(-1 + a*x)*acosh(a*x)^4)/(8*a^3*sqrt(1 - a*x))]
    @test_int [(x^1*acosh(a*x)^3)/sqrt(1 - a^2*x^2), x, 4, -((6*x*sqrt(-1 + a*x))/(a*sqrt(1 - a*x))) - (6*sqrt(1 - a*x)*sqrt(1 + a*x)*acosh(a*x))/a^2 - (3*x*sqrt(-1 + a*x)*acosh(a*x)^2)/(a*sqrt(1 - a*x)) - (sqrt(1 - a^2*x^2)*acosh(a*x)^3)/a^2]
    @test_int [x^0*acosh(a*x)^3/sqrt(1 - a^2*x^2), x, 1, (sqrt(-1 + a*x)*acosh(a*x)^4)/(4*a*sqrt(1 - a*x))]
    @test_int [acosh(a*x)^3/(x^1*sqrt(1 - a^2*x^2)), x, 10, (2*sqrt(-1 + a*x)*acosh(a*x)^3*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) - (3*im*sqrt(-1 + a*x)*acosh(a*x)^2*PolyLog(2, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (3*im*sqrt(-1 + a*x)*acosh(a*x)^2*PolyLog(2, im*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (6*im*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(3, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (6*im*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(3, im*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (6*im*sqrt(-1 + a*x)*PolyLog(4, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (6*im*sqrt(-1 + a*x)*PolyLog(4, im*ℯ^acosh(a*x)))/sqrt(1 - a*x)]
    @test_int [acosh(a*x)^3/(x^2*sqrt(1 - a^2*x^2)), x, 7, (a*sqrt(-1 + a*x)*acosh(a*x)^3)/sqrt(1 - a*x) - (sqrt(1 - a^2*x^2)*acosh(a*x)^3)/x - (3*a*sqrt(-1 + a*x)*acosh(a*x)^2*log(1 + ℯ^(2*acosh(a*x))))/sqrt(1 - a*x) - (3*a*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(2, -ℯ^(2*acosh(a*x))))/sqrt(1 - a*x) + (3*a*sqrt(-1 + a*x)*PolyLog(3, -ℯ^(2*acosh(a*x))))/(2*sqrt(1 - a*x))]
    @test_int [acosh(a*x)^3/(x^3*sqrt(1 - a^2*x^2)), x, 18, (3*a*sqrt(-1 + a*x)*acosh(a*x)^2)/(2*x*sqrt(1 - a*x)) - (sqrt(1 - a^2*x^2)*acosh(a*x)^3)/(2*x^2) - (6*a^2*sqrt(-1 + a*x)*acosh(a*x)*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) + (a^2*sqrt(-1 + a*x)*acosh(a*x)^3*atan(ℯ^acosh(a*x)))/sqrt(1 - a*x) + (3*im*a^2*sqrt(-1 + a*x)*PolyLog(2, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (3*im*a^2*sqrt(-1 + a*x)*acosh(a*x)^2*PolyLog(2, (-im)*ℯ^acosh(a*x)))/(2*sqrt(1 - a*x)) - (3*im*a^2*sqrt(-1 + a*x)*PolyLog(2, im*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (3*im*a^2*sqrt(-1 + a*x)*acosh(a*x)^2*PolyLog(2, im*ℯ^acosh(a*x)))/(2*sqrt(1 - a*x)) + (3*im*a^2*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(3, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (3*im*a^2*sqrt(-1 + a*x)*acosh(a*x)*PolyLog(3, im*ℯ^acosh(a*x)))/sqrt(1 - a*x) - (3*im*a^2*sqrt(-1 + a*x)*PolyLog(4, (-im)*ℯ^acosh(a*x)))/sqrt(1 - a*x) + (3*im*a^2*sqrt(-1 + a*x)*PolyLog(4, im*ℯ^acosh(a*x)))/sqrt(1 - a*x)]

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

    @test_int [(f*x)^m*(a + b*acosh(c*x))^3/sqrt(1 - c^2*x^2), x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^3)/sqrt(1 - c^2*x^2), x)]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p / (a+b*acosh(c*x))^1=#

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

    @test_int [(c - a^2*c*x^2)^3/acosh(a*x), x, 7, (35*c^3*SinhIntegral(acosh(a*x)))/(64*a) - (21*c^3*SinhIntegral(3*acosh(a*x)))/(64*a) + (7*c^3*SinhIntegral(5*acosh(a*x)))/(64*a) - (c^3*SinhIntegral(7*acosh(a*x)))/(64*a)]
    @test_int [(c - a^2*c*x^2)^2/acosh(a*x), x, 6, (5*c^2*SinhIntegral(acosh(a*x)))/(8*a) - (5*c^2*SinhIntegral(3*acosh(a*x)))/(16*a) + (c^2*SinhIntegral(5*acosh(a*x)))/(16*a)]
    @test_int [(c - a^2*c*x^2)/acosh(a*x), x, 5, (3*c*SinhIntegral(acosh(a*x)))/(4*a) - (c*SinhIntegral(3*acosh(a*x)))/(4*a)]
    @test_int [1/((c - a^2*c*x^2)*acosh(a*x)), x, 0, Unintegrable(1/((c - a^2*c*x^2)*acosh(a*x)), x)]
    @test_int [1/((c - a^2*c*x^2)^2*acosh(a*x)), x, 0, Unintegrable(1/((c - a^2*c*x^2)^2*acosh(a*x)), x)]

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

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

    @test_int [(x^4*sqrt(1 - c^2*x^2))/(a + b*acosh(c*x)), x, 12, -((sqrt(1 - c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c^5*sqrt(-1 + c*x))) + (sqrt(1 - c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(16*b*c^5*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((6*a)/b)*CoshIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c^5*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(16*b*c^5*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c^5*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(16*b*c^5*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c^5*sqrt(-1 + c*x))]
    @test_int [(x^3*sqrt(1 - c^2*x^2))/(a + b*acosh(c*x)), x, 12, -((sqrt(1 - c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(8*b*c^4*sqrt(-1 + c*x))) + (sqrt(1 - c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*c^4*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*c^4*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*c^4*sqrt(-1 + c*x))]
    @test_int [(x^2*sqrt(1 - c^2*x^2))/(a + b*acosh(c*x)), x, 6, (sqrt(1 - c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(8*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(8*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(8*b*c^3*sqrt(-1 + c*x))]
    @test_int [(x^1*sqrt(1 - c^2*x^2))/(a + b*acosh(c*x)), x, 9, -((sqrt(1 - c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(4*b*c^2*sqrt(-1 + c*x))) + (sqrt(1 - c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*c^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b*c^2*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*c^2*sqrt(-1 + c*x))]
    @test_int [x^0*sqrt(1 - c^2*x^2)/(a + b*acosh(c*x)), x, 6, (sqrt(1 - c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*c*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(2*b*c*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*c*sqrt(-1 + c*x))]
    @test_int [sqrt(1 - c^2*x^2)/(x^1*(a + b*acosh(c*x))), x, 6, -((sqrt(-1 + c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b*sqrt(1 - c*x))) + (sqrt(-1 + c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b*sqrt(1 - c*x)) + Unintegrable(1/(x*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [sqrt(1 - c^2*x^2)/(x^2*(a + b*acosh(c*x))), x, 3, -((c*sqrt(-1 + c*x)*log(a + b*acosh(c*x)))/(b*sqrt(1 - c*x))) + Unintegrable(1/(x^2*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [sqrt(1 - c^2*x^2)/(x^3*(a + b*acosh(c*x))), x, 0, Unintegrable(sqrt(1 - c^2*x^2)/(x^3*(a + b*acosh(c*x))), x)]
    @test_int [sqrt(1 - c^2*x^2)/(x^4*(a + b*acosh(c*x))), x, 0, Unintegrable(sqrt(1 - c^2*x^2)/(x^4*(a + b*acosh(c*x))), x)]

    @test_int [(x^3*(1 - c^2*x^2)^(3/2))/(a + b*acosh(c*x)), x, 15, -((3*sqrt(1 - c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(64*b*c^4*sqrt(-1 + c*x))) + (3*sqrt(1 - c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(64*b*c^4*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c*x)))/b))/(64*b*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh((7*a)/b)*CoshIntegral((7*(a + b*acosh(c*x)))/b))/(64*b*c^4*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(64*b*c^4*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(64*b*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(64*b*c^4*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh((7*a)/b)*SinhIntegral((7*(a + b*acosh(c*x)))/b))/(64*b*c^4*sqrt(-1 + c*x))]
    @test_int [(x^2*(1 - c^2*x^2)^(3/2))/(a + b*acosh(c*x)), x, 12, (sqrt(1 - c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(16*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh((6*a)/b)*CoshIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(16*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(16*b*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x))]
    @test_int [(x^1*(1 - c^2*x^2)^(3/2))/(a + b*acosh(c*x)), x, 12, -((sqrt(1 - c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(8*b*c^2*sqrt(-1 + c*x))) + (3*sqrt(1 - c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*c^2*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*c^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b*c^2*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*c^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*c^2*sqrt(-1 + c*x))]
    @test_int [x^0*(1 - c^2*x^2)^(3/2)/(a + b*acosh(c*x)), x, 9, (sqrt(1 - c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*c*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(8*b*c*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(8*b*c*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*c*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(8*b*c*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^1*(a + b*acosh(c*x))), x, 15, -((5*sqrt(-1 + c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(4*b*sqrt(1 - c*x))) + (sqrt(-1 + c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*sqrt(1 - c*x)) + (5*sqrt(-1 + c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b*sqrt(1 - c*x)) - (sqrt(-1 + c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*sqrt(1 - c*x)) + Unintegrable(1/(x*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^2*(a + b*acosh(c*x))), x, 9, (c*sqrt(-1 + c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*sqrt(1 - c*x)) - (3*c*sqrt(-1 + c*x)*log(a + b*acosh(c*x)))/(2*b*sqrt(1 - c*x)) - (c*sqrt(-1 + c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*sqrt(1 - c*x)) + Unintegrable(1/(x^2*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^3*(a + b*acosh(c*x))), x, 0, Unintegrable((1 - c^2*x^2)^(3/2)/(x^3*(a + b*acosh(c*x))), x)]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^4*(a + b*acosh(c*x))), x, 0, Unintegrable((1 - c^2*x^2)^(3/2)/(x^4*(a + b*acosh(c*x))), x)]

    @test_int [(x^3*(1 - c^2*x^2)^(5/2))/(a + b*acosh(c*x)), x, 15, -((3*sqrt(1 - c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(128*b*c^4*sqrt(-1 + c*x))) + (sqrt(1 - c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(32*b*c^4*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*cosh((7*a)/b)*CoshIntegral((7*(a + b*acosh(c*x)))/b))/(256*b*c^4*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((9*a)/b)*CoshIntegral((9*(a + b*acosh(c*x)))/b))/(256*b*c^4*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(128*b*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(32*b*c^4*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*sinh((7*a)/b)*SinhIntegral((7*(a + b*acosh(c*x)))/b))/(256*b*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((9*a)/b)*SinhIntegral((9*(a + b*acosh(c*x)))/b))/(256*b*c^4*sqrt(-1 + c*x))]
    @test_int [(x^2*(1 - c^2*x^2)^(5/2))/(a + b*acosh(c*x)), x, 15, (sqrt(1 - c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh((6*a)/b)*CoshIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((8*a)/b)*CoshIntegral((8*(a + b*acosh(c*x)))/b))/(128*b*c^3*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(128*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*sinh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((8*a)/b)*SinhIntegral((8*(a + b*acosh(c*x)))/b))/(128*b*c^3*sqrt(-1 + c*x))]
    @test_int [(x^1*(1 - c^2*x^2)^(5/2))/(a + b*acosh(c*x)), x, 15, -((5*sqrt(1 - c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(64*b*c^2*sqrt(-1 + c*x))) + (9*sqrt(1 - c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(64*b*c^2*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c*x)))/b))/(64*b*c^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((7*a)/b)*CoshIntegral((7*(a + b*acosh(c*x)))/b))/(64*b*c^2*sqrt(-1 + c*x)) + (5*sqrt(1 - c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(64*b*c^2*sqrt(-1 + c*x)) - (9*sqrt(1 - c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(64*b*c^2*sqrt(-1 + c*x)) + (5*sqrt(1 - c*x)*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(64*b*c^2*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((7*a)/b)*SinhIntegral((7*(a + b*acosh(c*x)))/b))/(64*b*c^2*sqrt(-1 + c*x))]
    @test_int [x^0*(1 - c^2*x^2)^(5/2)/(a + b*acosh(c*x)), x, 12, (15*sqrt(1 - c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(16*b*c*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((6*a)/b)*CoshIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*log(a + b*acosh(c*x)))/(16*b*c*sqrt(-1 + c*x)) - (15*sqrt(1 - c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(32*b*c*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(16*b*c*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*sinh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(32*b*c*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^1*(a + b*acosh(c*x))), x, 27, -((11*sqrt(-1 + c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(8*b*sqrt(1 - c*x))) + (7*sqrt(-1 + c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*sqrt(1 - c*x)) - (sqrt(-1 + c*x)*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*sqrt(1 - c*x)) + (11*sqrt(-1 + c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b*sqrt(1 - c*x)) - (7*sqrt(-1 + c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*sqrt(1 - c*x)) + Unintegrable(1/(x*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^2*(a + b*acosh(c*x))), x, 18, (c*sqrt(-1 + c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(b*sqrt(1 - c*x)) - (c*sqrt(-1 + c*x)*cosh((4*a)/b)*CoshIntegral((4*(a + b*acosh(c*x)))/b))/(8*b*sqrt(1 - c*x)) - (15*c*sqrt(-1 + c*x)*log(a + b*acosh(c*x)))/(8*b*sqrt(1 - c*x)) - (c*sqrt(-1 + c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b*sqrt(1 - c*x)) + (c*sqrt(-1 + c*x)*sinh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(8*b*sqrt(1 - c*x)) + Unintegrable(1/(x^2*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^3*(a + b*acosh(c*x))), x, 0, Unintegrable((1 - c^2*x^2)^(5/2)/(x^3*(a + b*acosh(c*x))), x)]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^4*(a + b*acosh(c*x))), x, 0, Unintegrable((1 - c^2*x^2)^(5/2)/(x^4*(a + b*acosh(c*x))), x)]

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

    @test_int [x^4/(sqrt(1 - a^2*x^2)*acosh(a*x)), x, 5, (sqrt(-1 + a*x)*CoshIntegral(2*acosh(a*x)))/(2*a^5*sqrt(1 - a*x)) + (sqrt(-1 + a*x)*CoshIntegral(4*acosh(a*x)))/(8*a^5*sqrt(1 - a*x)) + (3*sqrt(-1 + a*x)*log(acosh(a*x)))/(8*a^5*sqrt(1 - a*x))]
    @test_int [x^3/(sqrt(1 - a^2*x^2)*acosh(a*x)), x, 5, (3*sqrt(-1 + a*x)*CoshIntegral(acosh(a*x)))/(4*a^4*sqrt(1 - a*x)) + (sqrt(-1 + a*x)*CoshIntegral(3*acosh(a*x)))/(4*a^4*sqrt(1 - a*x))]
    @test_int [x^2/(sqrt(1 - a^2*x^2)*acosh(a*x)), x, 4, (sqrt(-1 + a*x)*CoshIntegral(2*acosh(a*x)))/(2*a^3*sqrt(1 - a*x)) + (sqrt(-1 + a*x)*log(acosh(a*x)))/(2*a^3*sqrt(1 - a*x))]
    @test_int [x^1/(sqrt(1 - a^2*x^2)*acosh(a*x)), x, 2, (sqrt(-1 + a*x)*CoshIntegral(acosh(a*x)))/(a^2*sqrt(1 - a*x))]
    @test_int [x^0/(sqrt(1 - a^2*x^2)*acosh(a*x)), x, 1, (sqrt(-1 + a*x)*log(acosh(a*x)))/(a*sqrt(1 - a*x))]
    @test_int [1/(x^1*sqrt(1 - a^2*x^2)*acosh(a*x)), x, 0, Unintegrable(1/(x*sqrt(1 - a^2*x^2)*acosh(a*x)), x)]
    @test_int [1/(x^2*sqrt(1 - a^2*x^2)*acosh(a*x)), x, 0, Unintegrable(1/(x^2*sqrt(1 - a^2*x^2)*acosh(a*x)), x)]

    @test_int [x^3/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x, 9, (3*sqrt(-1 + c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(4*b*c^4*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*c^4*sqrt(1 - c*x)) - (3*sqrt(-1 + c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b*c^4*sqrt(1 - c*x)) - (sqrt(-1 + c*x)*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*c^4*sqrt(1 - c*x))]
    @test_int [x^2/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x, 6, (sqrt(-1 + c*x)*cosh((2*a)/b)*CoshIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*c^3*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*log(a + b*acosh(c*x)))/(2*b*c^3*sqrt(1 - c*x)) - (sqrt(-1 + c*x)*sinh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(2*b*c^3*sqrt(1 - c*x))]
    @test_int [x^1/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x, 4, (sqrt(-1 + c*x)*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b*c^2*sqrt(1 - c*x)) - (sqrt(-1 + c*x)*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b*c^2*sqrt(1 - c*x))]
    @test_int [x^0/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x, 1, (sqrt(-1 + c*x)*log(a + b*acosh(c*x)))/(b*c*sqrt(1 - c*x))]
    @test_int [1/(x^1*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/(x*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [1/(x^2*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/(x^2*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]

    @test_int [x^2/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(x^2/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x)]
    @test_int [x^1/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(x/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x)]
    @test_int [x^0/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x)]
    @test_int [1/(x^1*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/(x*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x)]
    @test_int [1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x)]

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

    @test_int [(x^m*(1 - c^2*x^2)^(3/2))/(a + b*acosh(c*x)), x, 0, Unintegrable((x^m*(1 - c^2*x^2)^(3/2))/(a + b*acosh(c*x)), x)]
    @test_int [(x^m*(1 - c^2*x^2)^(1/2))/(a + b*acosh(c*x)), x, 0, Unintegrable((x^m*sqrt(1 - c^2*x^2))/(a + b*acosh(c*x)), x)]
    @test_int [x^m/((1 - c^2*x^2)^(1/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(x^m/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [x^m/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(x^m/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))), x)]
    @test_int [x^m/((1 - c^2*x^2)^(5/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(x^m/((1 - c^2*x^2)^(5/2)*(a + b*acosh(c*x))), x)]

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

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

    @test_int [(c - a^2*c*x^2)^3/acosh(a*x)^2, x, 8, (c^3*(-1 + a*x)^(7/2)*(1 + a*x)^(7/2))/(a*acosh(a*x)) + (35*c^3*CoshIntegral(acosh(a*x)))/(64*a) - (63*c^3*CoshIntegral(3*acosh(a*x)))/(64*a) + (35*c^3*CoshIntegral(5*acosh(a*x)))/(64*a) - (7*c^3*CoshIntegral(7*acosh(a*x)))/(64*a)]
    @test_int [(c - a^2*c*x^2)^2/acosh(a*x)^2, x, 7, -((c^2*(-1 + a*x)^(5/2)*(1 + a*x)^(5/2))/(a*acosh(a*x))) + (5*c^2*CoshIntegral(acosh(a*x)))/(8*a) - (15*c^2*CoshIntegral(3*acosh(a*x)))/(16*a) + (5*c^2*CoshIntegral(5*acosh(a*x)))/(16*a)]
    @test_int [(c - a^2*c*x^2)/acosh(a*x)^2, x, 6, (c*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2))/(a*acosh(a*x)) + (3*c*CoshIntegral(acosh(a*x)))/(4*a) - (3*c*CoshIntegral(3*acosh(a*x)))/(4*a)]
    @test_int [1/((c - a^2*c*x^2)*acosh(a*x)^2), x, 1, 1/(a*c*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)) + (a*Unintegrable(x/((-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x)), x))/c]
    @test_int [1/((c - a^2*c*x^2)^2*acosh(a*x)^2), x, 1, -(1/(a*c^2*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*acosh(a*x))) - (3*a*Unintegrable(x/((-1 + a*x)^(5/2)*(1 + a*x)^(5/2)*acosh(a*x)), x))/c^2]

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

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

    @test_int [x^3*sqrt(1 - c^2*x^2)/(a + b*acosh(c*x))^2, x, 22, -((x^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(1 - c^2*x^2))/(b*c*(a + b*acosh(c*x)))) + (sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(8*b^2*c^4*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(16*b^2*c^4*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*CoshIntegral((5*(a + b*acosh(c*x)))/b)*sinh((5*a)/b))/(16*b^2*c^4*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b^2*c^4*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b^2*c^4*sqrt(-1 + c*x)) + (5*sqrt(1 - c*x)*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b^2*c^4*sqrt(-1 + c*x))]
    @test_int [x^2*sqrt(1 - c^2*x^2)/(a + b*acosh(c*x))^2, x, 16, -((x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(1 - c^2*x^2))/(b*c*(a + b*acosh(c*x)))) - (sqrt(1 - c*x)*CoshIntegral((4*(a + b*acosh(c*x)))/b)*sinh((4*a)/b))/(2*b^2*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(2*b^2*c^3*sqrt(-1 + c*x))]
    @test_int [x^1*sqrt(1 - c^2*x^2)/(a + b*acosh(c*x))^2, x, 14, -((x*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(1 - c^2*x^2))/(b*c*(a + b*acosh(c*x)))) + (sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(4*b^2*c^2*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(4*b^2*c^2*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b^2*c^2*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*c^2*sqrt(-1 + c*x))]
    @test_int [x^0*sqrt(1 - c^2*x^2)/(a + b*acosh(c*x))^2, x, 7, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(1 - c^2*x^2))/(b*c*(a + b*acosh(c*x)))) - (sqrt(1 - c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(b^2*c*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c*sqrt(-1 + c*x))]
    @test_int [sqrt(1 - c^2*x^2)/(x^1*(a + b*acosh(c*x))^2), x, 5, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(1 - c^2*x^2))/(b*c*x*(a + b*acosh(c*x)))) - (sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(b^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*Unintegrable(1/(x^2*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x))]
    @test_int [sqrt(1 - c^2*x^2)/(x^2*(a + b*acosh(c*x))^2), x, 1, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(1 - c^2*x^2))/(b*c*x^2*(a + b*acosh(c*x)))) + (2*sqrt(1 - c*x)*Unintegrable(1/(x^3*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x))]
    @test_int [sqrt(1 - c^2*x^2)/(x^3*(a + b*acosh(c*x))^2), x, 0, Unintegrable(sqrt(1 - c^2*x^2)/(x^3*(a + b*acosh(c*x))^2), x)]
    @test_int [sqrt(1 - c^2*x^2)/(x^4*(a + b*acosh(c*x))^2), x, 0, Unintegrable(sqrt(1 - c^2*x^2)/(x^4*(a + b*acosh(c*x))^2), x)]

    @test_int [x^2*(1 - c^2*x^2)^(3/2)/(a + b*acosh(c*x))^2, x, 21, -((x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(3/2))/(b*c*(a + b*acosh(c*x)))) - (sqrt(1 - c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(16*b^2*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*CoshIntegral((4*(a + b*acosh(c*x)))/b)*sinh((4*a)/b))/(4*b^2*c^3*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*CoshIntegral((6*(a + b*acosh(c*x)))/b)*sinh((6*a)/b))/(16*b^2*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(16*b^2*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(4*b^2*c^3*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*cosh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(16*b^2*c^3*sqrt(-1 + c*x))]
    @test_int [x^1*(1 - c^2*x^2)^(3/2)/(a + b*acosh(c*x))^2, x, 24, -((x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(3/2))/(b*c*(a + b*acosh(c*x)))) + (sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(8*b^2*c^2*sqrt(-1 + c*x)) - (9*sqrt(1 - c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(16*b^2*c^2*sqrt(-1 + c*x)) + (5*sqrt(1 - c*x)*CoshIntegral((5*(a + b*acosh(c*x)))/b)*sinh((5*a)/b))/(16*b^2*c^2*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b^2*c^2*sqrt(-1 + c*x)) + (9*sqrt(1 - c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b^2*c^2*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b^2*c^2*sqrt(-1 + c*x))]
    @test_int [x^0*(1 - c^2*x^2)^(3/2)/(a + b*acosh(c*x))^2, x, 11, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(3/2))/(b*c*(a + b*acosh(c*x)))) - (sqrt(1 - c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(b^2*c*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*CoshIntegral((4*(a + b*acosh(c*x)))/b)*sinh((4*a)/b))/(2*b^2*c*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(2*b^2*c*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^1*(a + b*acosh(c*x))^2), x, 12, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(3/2))/(b*c*x*(a + b*acosh(c*x)))) - (9*sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(4*b^2*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(4*b^2*sqrt(-1 + c*x)) + (9*sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b^2*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)/(x^2*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^2*(a + b*acosh(c*x))^2), x, 3, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(3/2))/(b*c*x^2*(a + b*acosh(c*x)))) - (2*sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)/(x^3*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x)) - (2*c*sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)/(x*(a + b*acosh(c*x))), x))/(b*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^3*(a + b*acosh(c*x))^2), x, 0, Unintegrable((1 - c^2*x^2)^(3/2)/(x^3*(a + b*acosh(c*x))^2), x)]
    @test_int [(1 - c^2*x^2)^(3/2)/(x^4*(a + b*acosh(c*x))^2), x, 2, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(3/2))/(b*c*x^4*(a + b*acosh(c*x)))) - (4*sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)/(x^5*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x))]

    @test_int [x^2*(1 - c^2*x^2)^(5/2)/(a + b*acosh(c*x))^2, x, 30, -((x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(5/2))/(b*c*(a + b*acosh(c*x)))) - (sqrt(1 - c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(16*b^2*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*CoshIntegral((4*(a + b*acosh(c*x)))/b)*sinh((4*a)/b))/(8*b^2*c^3*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*CoshIntegral((6*(a + b*acosh(c*x)))/b)*sinh((6*a)/b))/(16*b^2*c^3*sqrt(-1 + c*x)) - (sqrt(1 - c*x)*CoshIntegral((8*(a + b*acosh(c*x)))/b)*sinh((8*a)/b))/(16*b^2*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(16*b^2*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(8*b^2*c^3*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*cosh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(16*b^2*c^3*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*cosh((8*a)/b)*SinhIntegral((8*(a + b*acosh(c*x)))/b))/(16*b^2*c^3*sqrt(-1 + c*x))]
    @test_int [x^1*(1 - c^2*x^2)^(5/2)/(a + b*acosh(c*x))^2, x, 30, -((x*sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(5/2))/(b*c*(a + b*acosh(c*x)))) + (5*sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(64*b^2*c^2*sqrt(-1 + c*x)) - (27*sqrt(1 - c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(64*b^2*c^2*sqrt(-1 + c*x)) + (25*sqrt(1 - c*x)*CoshIntegral((5*(a + b*acosh(c*x)))/b)*sinh((5*a)/b))/(64*b^2*c^2*sqrt(-1 + c*x)) - (7*sqrt(1 - c*x)*CoshIntegral((7*(a + b*acosh(c*x)))/b)*sinh((7*a)/b))/(64*b^2*c^2*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(64*b^2*c^2*sqrt(-1 + c*x)) + (27*sqrt(1 - c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(64*b^2*c^2*sqrt(-1 + c*x)) - (25*sqrt(1 - c*x)*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(64*b^2*c^2*sqrt(-1 + c*x)) + (7*sqrt(1 - c*x)*cosh((7*a)/b)*SinhIntegral((7*(a + b*acosh(c*x)))/b))/(64*b^2*c^2*sqrt(-1 + c*x))]
    @test_int [x^0*(1 - c^2*x^2)^(5/2)/(a + b*acosh(c*x))^2, x, 14, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(5/2))/(b*c*(a + b*acosh(c*x)))) - (15*sqrt(1 - c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(16*b^2*c*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*CoshIntegral((4*(a + b*acosh(c*x)))/b)*sinh((4*a)/b))/(4*b^2*c*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*CoshIntegral((6*(a + b*acosh(c*x)))/b)*sinh((6*a)/b))/(16*b^2*c*sqrt(-1 + c*x)) + (15*sqrt(1 - c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(16*b^2*c*sqrt(-1 + c*x)) - (3*sqrt(1 - c*x)*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(4*b^2*c*sqrt(-1 + c*x)) + (3*sqrt(1 - c*x)*cosh((6*a)/b)*SinhIntegral((6*(a + b*acosh(c*x)))/b))/(16*b^2*c*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^1*(a + b*acosh(c*x))^2), x, 15, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(5/2))/(b*c*x*(a + b*acosh(c*x)))) - (25*sqrt(1 - c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(8*b^2*sqrt(-1 + c*x)) + (25*sqrt(1 - c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(16*b^2*sqrt(-1 + c*x)) - (5*sqrt(1 - c*x)*CoshIntegral((5*(a + b*acosh(c*x)))/b)*sinh((5*a)/b))/(16*b^2*sqrt(-1 + c*x)) + (25*sqrt(1 - c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b^2*sqrt(-1 + c*x)) - (25*sqrt(1 - c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b^2*sqrt(-1 + c*x)) + (5*sqrt(1 - c*x)*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b^2*sqrt(-1 + c*x)) + (sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)^2/(x^2*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^2*(a + b*acosh(c*x))^2), x, 3, -((sqrt(-1 + c*x)*sqrt(1 + c*x)*(1 - c^2*x^2)^(5/2))/(b*c*x^2*(a + b*acosh(c*x)))) + (2*sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)^2/(x^3*(a + b*acosh(c*x))), x))/(b*c*sqrt(-1 + c*x)) + (4*c*sqrt(1 - c*x)*Unintegrable((-1 + c^2*x^2)^2/(x*(a + b*acosh(c*x))), x))/(b*sqrt(-1 + c*x))]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^3*(a + b*acosh(c*x))^2), x, 0, Unintegrable((1 - c^2*x^2)^(5/2)/(x^3*(a + b*acosh(c*x))^2), x)]
    @test_int [(1 - c^2*x^2)^(5/2)/(x^4*(a + b*acosh(c*x))^2), x, 0, Unintegrable((1 - c^2*x^2)^(5/2)/(x^4*(a + b*acosh(c*x))^2), x)]

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

    @test_int [x^5/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 13, -((x^5*sqrt(-1 + c*x))/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (5*sqrt(-1 + c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(8*b^2*c^6*sqrt(1 - c*x)) - (15*sqrt(-1 + c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(16*b^2*c^6*sqrt(1 - c*x)) - (5*sqrt(-1 + c*x)*CoshIntegral((5*(a + b*acosh(c*x)))/b)*sinh((5*a)/b))/(16*b^2*c^6*sqrt(1 - c*x)) + (5*sqrt(-1 + c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b^2*c^6*sqrt(1 - c*x)) + (15*sqrt(-1 + c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b^2*c^6*sqrt(1 - c*x)) + (5*sqrt(-1 + c*x)*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b^2*c^6*sqrt(1 - c*x))]
    @test_int [x^4/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 10, -((x^4*sqrt(-1 + c*x))/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (sqrt(-1 + c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(b^2*c^5*sqrt(1 - c*x)) - (sqrt(-1 + c*x)*CoshIntegral((4*(a + b*acosh(c*x)))/b)*sinh((4*a)/b))/(2*b^2*c^5*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c^5*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*cosh((4*a)/b)*SinhIntegral((4*(a + b*acosh(c*x)))/b))/(2*b^2*c^5*sqrt(1 - c*x))]
    @test_int [x^3/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 10, -((x^3*sqrt(-1 + c*x))/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (3*sqrt(-1 + c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(4*b^2*c^4*sqrt(1 - c*x)) - (3*sqrt(-1 + c*x)*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(4*b^2*c^4*sqrt(1 - c*x)) + (3*sqrt(-1 + c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b^2*c^4*sqrt(1 - c*x)) + (3*sqrt(-1 + c*x)*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*c^4*sqrt(1 - c*x))]
    @test_int [x^2/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 7, -((x^2*sqrt(-1 + c*x))/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (sqrt(-1 + c*x)*CoshIntegral((2*(a + b*acosh(c*x)))/b)*sinh((2*a)/b))/(b^2*c^3*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*cosh((2*a)/b)*SinhIntegral((2*(a + b*acosh(c*x)))/b))/(b^2*c^3*sqrt(1 - c*x))]
    @test_int [x/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 5, -((x*sqrt(-1 + c*x))/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (sqrt(-1 + c*x)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(b^2*c^2*sqrt(1 - c*x)) + (sqrt(-1 + c*x)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*c^2*sqrt(1 - c*x))]
    @test_int [1/(sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 1, -(sqrt(-1 + c*x)/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x))))]
    @test_int [1/(x*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 1, -(sqrt(-1 + c*x)/(b*c*x*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (sqrt(-1 + c*x)*Unintegrable(1/(x^2*(a + b*acosh(c*x))), x))/(b*c*sqrt(1 - c*x))]
    @test_int [1/(x^2*sqrt(1 - c^2*x^2)*(a + b*acosh(c*x))^2), x, 1, -(sqrt(-1 + c*x)/(b*c*x^2*sqrt(1 - c*x)*(a + b*acosh(c*x)))) - (2*sqrt(-1 + c*x)*Unintegrable(1/(x^3*(a + b*acosh(c*x))), x))/(b*c*sqrt(1 - c*x))]

    @test_int [x^3/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(x^3/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x)]
    @test_int [x^2/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 2, -((x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x)))) + (2*sqrt(-1 + c*x)*Unintegrable(x/((-1 + c^2*x^2)^2*(a + b*acosh(c*x))), x))/(b*c*sqrt(1 - c*x))]
    @test_int [x^1/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(x/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x)]
    @test_int [x^0/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 2, -((sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x)))) + (2*c*sqrt(-1 + c*x)*Unintegrable(x/((-1 + c^2*x^2)^2*(a + b*acosh(c*x))), x))/(b*sqrt(1 - c*x))]
    @test_int [1/(x^1*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/(x*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x)]
    @test_int [1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/(x^2*(1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x)]

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

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

    @test_int [(f*x)^m*(1 - c^2*x^2)^(3/2)/(a + b*acosh(c*x))^2, x, 0, Unintegrable(((f*x)^m*(1 - c^2*x^2)^(3/2))/(a + b*acosh(c*x))^2, x)]
    @test_int [(f*x)^m*(1 - c^2*x^2)^(1/2)/(a + b*acosh(c*x))^2, x, 0, Unintegrable(((f*x)^m*sqrt(1 - c^2*x^2))/(a + b*acosh(c*x))^2, x)]
    @test_int [(f*x)^m/((1 - c^2*x^2)^(1/2)*(a + b*acosh(c*x))^2), x, 1, -(((f*x)^m*sqrt(-1 + c*x))/(b*c*sqrt(1 - c*x)*(a + b*acosh(c*x)))) + (f*m*sqrt(-1 + c*x)*Unintegrable((f*x)^(-1 + m)/(a + b*acosh(c*x)), x))/(b*c*sqrt(1 - c*x))]
    @test_int [(f*x)^m/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable((f*x)^m/((1 - c^2*x^2)^(3/2)*(a + b*acosh(c*x))^2), x)]
    @test_int [(f*x)^m/((1 - c^2*x^2)^(5/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable((f*x)^m/((1 - c^2*x^2)^(5/2)*(a + b*acosh(c*x))^2), x)]

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

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

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

    @test_int [1/(sqrt(1 - a^2*x^2)*acosh(a*x)^3), x, 1, -(sqrt(-1 + a*x)/(2*a*sqrt(1 - a*x)*acosh(a*x)^2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^(n/2)=#

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

    #= ::Subsubsection:: =#
    #=n>0=#

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(x^3*(d - c^2*d*x^2))/(a + b*acosh(c*x))^(3/2), x, 27, (2*d*x^3*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(b*c*sqrt(a + b*acosh(c*x))) + (3*d*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^4) - (d*ℯ^((6*a)/b)*sqrt((3*pi)/2)*erf((sqrt(6)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^4) + (3*d*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(16*b^(3/2)*c^4)) - (d*sqrt((3*pi)/2)*erfi((sqrt(6)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((6*a)/b)*(16*b^(3/2)*c^4))]
    @test_int [(x^2*(d - c^2*d*x^2))/(a + b*acosh(c*x))^(3/2), x, 32, (2*d*x^2*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(b*c*sqrt(a + b*acosh(c*x))) + (d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*b^(3/2)*c^3) + (d*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^3) - (d*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^3) + (d*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(ℯ^(a/b)*(8*b^(3/2)*c^3)) + (d*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((3*a)/b)*(16*b^(3/2)*c^3)) - (d*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((5*a)/b)*(16*b^(3/2)*c^3))]
    @test_int [(x^1*(d - c^2*d*x^2))/(a + b*acosh(c*x))^(3/2), x, 17, (2*d*x*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(b*c*sqrt(a + b*acosh(c*x))) - (d*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^2) + (d*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(2*b^(3/2)*c^2) - (d*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((4*a)/b)*(4*b^(3/2)*c^2)) + (d*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(2*b^(3/2)*c^2))]
    @test_int [x^0*(d - c^2*d*x^2)/(a + b*acosh(c*x))^(3/2), x, 14, (2*d*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(b*c*sqrt(a + b*acosh(c*x))) + (3*d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*b^(3/2)*c) - (d*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)*c) + (3*d*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*b^(3/2)*c*ℯ^(a/b)) - (d*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)*c*ℯ^((3*a)/b))]
    @test_int [(d - c^2*d*x^2)/(x^1*(a + b*acosh(c*x))^(3/2)), x, 12, (2*d*(-1 + c*x)^(3/2)*(1 + c*x)^(3/2))/(b*c*x*sqrt(a + b*acosh(c*x))) - (d*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/b^(3/2) - (d*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*b^(3/2)) + (2*d*Unintegrable(1/(x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x))), x))/(b*c)]

    @test_int [(x^3*(d - c^2*d*x^2)^2)/(a + b*acosh(c*x))^(3/2), x, 32, -((2*d^2*x^3*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*sqrt(a + b*acosh(c*x)))) - (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) + (3*d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) + (d^2*ℯ^((8*a)/b)*sqrt(pi/2)*erf((2*sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) - (d^2*ℯ^((6*a)/b)*sqrt((3*pi)/2)*erf((sqrt(6)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*b^(3/2)*c^4) - (d^2*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((4*a)/b)*(32*b^(3/2)*c^4)) + (3*d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(32*b^(3/2)*c^4)) + (d^2*sqrt(pi/2)*erfi((2*sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((8*a)/b)*(32*b^(3/2)*c^4)) - (d^2*sqrt((3*pi)/2)*erfi((sqrt(6)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((6*a)/b)*(32*b^(3/2)*c^4))]
    @test_int [(x^2*(d - c^2*d*x^2)^2)/(a + b*acosh(c*x))^(3/2), x, 42, -((2*d^2*x^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*sqrt(a + b*acosh(c*x)))) + (5*d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(64*b^(3/2)*c^3) + (d^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3) - (3*d^2*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3) + (d^2*ℯ^((7*a)/b)*sqrt(7*pi)*erf((sqrt(7)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(64*b^(3/2)*c^3) + (5*d^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(ℯ^(a/b)*(64*b^(3/2)*c^3)) + (d^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((3*a)/b)*(64*b^(3/2)*c^3)) - (3*d^2*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((5*a)/b)*(64*b^(3/2)*c^3)) + (d^2*sqrt(7*pi)*erfi((sqrt(7)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((7*a)/b)*(64*b^(3/2)*c^3))]
    @test_int [(x*(d - c^2*d*x^2)^2)/(a + b*acosh(c*x))^(3/2), x, 32, -((2*d^2*x*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*sqrt(a + b*acosh(c*x)))) - (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^2) + (5*d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^2) + (d^2*ℯ^((6*a)/b)*sqrt((3*pi)/2)*erf((sqrt(6)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c^2) - (d^2*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((4*a)/b)*(4*b^(3/2)*c^2)) + (5*d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(16*b^(3/2)*c^2)) + (d^2*sqrt((3*pi)/2)*erfi((sqrt(6)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((6*a)/b)*(16*b^(3/2)*c^2))]
    @test_int [(d - c^2*d*x^2)^2/(a + b*acosh(c*x))^(3/2), x, 19, (-2*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*sqrt(a + b*acosh(c*x))) + (5*d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*b^(3/2)*c) - (5*d^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c) + (d^2*ℯ^((5*a)/b)*sqrt(5*pi)*erf((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c) + (5*d^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*b^(3/2)*c*ℯ^(a/b)) - (5*d^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c*ℯ^((3*a)/b)) + (d^2*sqrt(5*pi)*erfi((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(16*b^(3/2)*c*ℯ^((5*a)/b))]
    @test_int [(d - c^2*d*x^2)^2/(x*(a + b*acosh(c*x))^(3/2)), x, 25, -((2*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*x*sqrt(a + b*acosh(c*x)))) + (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)) - (3*d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(2*b^(3/2)) + (d^2*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((4*a)/b)*(4*b^(3/2))) - (3*d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(2*b^(3/2))) + (2*d^2*Unintegrable(1/(x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x))), x))/(b*c), -((2*d^2*(-1 + c*x)^(5/2)*(1 + c*x)^(5/2))/(b*c*x*sqrt(a + b*acosh(c*x)))) + (d^2*ℯ^((4*a)/b)*sqrt(pi)*erf((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)) + (d^2*ℯ^((2*a)/b)*sqrt(pi/2)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(2*b^(3/2)) - (d^2*ℯ^((2*a)/b)*sqrt(2*pi)*erf((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/b^(3/2) + (d^2*sqrt(pi)*erfi((2*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((4*a)/b)*(4*b^(3/2))) + (d^2*sqrt(pi/2)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*(2*b^(3/2))) - (d^2*sqrt(2*pi)*erfi((sqrt(2)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(ℯ^((2*a)/b)*b^(3/2)) + (2*d^2*Unintegrable(1/(x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x))), x))/(b*c)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*x^m*(d-c^2*d*x^2)^(p/2)*acosh(c*x)^(n/2)=#

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(c - a^2*c*x^2)^(3/2)*sqrt(acosh(a*x)), x, 25, (3/8)*c*x*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)) + (1/4)*x*(c - a^2*c*x^2)^(3/2)*sqrt(acosh(a*x)) - (c*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)), x, 10, (x*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/2 - (sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [sqrt(acosh(a*x))/sqrt(c - a^2*c*x^2), x, 1, (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^(3/2))/(3*a*sqrt(c - a^2*c*x^2))]
    @test_int [sqrt(acosh(a*x))/(c - a^2*c*x^2)^(3/2), x, 1, (x*sqrt(acosh(a*x)))/(c*sqrt(c - a^2*c*x^2)) + (a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((1 - a^2*x^2)*sqrt(acosh(a*x))), x))/(2*c*sqrt(c - a^2*c*x^2))]
    @test_int [sqrt(acosh(a*x))/(c - a^2*c*x^2)^(5/2), x, 3, (x*sqrt(acosh(a*x)))/(3*c*(c - a^2*c*x^2)^(3/2)) + (2*x*sqrt(acosh(a*x)))/(3*c^2*sqrt(c - a^2*c*x^2)) + (a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((1 - a^2*x^2)*sqrt(acosh(a*x))), x))/(3*c^2*sqrt(c - a^2*c*x^2)) + (a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((-1 + a^2*x^2)^2*sqrt(acosh(a*x))), x))/(6*c^2*sqrt(c - a^2*c*x^2))]

    @test_int [(c - a^2*c*x^2)^(3/2)*acosh(a*x)^(3/2), x, 27, (27*c*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (9*a*c*x^2*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(32*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*c*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(32*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3/8)*c*x*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2) + (1/4)*x*(c - a^2*c*x^2)^(3/2)*acosh(a*x)^(3/2) - (3*c*sqrt(c - a^2*c*x^2)*acosh(a*x)^(5/2))/(20*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(2048*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(2048*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2), x, 11, (3*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*a*x^2*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(8*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (x*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/2 - (sqrt(c - a^2*c*x^2)*acosh(a*x)^(5/2))/(5*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [acosh(a*x)^(3/2)/sqrt(c - a^2*c*x^2), x, 1, (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^(5/2))/(5*a*sqrt(c - a^2*c*x^2))]
    @test_int [acosh(a*x)^(3/2)/(c - a^2*c*x^2)^(3/2), x, 1, (x*acosh(a*x)^(3/2))/(c*sqrt(c - a^2*c*x^2)) + (3*a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable((x*sqrt(acosh(a*x)))/(1 - a^2*x^2), x))/(2*c*sqrt(c - a^2*c*x^2))]

    @test_int [(c - a^2*c*x^2)^(3/2)*acosh(a*x)^(5/2), x, 41, (225/512)*c*x*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)) + (15/256)*c*x*(1 - a*x)*(1 + a*x)*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)) + (45*c*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (15*a*c*x^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(32*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (5*c*(1 - a^2*x^2)^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(32*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (3/8)*c*x*sqrt(c - a^2*c*x^2)*acosh(a*x)^(5/2) + (1/4)*x*(c - a^2*c*x^2)^(3/2)*acosh(a*x)^(5/2) - (3*c*sqrt(c - a^2*c*x^2)*acosh(a*x)^(7/2))/(28*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (15*c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(16384*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (15*c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (15*c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(16384*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (15*c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [sqrt(c - a^2*c*x^2)*acosh(a*x)^(5/2), x, 13, (15*x*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/32 + (5*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (5*a*x^2*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))/(8*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (x*sqrt(c - a^2*c*x^2)*acosh(a*x)^(5/2))/2 - (sqrt(c - a^2*c*x^2)*acosh(a*x)^(7/2))/(7*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (15*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (15*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(256*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [acosh(a*x)^(5/2)/sqrt(c - a^2*c*x^2), x, 1, (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*acosh(a*x)^(7/2))/(7*a*sqrt(c - a^2*c*x^2))]
    @test_int [acosh(a*x)^(5/2)/(c - a^2*c*x^2)^(3/2), x, 1, (x*acosh(a*x)^(5/2))/(c*sqrt(c - a^2*c*x^2)) + (5*a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable((x*acosh(a*x)^(3/2))/(1 - a^2*x^2), x))/(2*c*sqrt(c - a^2*c*x^2))]

    @test_int [(a^2 - x^2)^(3/2)*sqrt(acosh(x/a)), x, 25, (3/8)*a^2*x*sqrt(a^2 - x^2)*sqrt(acosh(x/a)) + (1/4)*x*(a^2 - x^2)^(3/2)*sqrt(acosh(x/a)) - (a^3*sqrt(a^2 - x^2)*acosh(x/a)^(3/2))/(4*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (a^3*sqrt(pi)*sqrt(a^2 - x^2)*erf(2*sqrt(acosh(x/a))))/(256*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (a^3*sqrt(pi/2)*sqrt(a^2 - x^2)*erf(sqrt(2)*sqrt(acosh(x/a))))/(16*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (a^3*sqrt(pi)*sqrt(a^2 - x^2)*erfi(2*sqrt(acosh(x/a))))/(256*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (a^3*sqrt(pi/2)*sqrt(a^2 - x^2)*erfi(sqrt(2)*sqrt(acosh(x/a))))/(16*sqrt(-1 + x/a)*sqrt(1 + x/a))]
    @test_int [sqrt(a^2 - x^2)*sqrt(acosh(x/a)), x, 10, (x*sqrt(a^2 - x^2)*sqrt(acosh(x/a)))/2 - (a*sqrt(a^2 - x^2)*acosh(x/a)^(3/2))/(3*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (a*sqrt(pi/2)*sqrt(a^2 - x^2)*erf(sqrt(2)*sqrt(acosh(x/a))))/(16*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (a*sqrt(pi/2)*sqrt(a^2 - x^2)*erfi(sqrt(2)*sqrt(acosh(x/a))))/(16*sqrt(-1 + x/a)*sqrt(1 + x/a))]
    @test_int [sqrt(acosh(x/a))/sqrt(a^2 - x^2), x, 1, (2*a*sqrt(-1 + x/a)*sqrt(1 + x/a)*acosh(x/a)^(3/2))/(3*sqrt(a^2 - x^2))]
    @test_int [sqrt(acosh(x/a))/(a^2 - x^2)^(3/2), x, 1, (x*sqrt(acosh(x/a)))/(a^2*sqrt(a^2 - x^2)) + (sqrt(-1 + x/a)*sqrt(1 + x/a)*Unintegrable(x/((1 - x^2/a^2)*sqrt(acosh(x/a))), x))/(2*a^3*sqrt(a^2 - x^2))]
    @test_int [sqrt(acosh(x/a))/(a^2 - x^2)^(5/2), x, 3, (x*sqrt(acosh(x/a)))/(3*a^2*(a^2 - x^2)^(3/2)) + (2*x*sqrt(acosh(x/a)))/(3*a^4*sqrt(a^2 - x^2)) + (sqrt(-1 + x/a)*sqrt(1 + x/a)*Unintegrable(x/((1 - x^2/a^2)*sqrt(acosh(x/a))), x))/(3*a^5*sqrt(a^2 - x^2)) + (sqrt(-1 + x/a)*sqrt(1 + x/a)*Unintegrable(x/((-1 + x^2/a^2)^2*sqrt(acosh(x/a))), x))/(6*a^5*sqrt(a^2 - x^2))]

    @test_int [(a^2 - x^2)^(3/2)*acosh(x/a)^(3/2), x, 27, (27*a^3*sqrt(a^2 - x^2)*sqrt(acosh(x/a)))/(256*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (9*a*x^2*sqrt(a^2 - x^2)*sqrt(acosh(x/a)))/(32*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (3*(a^2 - x^2)^(5/2)*sqrt(acosh(x/a)))/(32*a*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (3/8)*a^2*x*sqrt(a^2 - x^2)*acosh(x/a)^(3/2) + (1/4)*x*(a^2 - x^2)^(3/2)*acosh(x/a)^(3/2) - (3*a^3*sqrt(a^2 - x^2)*acosh(x/a)^(5/2))/(20*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (3*a^3*sqrt(pi)*sqrt(a^2 - x^2)*erf(2*sqrt(acosh(x/a))))/(2048*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (3*a^3*sqrt(pi/2)*sqrt(a^2 - x^2)*erf(sqrt(2)*sqrt(acosh(x/a))))/(64*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (3*a^3*sqrt(pi)*sqrt(a^2 - x^2)*erfi(2*sqrt(acosh(x/a))))/(2048*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (3*a^3*sqrt(pi/2)*sqrt(a^2 - x^2)*erfi(sqrt(2)*sqrt(acosh(x/a))))/(64*sqrt(-1 + x/a)*sqrt(1 + x/a))]
    @test_int [sqrt(a^2 - x^2)*acosh(x/a)^(3/2), x, 11, (3*a*sqrt(a^2 - x^2)*sqrt(acosh(x/a)))/(16*sqrt(-1 + x/a)*sqrt(1 + x/a)) - (3*x^2*sqrt(a^2 - x^2)*sqrt(acosh(x/a)))/(8*a*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (x*sqrt(a^2 - x^2)*acosh(x/a)^(3/2))/2 - (a*sqrt(a^2 - x^2)*acosh(x/a)^(5/2))/(5*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (3*a*sqrt(pi/2)*sqrt(a^2 - x^2)*erf(sqrt(2)*sqrt(acosh(x/a))))/(64*sqrt(-1 + x/a)*sqrt(1 + x/a)) + (3*a*sqrt(pi/2)*sqrt(a^2 - x^2)*erfi(sqrt(2)*sqrt(acosh(x/a))))/(64*sqrt(-1 + x/a)*sqrt(1 + x/a))]
    @test_int [acosh(x/a)^(3/2)/sqrt(a^2 - x^2), x, 1, (2*a*sqrt(-1 + x/a)*sqrt(1 + x/a)*acosh(x/a)^(5/2))/(5*sqrt(a^2 - x^2))]
    @test_int [acosh(x/a)^(3/2)/(a^2 - x^2)^(3/2), x, 1, (x*acosh(x/a)^(3/2))/(a^2*sqrt(a^2 - x^2)) + (3*sqrt(-1 + x/a)*sqrt(1 + x/a)*Unintegrable((x*sqrt(acosh(x/a)))/(1 - x^2/a^2), x))/(2*a^3*sqrt(a^2 - x^2))]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [x/(sqrt(1 - x^2)*sqrt(acosh(x))), x, 6, (sqrt(pi)*sqrt(-1 + x)*erf(sqrt(acosh(x))))/(2*sqrt(1 - x)) + (sqrt(pi)*sqrt(-1 + x)*erfi(sqrt(acosh(x))))/(2*sqrt(1 - x))]

    @test_int [(c - a^2*c*x^2)^(5/2)/sqrt(acosh(a*x)), x, 18, (-5*c^2*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(8*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*c^2*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (15*c^2*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c^2*sqrt(pi/6)*sqrt(c - a^2*c*x^2)*erf(sqrt(6)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*c^2*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (15*c^2*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c^2*sqrt(pi/6)*sqrt(c - a^2*c*x^2)*erfi(sqrt(6)*sqrt(acosh(a*x))))/(64*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [(c - a^2*c*x^2)^(3/2)/sqrt(acosh(a*x)), x, 13, (-3*c*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(32*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(32*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [(c - a^2*c*x^2)^(1/2)/sqrt(acosh(a*x)), x, 8, -((sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))/(a*sqrt(-1 + a*x)*sqrt(1 + a*x))) + (sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [1/((c - a^2*c*x^2)^(1/2)*sqrt(acosh(a*x))), x, 1, (2*sqrt(-1 + a*x)*sqrt(1 + a*x)*sqrt(acosh(a*x)))/(a*sqrt(c - a^2*c*x^2))]
    @test_int [1/((c - a^2*c*x^2)^(3/2)*sqrt(acosh(a*x))), x, 0, Unintegrable(1/((c - a^2*c*x^2)^(3/2)*sqrt(acosh(a*x))), x)]
    @test_int [1/((c - a^2*c*x^2)^(5/2)*sqrt(acosh(a*x))), x, 0, Unintegrable(1/((c - a^2*c*x^2)^(5/2)*sqrt(acosh(a*x))), x)]

    @test_int [(c - a^2*c*x^2)^(5/2)/acosh(a*x)^(3/2), x, 20, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x)*(c - a^2*c*x^2)^(5/2))/(a*sqrt(acosh(a*x)))) + (3*c^2*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(8*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (15*c^2*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c^2*sqrt((3*pi)/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(6)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (3*c^2*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(8*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (15*c^2*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c^2*sqrt((3*pi)/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(6)*sqrt(acosh(a*x))))/(16*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [(c - a^2*c*x^2)^(3/2)/acosh(a*x)^(3/2), x, 15, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x)*(c - a^2*c*x^2)^(3/2))/(a*sqrt(acosh(a*x)))) + (c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (c*sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [(c - a^2*c*x^2)^(1/2)/acosh(a*x)^(3/2), x, 9, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x)*sqrt(c - a^2*c*x^2))/(a*sqrt(acosh(a*x)))) - (sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (sqrt(pi/2)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [1/((c - a^2*c*x^2)^(1/2)*acosh(a*x)^(3/2)), x, 1, (-2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(a*sqrt(c - a^2*c*x^2)*sqrt(acosh(a*x)))]
    @test_int [1/((c - a^2*c*x^2)^(3/2)*acosh(a*x)^(3/2)), x, 2, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(a*(c - a^2*c*x^2)^(3/2)*sqrt(acosh(a*x)))) + (4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((-1 + a^2*x^2)^2*sqrt(acosh(a*x))), x))/(c*sqrt(c - a^2*c*x^2))]
    @test_int [1/((c - a^2*c*x^2)^(5/2)*acosh(a*x)^(3/2)), x, 2, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(a*(c - a^2*c*x^2)^(5/2)*sqrt(acosh(a*x)))) - (8*a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((-1 + a^2*x^2)^3*sqrt(acosh(a*x))), x))/(c^2*sqrt(c - a^2*c*x^2))]

    @test_int [(c - a^2*c*x^2)^(3/2)/acosh(a*x)^(5/2), x, 19, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x)*(c - a^2*c*x^2)^(3/2))/(3*a*acosh(a*x)^(3/2))) - (16*c*x*(1 - a*x)*(1 + a*x)*sqrt(c - a^2*c*x^2))/(3*sqrt(acosh(a*x))) - (2*c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erf(2*sqrt(acosh(a*x))))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (2*c*sqrt(2*pi)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) - (2*c*sqrt(pi)*sqrt(c - a^2*c*x^2)*erfi(2*sqrt(acosh(a*x))))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (2*c*sqrt(2*pi)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [(c - a^2*c*x^2)^(1/2)/acosh(a*x)^(5/2), x, 7, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x)*sqrt(c - a^2*c*x^2))/(3*a*acosh(a*x)^(3/2))) - (8*x*sqrt(c - a^2*c*x^2))/(3*sqrt(acosh(a*x))) + (2*sqrt(2*pi)*sqrt(c - a^2*c*x^2)*erf(sqrt(2)*sqrt(acosh(a*x))))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x)) + (2*sqrt(2*pi)*sqrt(c - a^2*c*x^2)*erfi(sqrt(2)*sqrt(acosh(a*x))))/(3*a*sqrt(-1 + a*x)*sqrt(1 + a*x))]
    @test_int [1/((c - a^2*c*x^2)^(1/2)*acosh(a*x)^(5/2)), x, 1, (-2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(3*a*sqrt(c - a^2*c*x^2)*acosh(a*x)^(3/2))]
    @test_int [1/((c - a^2*c*x^2)^(3/2)*acosh(a*x)^(5/2)), x, 2, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(3*a*(c - a^2*c*x^2)^(3/2)*acosh(a*x)^(3/2))) + (4*a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((-1 + a^2*x^2)^2*acosh(a*x)^(3/2)), x))/(3*c*sqrt(c - a^2*c*x^2))]
    @test_int [1/((c - a^2*c*x^2)^(5/2)*acosh(a*x)^(5/2)), x, 2, -((2*sqrt(-1 + a*x)*sqrt(1 + a*x))/(3*a*(c - a^2*c*x^2)^(5/2)*acosh(a*x)^(3/2))) - (8*a*sqrt(-1 + a*x)*sqrt(1 + a*x)*Unintegrable(x/((-1 + a^2*x^2)^3*acosh(a*x)^(3/2)), x))/(3*c^2*sqrt(c - a^2*c*x^2))]

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^n*when*n*symbolic=#

    #= ::Subsection:: =#
    #=Integrands*of*the*form*x^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^n*when*n*symbolic=#

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

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

    @test_int [x^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n, x, 6, -(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^(1 + n))/(8*b*c^3*(1 + n)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-4*(a + b*acosh(c*x)))/b))/(2^(2*(3 + n))*c^3*ℯ^((4*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (ℯ^((4*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (4*(a + b*acosh(c*x)))/b))/(2^(2*(3 + n))*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [x^1*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n, x, 9, (3^(-1 - n)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-3*(a + b*acosh(c*x)))/b))/(8*c^2*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(8*c^2*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (ℯ^(a/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(8*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (3^(-1 - n)*ℯ^((3*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(8*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [x^0*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n, x, 6, -(sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^(1 + n))/(2*b*c*(1 + n)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2^(-3 - n)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-2*(a + b*acosh(c*x)))/b))/(c*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (2^(-3 - n)*ℯ^((2*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n/x^1, x, 6, -((d*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(2*sqrt(d - c^2*d*x^2)))) + (d*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(2*sqrt(d - c^2*d*x^2))) + d*Unintegrable((a + b*acosh(c*x))^n/(x*sqrt(d - c^2*d*x^2)), x)]
    @test_int [sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n/x^2, x, 3, -((c*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(b*(1 + n)*sqrt(d - c^2*d*x^2))) + d*Unintegrable((a + b*acosh(c*x))^n/(x^2*sqrt(d - c^2*d*x^2)), x)]

    @test_int [x^2*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n, x, 12, -(d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^(1 + n))/(16*b*c^3*(1 + n)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2^(-7 - n)*3^(-1 - n)*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-6*(a + b*acosh(c*x)))/b))/(c^3*ℯ^((6*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (2^(-7 - 2*n)*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-4*(a + b*acosh(c*x)))/b))/(c^3*ℯ^((4*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (2^(-7 - n)*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-2*(a + b*acosh(c*x)))/b))/(c^3*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (2^(-7 - n)*d*ℯ^((2*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (2^(-7 - 2*n)*d*ℯ^((4*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (4*(a + b*acosh(c*x)))/b))/(c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) + (2^(-7 - n)*3^(-1 - n)*d*ℯ^((6*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (6*(a + b*acosh(c*x)))/b))/(c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [x^1*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n, x, 12, -(5^(-1 - n)*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-5*(a + b*acosh(c*x)))/b))/(32*c^2*ℯ^((5*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-3*(a + b*acosh(c*x)))/b))/(32*3^n*c^2*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(16*c^2*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (d*ℯ^(a/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(16*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (d*ℯ^((3*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(32*3^n*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) + (5^(-1 - n)*d*ℯ^((5*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (5*(a + b*acosh(c*x)))/b))/(32*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [x^0*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n, x, 9, (-3*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^(1 + n))/(8*b*c*(1 + n)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-4*(a + b*acosh(c*x)))/b))/(2^(2*(3 + n))*c*ℯ^((4*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (2^(-3 - n)*d*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-2*(a + b*acosh(c*x)))/b))/(c*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (2^(-3 - n)*d*ℯ^((2*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) + (d*ℯ^((4*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (4*(a + b*acosh(c*x)))/b))/(2^(2*(3 + n))*c*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n/x^1, x, 15, (3^(-1 - n)*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((3*(a + b*acosh(c*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*acosh(c*x))/b))^n*(8*sqrt(d - c^2*d*x^2))) - (5*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(8*sqrt(d - c^2*d*x^2))) + (5*d^2*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(8*sqrt(d - c^2*d*x^2))) - (3^(-1 - n)*d^2*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(8*sqrt(d - c^2*d*x^2))) + d^2*Unintegrable((a + b*acosh(c*x))^n/(x*sqrt(d - c^2*d*x^2)), x)]
    @test_int [(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n/x^2, x, 9, -((3*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(2*b*(1 + n)*sqrt(d - c^2*d*x^2))) + (2^(-3 - n)*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((2*(a + b*acosh(c*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*acosh(c*x))/b))^n*sqrt(d - c^2*d*x^2)) - (2^(-3 - n)*c*d^2*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*sqrt(d - c^2*d*x^2)) + d^2*Unintegrable((a + b*acosh(c*x))^n/(x^2*sqrt(d - c^2*d*x^2)), x)]

    @test_int [x^2*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^n, x, 15, (-5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^(1 + n))/(128*b*c^3*(1 + n)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2^(-11 - 3*n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-8*(a + b*acosh(c*x)))/b))/(c^3*ℯ^((8*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (2^(-7 - n)*3^(-1 - n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-6*(a + b*acosh(c*x)))/b))/(c^3*ℯ^((6*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-4*(a + b*acosh(c*x)))/b))/(2^(2*(4 + n))*c^3*ℯ^((4*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (2^(-7 - n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-2*(a + b*acosh(c*x)))/b))/(c^3*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (2^(-7 - n)*d^2*ℯ^((2*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (d^2*ℯ^((4*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (4*(a + b*acosh(c*x)))/b))/(2^(2*(4 + n))*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) + (2^(-7 - n)*3^(-1 - n)*d^2*ℯ^((6*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (6*(a + b*acosh(c*x)))/b))/(c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (2^(-11 - 3*n)*d^2*ℯ^((8*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (8*(a + b*acosh(c*x)))/b))/(c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [x^1*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^n, x, 15, (7^(-1 - n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-7*(a + b*acosh(c*x)))/b))/(128*c^2*ℯ^((7*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-5*(a + b*acosh(c*x)))/b))/(128*5^n*c^2*ℯ^((5*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (3^(1 - n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-3*(a + b*acosh(c*x)))/b))/(128*c^2*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(128*c^2*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (5*d^2*ℯ^(a/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(128*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (3^(1 - n)*d^2*ℯ^((3*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(128*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) + (d^2*ℯ^((5*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (5*(a + b*acosh(c*x)))/b))/(128*5^n*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (7^(-1 - n)*d^2*ℯ^((7*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (7*(a + b*acosh(c*x)))/b))/(128*c^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [x^0*(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^n, x, 12, (-5*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^(1 + n))/(16*b*c*(1 + n)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2^(-7 - n)*3^(-1 - n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-6*(a + b*acosh(c*x)))/b))/(c*ℯ^((6*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (3*2^(-7 - 2*n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-4*(a + b*acosh(c*x)))/b))/(c*ℯ^((4*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) + (15*2^(-7 - n)*d^2*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (-2*(a + b*acosh(c*x)))/b))/(c*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(-((a + b*acosh(c*x))/b))^n) - (15*2^(-7 - n)*d^2*ℯ^((2*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) + (3*2^(-7 - 2*n)*d^2*ℯ^((4*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (4*(a + b*acosh(c*x)))/b))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n) - (2^(-7 - n)*3^(-1 - n)*d^2*ℯ^((6*a)/b)*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n*Gamma(1 + n, (6*(a + b*acosh(c*x)))/b))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)*((a + b*acosh(c*x))/b)^n)]
    @test_int [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^n/x^1, x, 27, -((5^(-1 - n)*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((5*(a + b*acosh(c*x)))/b)))/(ℯ^((5*a)/b)*(-((a + b*acosh(c*x))/b))^n*(32*sqrt(d - c^2*d*x^2)))) - (5*3^(-1 - n)*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((3*(a + b*acosh(c*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*acosh(c*x))/b))^n*(32*sqrt(d - c^2*d*x^2))) + (d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((3*(a + b*acosh(c*x)))/b)))/(3^n*ℯ^((3*a)/b)*(-((a + b*acosh(c*x))/b))^n*(8*sqrt(d - c^2*d*x^2))) - (11*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(16*sqrt(d - c^2*d*x^2))) + (11*d^3*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(16*sqrt(d - c^2*d*x^2))) + (5*3^(-1 - n)*d^3*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(32*sqrt(d - c^2*d*x^2))) - (d^3*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(3^n*((a + b*acosh(c*x))/b)^n*(8*sqrt(d - c^2*d*x^2))) + (5^(-1 - n)*d^3*ℯ^((5*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (5*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(32*sqrt(d - c^2*d*x^2))) + d^3*Unintegrable((a + b*acosh(c*x))^n/(x*sqrt(d - c^2*d*x^2)), x)]
    @test_int [(d - c^2*d*x^2)^(5/2)*(a + b*acosh(c*x))^n/x^2, x, 18, -((15*c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(8*b*(1 + n)*sqrt(d - c^2*d*x^2))) - (c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((4*(a + b*acosh(c*x)))/b)))/(2^(2*(3 + n))*ℯ^((4*a)/b)*(-((a + b*acosh(c*x))/b))^n*sqrt(d - c^2*d*x^2)) + (2^(-2 - n)*c*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((2*(a + b*acosh(c*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*acosh(c*x))/b))^n*sqrt(d - c^2*d*x^2)) - (2^(-2 - n)*c*d^3*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*sqrt(d - c^2*d*x^2)) + (c*d^3*ℯ^((4*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (4*(a + b*acosh(c*x)))/b))/(2^(2*(3 + n))*((a + b*acosh(c*x))/b)^n*sqrt(d - c^2*d*x^2)) + d^3*Unintegrable((a + b*acosh(c*x))^n/(x^2*sqrt(d - c^2*d*x^2)), x)]

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

    @test_int [x^3*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x, 9, (3^(-1 - n)*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((3*(a + b*acosh(c*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*acosh(c*x))/b))^n*(8*c^4*sqrt(1 - c*x))) + (3*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(8*c^4*sqrt(1 - c*x))) - (3*ℯ^(a/b)*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(8*c^4*sqrt(1 - c*x))) - (3^(-1 - n)*ℯ^((3*a)/b)*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(8*c^4*sqrt(1 - c*x)))]
    @test_int [x^2*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x, 6, (sqrt(-1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(2*b*c^3*(1 + n)*sqrt(1 - c*x)) + (2^(-3 - n)*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((2*(a + b*acosh(c*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*acosh(c*x))/b))^n*(c^3*sqrt(1 - c*x))) - (2^(-3 - n)*ℯ^((2*a)/b)*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(c^3*sqrt(1 - c*x)))]
    @test_int [x^1*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x, 4, (sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(2*c^2*sqrt(1 - c*x))) - (ℯ^(a/b)*sqrt(-1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(2*c^2*sqrt(1 - c*x)))]
    @test_int [x^0*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x, 1, (sqrt(-1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(b*c*(1 + n)*sqrt(1 - c*x))]
    @test_int [(a + b*acosh(c*x))^n/(x^1*sqrt(1 - c^2*x^2)), x, 0, Unintegrable((a + b*acosh(c*x))^n/(x*sqrt(1 - c^2*x^2)), x)]
    @test_int [(a + b*acosh(c*x))^n/(x^2*sqrt(1 - c^2*x^2)), x, 0, Unintegrable((a + b*acosh(c*x))^n/(x^2*sqrt(1 - c^2*x^2)), x)]

    @test_int [x^3*(a + b*acosh(c*x))^n/sqrt(d - c^2*d*x^2), x, 9, (3^(-1 - n)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((3*(a + b*acosh(c*x)))/b)))/(ℯ^((3*a)/b)*(-((a + b*acosh(c*x))/b))^n*(8*c^4*sqrt(d - c^2*d*x^2))) + (3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(8*c^4*sqrt(d - c^2*d*x^2))) - (3*ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(8*c^4*sqrt(d - c^2*d*x^2))) - (3^(-1 - n)*ℯ^((3*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (3*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(8*c^4*sqrt(d - c^2*d*x^2)))]
    @test_int [x^2*(a + b*acosh(c*x))^n/sqrt(d - c^2*d*x^2), x, 6, (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(2*b*c^3*(1 + n)*sqrt(d - c^2*d*x^2)) + (2^(-3 - n)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((2*(a + b*acosh(c*x)))/b)))/(ℯ^((2*a)/b)*(-((a + b*acosh(c*x))/b))^n*(c^3*sqrt(d - c^2*d*x^2))) - (2^(-3 - n)*ℯ^((2*a)/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (2*(a + b*acosh(c*x)))/b))/(((a + b*acosh(c*x))/b)^n*(c^3*sqrt(d - c^2*d*x^2)))]
    @test_int [x^1*(a + b*acosh(c*x))^n/sqrt(d - c^2*d*x^2), x, 4, (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, -((a + b*acosh(c*x))/b)))/(ℯ^(a/b)*(-((a + b*acosh(c*x))/b))^n*(2*c^2*sqrt(d - c^2*d*x^2))) - (ℯ^(a/b)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^n*Gamma(1 + n, (a + b*acosh(c*x))/b))/(((a + b*acosh(c*x))/b)^n*(2*c^2*sqrt(d - c^2*d*x^2)))]
    @test_int [x^0*(a + b*acosh(c*x))^n/sqrt(d - c^2*d*x^2), x, 1, (sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x))^(1 + n))/(b*c*(1 + n)*sqrt(d - c^2*d*x^2))]
    @test_int [(a + b*acosh(c*x))^n/(x^1*sqrt(d - c^2*d*x^2)), x, 0, Unintegrable((a + b*acosh(c*x))^n/(x*sqrt(d - c^2*d*x^2)), x)]
    @test_int [(a + b*acosh(c*x))^n/(x^2*sqrt(d - c^2*d*x^2)), x, 0, Unintegrable((a + b*acosh(c*x))^n/(x^2*sqrt(d - c^2*d*x^2)), x)]

    @test_int [x^2*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^(3/2), x, 0, Unintegrable((x^2*(a + b*acosh(c*x))^n)/(d - c^2*d*x^2)^(3/2), x)]
    @test_int [x^1*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^(3/2), x, 0, Unintegrable((x*(a + b*acosh(c*x))^n)/(d - c^2*d*x^2)^(3/2), x)]
    @test_int [x^0*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^(3/2), x, 0, Unintegrable((a + b*acosh(c*x))^n/(d - c^2*d*x^2)^(3/2), x)]
    @test_int [(a + b*acosh(c*x))^n/(x^1*(d - c^2*d*x^2)^(3/2)), x, 0, Unintegrable((a + b*acosh(c*x))^n/(x*(d - c^2*d*x^2)^(3/2)), x)]
    @test_int [(a + b*acosh(c*x))^n/(x^2*(d - c^2*d*x^2)^(3/2)), x, 0, Unintegrable((a + b*acosh(c*x))^n/(x^2*(d - c^2*d*x^2)^(3/2)), x)]

    #= ::Subsection::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d-c^2*d*x^2)^p*(a+b*acosh(c*x))^n*when*m*and*n*symbolic=#

    @test_int [(f*x)^m*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x, 0, Unintegrable((f*x)^m*(a + b*acosh(c*x))^n/sqrt(1 - c^2*x^2), x)]

    @test_int [(f*x)^m*(d - c^2*d*x^2)^2*(a + b*acosh(c*x))^n, x, 0, Unintegrable((f*x)^m*(d - c^2*d*x^2)^2*(a + b*acosh(c*x))^n, x)]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^1*(a + b*acosh(c*x))^n, x, 0, Unintegrable((f*x)^m*(d - c^2*d*x^2)*(a + b*acosh(c*x))^n, x)]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^0*(a + b*acosh(c*x))^n, x, 0, Unintegrable((f*x)^m*(a + b*acosh(c*x))^n, x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^1, x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^n)/(d - c^2*d*x^2), x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^2, x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^n)/(d - c^2*d*x^2)^2, x)]

    @test_int [(f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n, x, 0, Unintegrable((f*x)^m*(d - c^2*d*x^2)^(3/2)*(a + b*acosh(c*x))^n, x)]
    @test_int [(f*x)^m*(d - c^2*d*x^2)^(1/2)*(a + b*acosh(c*x))^n, x, 0, Unintegrable((f*x)^m*sqrt(d - c^2*d*x^2)*(a + b*acosh(c*x))^n, x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^(1/2), x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^n)/sqrt(d - c^2*d*x^2), x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))^n/(d - c^2*d*x^2)^(3/2), x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x))^n)/(d - c^2*d*x^2)^(3/2), x)]

    #= ::Title:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x^2)^p*(a+b*acosh(c*x))^n=#

    #= ::Section::Closed:: =#
    #=Integrands*of*the*form*(f*x)^m*(d+e*x^2)^p*(a+b*acosh(c*x))^1=#

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

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

    @test_int [x^4*(d + e*x^2)*(a + b*acosh(c*x)), x, 7, -((8*b*(49*c^2*d + 30*e)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3675*c^7)) - (4*b*(49*c^2*d + 30*e)*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3675*c^5) - (b*(49*c^2*d + 30*e)*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))/(1225*c^3) - (b*e*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x))/(49*c) + (1/5)*d*x^5*(a + b*acosh(c*x)) + (1/7)*e*x^7*(a + b*acosh(c*x))]
    @test_int [x^3*(d + e*x^2)*(a + b*acosh(c*x)), x, 6, -((b*(9*c^2*d + 5*e)*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(96*c^5)) - (b*(9*c^2*d + 5*e)*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(144*c^3) - (b*e*x^5*sqrt(-1 + c*x)*sqrt(1 + c*x))/(36*c) - (b*(9*c^2*d + 5*e)*acosh(c*x))/(96*c^6) + (1/4)*d*x^4*(a + b*acosh(c*x)) + (1/6)*e*x^6*(a + b*acosh(c*x))]
    @test_int [x^2*(d + e*x^2)*(a + b*acosh(c*x)), x, 5, -((2*b*(25*c^2*d + 12*e)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(225*c^5)) - (b*(25*c^2*d + 12*e)*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(225*c^3) - (b*e*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))/(25*c) + (1/3)*d*x^3*(a + b*acosh(c*x)) + (1/5)*e*x^5*(a + b*acosh(c*x))]
    @test_int [x^1*(d + e*x^2)*(a + b*acosh(c*x)), x, 4, -((b*(8*c^2*d + 3*e)*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(32*c^3)) - (b*e*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*c) - (b*(8*c^2*d + 3*e)*acosh(c*x))/(32*c^4) + (1/2)*d*x^2*(a + b*acosh(c*x)) + (1/4)*e*x^4*(a + b*acosh(c*x))]
    @test_int [x^0*(d + e*x^2)*(a + b*acosh(c*x)), x, 3, -((b*(9*c^2*d + 2*e)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c^3)) - (b*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c) + d*x*(a + b*acosh(c*x)) + (1/3)*e*x^3*(a + b*acosh(c*x))]
    @test_int [((d + e*x^2)*(a + b*acosh(c*x)))/x^1, x, 13, -((b*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c)) - (b*e*acosh(c*x))/(4*c^2) + (1/2)*e*x^2*(a + b*acosh(c*x)) - (im*b*d*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + d*(a + b*acosh(c*x))*log(x) - (b*d*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)*(a + b*acosh(c*x)))/x^2, x, 4, -((b*e*sqrt(-1 + c*x)*sqrt(1 + c*x))/c) - (d*(a + b*acosh(c*x)))/x + e*x*(a + b*acosh(c*x)) + b*c*d*atan(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)*(a + b*acosh(c*x)))/x^3, x, 11, (b*c*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*x) - (d*(a + b*acosh(c*x)))/(2*x^2) - (im*b*e*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + e*(a + b*acosh(c*x))*log(x) - (b*e*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*e*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)*(a + b*acosh(c*x)))/x^4, x, 4, (b*c*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*x^2) - (d*(a + b*acosh(c*x)))/(3*x^3) - (e*(a + b*acosh(c*x)))/x + (1/6)*b*c*(c^2*d + 6*e)*atan(sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^4*(d + e*x^2)^2*(a + b*acosh(c*x)), x, 7, (b*(63*c^4*d^2 + 90*c^2*d*e + 35*e^2)*(1 - c^2*x^2))/(315*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*(63*c^4*d^2 + 135*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^2)/(945*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*(21*c^4*d^2 + 90*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^3)/(525*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*e*(9*c^2*d + 14*e)*(1 - c^2*x^2)^4)/(441*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*(1 - c^2*x^2)^5)/(81*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^2*x^5*(a + b*acosh(c*x)))/5 + (2*d*e*x^7*(a + b*acosh(c*x)))/7 + (e^2*x^9*(a + b*acosh(c*x)))/9]
    @test_int [x^3*(d + e*x^2)^2*(a + b*acosh(c*x)), x, 9, (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*x*(1 - c^2*x^2))/(3072*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*x^3*(1 - c^2*x^2))/(4608*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e*(64*c^2*d + 21*e)*x^5*(1 - c^2*x^2))/(1152*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*x^7*(1 - c^2*x^2))/(64*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/4)*d^2*x^4*(a + b*acosh(c*x)) + (1/3)*d*e*x^6*(a + b*acosh(c*x)) + (1/8)*e^2*x^8*(a + b*acosh(c*x)) - (b*(288*c^4*d^2 + 320*c^2*d*e + 105*e^2)*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(3072*c^8*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*(d + e*x^2)^2*(a + b*acosh(c*x)), x, 6, (b*(35*c^4*d^2 + 42*c^2*d*e + 15*e^2)*(1 - c^2*x^2))/(105*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*(35*c^4*d^2 + 84*c^2*d*e + 45*e^2)*(1 - c^2*x^2)^2)/(315*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e*(14*c^2*d + 15*e)*(1 - c^2*x^2)^3)/(175*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^2*(1 - c^2*x^2)^4)/(49*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^2*x^3*(a + b*acosh(c*x)))/3 + (2*d*e*x^5*(a + b*acosh(c*x)))/5 + (e^2*x^7*(a + b*acosh(c*x)))/7]
    @test_int [x^1*(d + e*x^2)^2*(a + b*acosh(c*x)), x, 7, (b*(44*c^4*d^2 + 44*c^2*d*e + 15*e^2)*x*(1 - c^2*x^2))/(288*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (5*b*(2*c^2*d + e)*x*(1 - c^2*x^2)*(d + e*x^2))/(144*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x*(1 - c^2*x^2)*(d + e*x^2)^2)/(36*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((d + e*x^2)^3*(a + b*acosh(c*x)))/(6*e) - (b*(2*c^2*d + e)*(8*c^4*d^2 + 8*c^2*d*e + 5*e^2)*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(96*c^6*e*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^0*(d + e*x^2)^2*(a + b*acosh(c*x)), x, 6, (b*(15*c^4*d^2 + 10*c^2*d*e + 3*e^2)*(1 - c^2*x^2))/(15*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*b*e*(5*c^2*d + 3*e)*(1 - c^2*x^2)^2)/(45*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*(1 - c^2*x^2)^3)/(25*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^2*x*(a + b*acosh(c*x)) + (2*d*e*x^3*(a + b*acosh(c*x)))/3 + (e^2*x^5*(a + b*acosh(c*x)))/5]
    @test_int [((d + e*x^2)^2*(a + b*acosh(c*x)))/x^1, x, 16, -((b*e*(16*c^2*d + 3*e)*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(32*c^3)) - (b*e^2*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*c) - (b*e*(16*c^2*d + 3*e)*acosh(c*x))/(32*c^4) + d*e*x^2*(a + b*acosh(c*x)) + (1/4)*e^2*x^4*(a + b*acosh(c*x)) - (im*b*d^2*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^2*(a + b*acosh(c*x))*log(x) - (b*d^2*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d^2*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*d*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*c)) - (3*b*e^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(32*c^3) - (b*e^2*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*c) - (b*d*e*acosh(c*x))/(2*c^2) - (3*b*e^2*acosh(c*x))/(32*c^4) + d*e*x^2*(a + b*acosh(c*x)) + (1/4)*e^2*x^4*(a + b*acosh(c*x)) - (im*b*d^2*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^2*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^2*(a + b*acosh(c*x))*log(x) - (b*d^2*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d^2*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)^2*(a + b*acosh(c*x)))/x^2, x, 7, (b*e*(6*c^2*d + e)*(1 - c^2*x^2))/(3*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^2*(1 - c^2*x^2)^2)/(9*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^2*(a + b*acosh(c*x)))/x + 2*d*e*x*(a + b*acosh(c*x)) + (1/3)*e^2*x^3*(a + b*acosh(c*x)) + b*c*d^2*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)), (b*e*(6*c^2*d + e)*(1 - c^2*x^2))/(3*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^2*(1 - c^2*x^2)^2)/(9*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^2*(a + b*acosh(c*x)))/x + 2*d*e*x*(a + b*acosh(c*x)) + (1/3)*e^2*x^3*(a + b*acosh(c*x)) + (b*c*d^2*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)^2*(a + b*acosh(c*x)))/x^3, x, 14, (b*c*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*x) - (b*e^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c) - (b*e^2*acosh(c*x))/(4*c^2) - (d^2*(a + b*acosh(c*x)))/(2*x^2) + (1/2)*e^2*x^2*(a + b*acosh(c*x)) - (im*b*d*e*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*d*e*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + 2*d*e*(a + b*acosh(c*x))*log(x) - (2*b*d*e*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d*e*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)^2*(a + b*acosh(c*x)))/x^4, x, 7, (b*e^2*(1 - c^2*x^2))/(c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^2*(1 - c^2*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^2*(a + b*acosh(c*x)))/(3*x^3) - (2*d*e*(a + b*acosh(c*x)))/x + e^2*x*(a + b*acosh(c*x)) + (b*c*d*(c^2*d + 12*e)*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(6*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [x^4*(d + e*x^2)^3*(a + b*acosh(c*x)), x, 6, (b*(231*c^6*d^3 + 495*c^4*d^2*e + 385*c^2*d*e^2 + 105*e^3)*(1 - c^2*x^2))/(1155*c^11*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*(462*c^6*d^3 + 1485*c^4*d^2*e + 1540*c^2*d*e^2 + 525*e^3)*(1 - c^2*x^2)^2)/(3465*c^11*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*(77*c^6*d^3 + 495*c^4*d^2*e + 770*c^2*d*e^2 + 350*e^3)*(1 - c^2*x^2)^3)/(1925*c^11*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e*(99*c^4*d^2 + 308*c^2*d*e + 210*e^2)*(1 - c^2*x^2)^4)/(1617*c^11*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*(11*c^2*d + 15*e)*(1 - c^2*x^2)^5)/(297*c^11*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^3*(1 - c^2*x^2)^6)/(121*c^11*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^3*x^5*(a + b*acosh(c*x)))/5 + (3*d^2*e*x^7*(a + b*acosh(c*x)))/7 + (d*e^2*x^9*(a + b*acosh(c*x)))/3 + (e^3*x^11*(a + b*acosh(c*x)))/11]
    @test_int [x^3*(d + e*x^2)^3*(a + b*acosh(c*x)), x, 10, -((b*(1232*c^8*d^4 - 2536*c^6*d^3*e - 7758*c^4*d^2*e^2 - 6615*c^2*d*e^3 - 1890*e^4)*x*(1 - c^2*x^2))/(76800*c^9*e*sqrt(-1 + c*x)*sqrt(1 + c*x))) - (b*(136*c^6*d^3 - 1096*c^4*d^2*e - 1617*c^2*d*e^2 - 630*e^3)*x*(1 - c^2*x^2)*(d + e*x^2))/(38400*c^7*e*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*(26*c^4*d^2 + 201*c^2*d*e + 126*e^2)*x*(1 - c^2*x^2)*(d + e*x^2)^2)/(9600*c^5*e*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*(11*c^2*d + 18*e)*x*(1 - c^2*x^2)*(d + e*x^2)^3)/(1600*c^3*e*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x*(1 - c^2*x^2)*(d + e*x^2)^4)/(100*c*e*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d*(d + e*x^2)^4*(a + b*acosh(c*x)))/(8*e^2) + ((d + e*x^2)^5*(a + b*acosh(c*x)))/(10*e^2) + (b*(128*c^10*d^5 - 480*c^6*d^3*e^2 - 800*c^4*d^2*e^3 - 525*c^2*d*e^4 - 126*e^5)*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(5120*c^10*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^2*(d + e*x^2)^3*(a + b*acosh(c*x)), x, 6, (b*(105*c^6*d^3 + 189*c^4*d^2*e + 135*c^2*d*e^2 + 35*e^3)*(1 - c^2*x^2))/(315*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*(105*c^6*d^3 + 378*c^4*d^2*e + 405*c^2*d*e^2 + 140*e^3)*(1 - c^2*x^2)^2)/(945*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e*(63*c^4*d^2 + 135*c^2*d*e + 70*e^2)*(1 - c^2*x^2)^3)/(525*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^2*(27*c^2*d + 28*e)*(1 - c^2*x^2)^4)/(441*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^3*(1 - c^2*x^2)^5)/(81*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (1/3)*d^3*x^3*(a + b*acosh(c*x)) + (3/5)*d^2*e*x^5*(a + b*acosh(c*x)) + (3/7)*d*e^2*x^7*(a + b*acosh(c*x)) + (1/9)*e^3*x^9*(a + b*acosh(c*x))]
    @test_int [x^1*(d + e*x^2)^3*(a + b*acosh(c*x)), x, 8, (5*b*(2*c^2*d + e)*(40*c^4*d^2 + 40*c^2*d*e + 21*e^2)*x*(1 - c^2*x^2))/(3072*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*(104*c^4*d^2 + 104*c^2*d*e + 35*e^2)*x*(1 - c^2*x^2)*(d + e*x^2))/(1536*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (7*b*(2*c^2*d + e)*x*(1 - c^2*x^2)*(d + e*x^2)^2)/(384*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*x*(1 - c^2*x^2)*(d + e*x^2)^3)/(64*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((d + e*x^2)^4*(a + b*acosh(c*x)))/(8*e) - (b*(128*c^8*d^4 + 256*c^6*d^3*e + 288*c^4*d^2*e^2 + 160*c^2*d*e^3 + 35*e^4)*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(1024*c^8*e*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [x^0*(d + e*x^2)^3*(a + b*acosh(c*x)), x, 6, (b*(35*c^6*d^3 + 35*c^4*d^2*e + 21*c^2*d*e^2 + 5*e^3)*(1 - c^2*x^2))/(35*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e*(35*c^4*d^2 + 42*c^2*d*e + 15*e^2)*(1 - c^2*x^2)^2)/(105*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*e^2*(7*c^2*d + 5*e)*(1 - c^2*x^2)^3)/(175*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^3*(1 - c^2*x^2)^4)/(49*c^7*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^3*x*(a + b*acosh(c*x)) + d^2*e*x^3*(a + b*acosh(c*x)) + (3*d*e^2*x^5*(a + b*acosh(c*x)))/5 + (e^3*x^7*(a + b*acosh(c*x)))/7]
    @test_int [((d + e*x^2)^3*(a + b*acosh(c*x)))/x^1, x, 23, -((3*b*d^2*e*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c)) - (9*b*d*e^2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(32*c^3) - (5*b*e^3*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(96*c^5) - (3*b*d*e^2*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*c) - (5*b*e^3*x^3*sqrt(-1 + c*x)*sqrt(1 + c*x))/(144*c^3) - (b*e^3*x^5*sqrt(-1 + c*x)*sqrt(1 + c*x))/(36*c) - (3*b*d^2*e*acosh(c*x))/(4*c^2) - (9*b*d*e^2*acosh(c*x))/(32*c^4) - (5*b*e^3*acosh(c*x))/(96*c^6) + (3/2)*d^2*e*x^2*(a + b*acosh(c*x)) + (3/4)*d*e^2*x^4*(a + b*acosh(c*x)) + (1/6)*e^3*x^6*(a + b*acosh(c*x)) - (im*b*d^3*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*d^3*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^3*(a + b*acosh(c*x))*log(x) - (b*d^3*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (im*b*d^3*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)^3*(a + b*acosh(c*x)))/x^2, x, 7, (b*e*(15*c^4*d^2 + 5*c^2*d*e + e^2)*(1 - c^2*x^2))/(5*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^2*(5*c^2*d + 2*e)*(1 - c^2*x^2)^2)/(15*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^3*(1 - c^2*x^2)^3)/(25*c^5*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^3*(a + b*acosh(c*x)))/x + 3*d^2*e*x*(a + b*acosh(c*x)) + d*e^2*x^3*(a + b*acosh(c*x)) + (1/5)*e^3*x^5*(a + b*acosh(c*x)) + (b*c*d^3*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)^3*(a + b*acosh(c*x)))/x^3, x, 18, -((b*c*d^3*(1 - c^2*x^2))/(2*x*sqrt(-1 + c*x)*sqrt(1 + c*x))) + (3*b*e^2*(8*c^2*d + e)*x*(1 - c^2*x^2))/(32*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^3*x^3*(1 - c^2*x^2))/(16*c*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^3*(a + b*acosh(c*x)))/(2*x^2) + (3/2)*d*e^2*x^2*(a + b*acosh(c*x)) + (1/4)*e^3*x^4*(a + b*acosh(c*x)) - (3*im*b*d^2*e*sqrt(1 - c^2*x^2)*asin(c*x)^2)/(2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*b*e^2*(8*c^2*d + e)*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(32*c^4*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (3*b*d^2*e*sqrt(1 - c^2*x^2)*asin(c*x)*log(1 - ℯ^(2*im*asin(c*x))))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) + 3*d^2*e*(a + b*acosh(c*x))*log(x) - (3*b*d^2*e*sqrt(1 - c^2*x^2)*asin(c*x)*log(x))/(sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*im*b*d^2*e*sqrt(1 - c^2*x^2)*PolyLog(2, ℯ^(2*im*asin(c*x))))/(2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [((d + e*x^2)^3*(a + b*acosh(c*x)))/x^4, x, 9, (b*e^2*(9*c^2*d + e)*(1 - c^2*x^2))/(3*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*d^3*(1 - c^2*x^2))/(6*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*e^3*(1 - c^2*x^2)^2)/(9*c^3*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (d^3*(a + b*acosh(c*x)))/(3*x^3) - (3*d^2*e*(a + b*acosh(c*x)))/x + 3*d*e^2*x*(a + b*acosh(c*x)) + (1/3)*e^3*x^3*(a + b*acosh(c*x)) + (b*c*d^2*(c^2*d + 18*e)*sqrt(-1 + c^2*x^2)*atan(sqrt(-1 + c^2*x^2)))/(6*sqrt(-1 + c*x)*sqrt(1 + c*x))]

    @test_int [(d + e*x^2)^4*(a + b*acosh(c*x)), x, 6, (b*(315*c^8*d^4 + 420*c^6*d^3*e + 378*c^4*d^2*e^2 + 180*c^2*d*e^3 + 35*e^4)*(1 - c^2*x^2))/(315*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*e*(105*c^6*d^3 + 189*c^4*d^2*e + 135*c^2*d*e^2 + 35*e^3)*(1 - c^2*x^2)^2)/(945*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (2*b*e^2*(63*c^4*d^2 + 90*c^2*d*e + 35*e^2)*(1 - c^2*x^2)^3)/(525*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (4*b*e^3*(9*c^2*d + 7*e)*(1 - c^2*x^2)^4)/(441*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^4*(1 - c^2*x^2)^5)/(81*c^9*sqrt(-1 + c*x)*sqrt(1 + c*x)) + d^4*x*(a + b*acosh(c*x)) + (4*d^3*e*x^3*(a + b*acosh(c*x)))/3 + (6*d^2*e^2*x^5*(a + b*acosh(c*x)))/5 + (4*d*e^3*x^7*(a + b*acosh(c*x)))/7 + (e^4*x^9*(a + b*acosh(c*x)))/9]

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

    @test_int [(x^4*(a + b*acosh(c*x)))/(d + e*x^2), x, 27, -((a*d*x)/e^2) + (b*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*e^2) - (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c^3*e) - (b*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(9*c*e) - (b*d*x*acosh(c*x))/e^2 + (x^3*(a + b*acosh(c*x)))/(3*e) + ((-d)^(3/2)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^(5/2)) - ((-d)^(3/2)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^(5/2)) + ((-d)^(3/2)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^(5/2)) - ((-d)^(3/2)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^(5/2)) - (b*(-d)^(3/2)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*e^(5/2)) + (b*(-d)^(3/2)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^(5/2)) - (b*(-d)^(3/2)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*e^(5/2)) + (b*(-d)^(3/2)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^(5/2))]
    @test_int [(x^3*(a + b*acosh(c*x)))/(d + e*x^2), x, 23, -((b*x*sqrt(-1 + c*x)*sqrt(1 + c*x))/(4*c*e)) - (b*acosh(c*x))/(4*c^2*e) + (x^2*(a + b*acosh(c*x)))/(2*e) + (d*(a + b*acosh(c*x))^2)/(2*b*e^2) - (d*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^2) - (d*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^2) - (d*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^2) - (d*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^2) - (b*d*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*e^2) - (b*d*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^2) - (b*d*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*e^2) - (b*d*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^2)]
    @test_int [(x^2*(a + b*acosh(c*x)))/(d + e*x^2), x, 23, (a*x)/e - (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*e) + (b*x*acosh(c*x))/e + (sqrt(-d)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^(3/2)) - (sqrt(-d)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^(3/2)) + (sqrt(-d)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^(3/2)) - (sqrt(-d)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^(3/2)) - (b*sqrt(-d)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*e^(3/2)) + (b*sqrt(-d)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^(3/2)) - (b*sqrt(-d)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*e^(3/2)) + (b*sqrt(-d)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^(3/2))]
    @test_int [(x*(a + b*acosh(c*x)))/(d + e*x^2), x, 18, -((a + b*acosh(c*x))^2/(2*b*e)) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*e) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*e) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e)]
    @test_int [(a + b*acosh(c*x))/(d + e*x^2), x, 18, ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*sqrt(-d)*sqrt(e)) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*sqrt(-d)*sqrt(e)) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e))]
    @test_int [(a + b*acosh(c*x))/(x*(d + e*x^2)), x, 25, (a + b*acosh(c*x))^2/(b*d) + ((a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/d - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d) - (b*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(2*d) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*d) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*d) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d)]
    @test_int [(a + b*acosh(c*x))/(x^2*(d + e*x^2)), x, 23, -((a + b*acosh(c*x))/(d*x)) + (b*c*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/d + (sqrt(e)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*(-d)^(3/2)) - (sqrt(e)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*(-d)^(3/2)) + (sqrt(e)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*(-d)^(3/2)) - (sqrt(e)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*(-d)^(3/2)) - (b*sqrt(e)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*(-d)^(3/2)) + (b*sqrt(e)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*(-d)^(3/2)) - (b*sqrt(e)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*(-d)^(3/2)) + (b*sqrt(e)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*(-d)^(3/2))]
    @test_int [(a + b*acosh(c*x))/(x^3*(d + e*x^2)), x, 27, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*d*x) - (a + b*acosh(c*x))/(2*d*x^2) - (e*(a + b*acosh(c*x))^2)/(b*d^2) - (e*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/d^2 + (e*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^2) + (e*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^2) + (e*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^2) + (e*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^2) + (b*e*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(2*d^2) + (b*e*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*d^2) + (b*e*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^2) + (b*e*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*d^2) + (b*e*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^2)]
    @test_int [(a + b*acosh(c*x))/(x^4*(d + e*x^2)), x, 28, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(6*d*x^2) - (a + b*acosh(c*x))/(3*d*x^3) + (e*(a + b*acosh(c*x)))/(d^2*x) + (b*c^3*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/(6*d) - (b*c*e*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/d^2 + (e^(3/2)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*(-d)^(5/2)) - (e^(3/2)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*(-d)^(5/2)) + (e^(3/2)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*(-d)^(5/2)) - (e^(3/2)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*(-d)^(5/2)) - (b*e^(3/2)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*(-d)^(5/2)) + (b*e^(3/2)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*(-d)^(5/2)) - (b*e^(3/2)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*(-d)^(5/2)) + (b*e^(3/2)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*(-d)^(5/2))]

    @test_int [(x^3*(a + b*acosh(c*x)))/(d + e*x^2)^2, x, 24, (d*(a + b*acosh(c*x)))/(2*e^2*(d + e*x^2)) - (a + b*acosh(c*x))^2/(2*b*e^2) - (b*c*sqrt(d)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(2*e^2*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^2) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^2) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^2) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^2) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*e^2) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^2) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*e^2) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^2)]
    @test_int [(x^1*(a + b*acosh(c*x)))/(d + e*x^2)^2, x, 4, -((a + b*acosh(c*x))/(2*e*(d + e*x^2))) + (b*c*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(2*sqrt(d)*e*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(a + b*acosh(c*x))/(x^1*(d + e*x^2)^2), x, 29, (a + b*acosh(c*x))/(2*d*(d + e*x^2)) + (a + b*acosh(c*x))^2/(b*d^2) - (b*c*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(2*d^(3/2)*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/d^2 - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^2) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^2) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^2) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^2) - (b*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(2*d^2) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*d^2) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^2) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*d^2) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^2)]
    @test_int [(a + b*acosh(c*x))/(x^3*(d + e*x^2)^2), x, 31, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*d^2*x) - (a + b*acosh(c*x))/(2*d^2*x^2) - (e*(a + b*acosh(c*x)))/(2*d^2*(d + e*x^2)) - (2*e*(a + b*acosh(c*x))^2)/(b*d^3) + (b*c*e*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(2*d^(5/2)*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (2*e*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/d^3 + (e*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/d^3 + (e*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/d^3 + (e*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/d^3 + (e*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/d^3 + (b*e*PolyLog(2, -ℯ^(-2*acosh(c*x))))/d^3 + (b*e*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/d^3 + (b*e*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/d^3 + (b*e*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/d^3 + (b*e*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/d^3]

    @test_int [(x^4*(a + b*acosh(c*x)))/(d + e*x^2)^2, x, 49, (a*x)/e^2 - (b*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*e^2) + (b*x*acosh(c*x))/e^2 - (d*(a + b*acosh(c*x)))/(4*e^(5/2)*(sqrt(-d) - sqrt(e)*x)) + (d*(a + b*acosh(c*x)))/(4*e^(5/2)*(sqrt(-d) + sqrt(e)*x)) + (b*c*d*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(5/2)) - (b*c*d*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(5/2)) + (3*sqrt(-d)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*e^(5/2)) - (3*sqrt(-d)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*e^(5/2)) + (3*sqrt(-d)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*e^(5/2)) - (3*sqrt(-d)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*e^(5/2)) - (3*b*sqrt(-d)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(4*e^(5/2)) + (3*b*sqrt(-d)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*e^(5/2)) - (3*b*sqrt(-d)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(4*e^(5/2)) + (3*b*sqrt(-d)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*e^(5/2))]
    @test_int [(x^2*(a + b*acosh(c*x)))/(d + e*x^2)^2, x, 46, (a + b*acosh(c*x))/(4*e^(3/2)*(sqrt(-d) - sqrt(e)*x)) - (a + b*acosh(c*x))/(4*e^(3/2)*(sqrt(-d) + sqrt(e)*x)) - (b*c*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(3/2)) + (b*c*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(3/2)) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*sqrt(-d)*e^(3/2)) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*sqrt(-d)*e^(3/2)) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*sqrt(-d)*e^(3/2)) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*sqrt(-d)*e^(3/2)) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(4*sqrt(-d)*e^(3/2)) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*sqrt(-d)*e^(3/2)) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(4*sqrt(-d)*e^(3/2)) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*sqrt(-d)*e^(3/2))]
    @test_int [(a + b*acosh(c*x))/(d + e*x^2)^2, x, 26, -((a + b*acosh(c*x))/(4*d*sqrt(e)*(sqrt(-d) - sqrt(e)*x))) + (a + b*acosh(c*x))/(4*d*sqrt(e)*(sqrt(-d) + sqrt(e)*x)) + (b*c*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(2*d*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*sqrt(e)) - (b*c*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(2*d*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*sqrt(e)) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*(-d)^(3/2)*sqrt(e)) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*(-d)^(3/2)*sqrt(e)) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*(-d)^(3/2)*sqrt(e)) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*(-d)^(3/2)*sqrt(e)) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(4*(-d)^(3/2)*sqrt(e)) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*(-d)^(3/2)*sqrt(e)) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(4*(-d)^(3/2)*sqrt(e)) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*(-d)^(3/2)*sqrt(e))]
    @test_int [(a + b*acosh(c*x))/(x^2*(d + e*x^2)^2), x, 49, -((a + b*acosh(c*x))/(d^2*x)) + (sqrt(e)*(a + b*acosh(c*x)))/(4*d^2*(sqrt(-d) - sqrt(e)*x)) - (sqrt(e)*(a + b*acosh(c*x)))/(4*d^2*(sqrt(-d) + sqrt(e)*x)) + (b*c*atan(sqrt(-1 + c*x)*sqrt(1 + c*x)))/d^2 - (b*c*sqrt(e)*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(2*d^2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))) + (b*c*sqrt(e)*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(2*d^2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))) - (3*sqrt(e)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*(-d)^(5/2)) + (3*sqrt(e)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*(-d)^(5/2)) - (3*sqrt(e)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*(-d)^(5/2)) + (3*sqrt(e)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*(-d)^(5/2)) + (3*b*sqrt(e)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(4*(-d)^(5/2)) - (3*b*sqrt(e)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(4*(-d)^(5/2)) + (3*b*sqrt(e)*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(4*(-d)^(5/2)) - (3*b*sqrt(e)*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(4*(-d)^(5/2))]

    @test_int [(x^5*(a + b*acosh(c*x)))/(d + e*x^2)^3, x, 29, (b*c*d*x*(1 - c^2*x^2))/(8*e^2*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2)) - (d^2*(a + b*acosh(c*x)))/(4*e^3*(d + e*x^2)^2) + (d*(a + b*acosh(c*x)))/(e^3*(d + e*x^2)) - (a + b*acosh(c*x))^2/(2*b*e^3) - (b*c*sqrt(d)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(e^3*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*sqrt(d)*(2*c^2*d + e)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(8*e^3*(c^2*d + e)^(3/2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^3) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^3) + ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^3) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^3) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*e^3) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*e^3) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*e^3) + (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*e^3)]
    @test_int [(x^3*(a + b*acosh(c*x)))/(d + e*x^2)^3, x, 9, -(b*c*x*(1 - c^2*x^2))/(8*e*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2)) + (x^4*(a + b*acosh(c*x)))/(4*d*(d + e*x^2)^2) - (b*sqrt(1 - c^2*x^2)*asin(c*x))/(4*d*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*(2*c^2*d + 3*e)*sqrt(1 - c^2*x^2)*atan((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(1 - c^2*x^2))))/(8*sqrt(d)*e^2*(c^2*d + e)^(3/2)*sqrt(-1 + c*x)*sqrt(1 + c*x)), -((b*c*x*(1 - c^2*x^2))/(8*e*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2))) + (x^4*(a + b*acosh(c*x)))/(4*d*(d + e*x^2)^2) - (b*sqrt(-1 + c^2*x^2)*atanh((c*x)/sqrt(-1 + c^2*x^2)))/(4*d*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*(2*c^2*d + 3*e)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(8*sqrt(d)*e^2*(c^2*d + e)^(3/2)*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(x*(a + b*acosh(c*x)))/(d + e*x^2)^3, x, 5, (b*c*x*(1 - c^2*x^2))/(8*d*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2)) - (a + b*acosh(c*x))/(4*e*(d + e*x^2)^2) + (b*c*(2*c^2*d + e)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(8*d^(3/2)*e*(c^2*d + e)^(3/2)*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(a + b*acosh(c*x))/(x*(d + e*x^2)^3), x, 34, -((b*c*e*x*(1 - c^2*x^2))/(8*d^2*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2))) + (a + b*acosh(c*x))/(4*d*(d + e*x^2)^2) + (a + b*acosh(c*x))/(2*d^2*(d + e*x^2)) + (a + b*acosh(c*x))^2/(b*d^3) - (b*c*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(2*d^(5/2)*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (b*c*(2*c^2*d + e)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(8*d^(5/2)*(c^2*d + e)^(3/2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + ((a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/d^3 - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^3) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^3) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^3) - ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^3) - (b*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(2*d^3) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*d^3) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^3) - (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*d^3) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^3)]
    @test_int [(a + b*acosh(c*x))/(x^3*(d + e*x^2)^3), x, 36, (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(2*d^3*x) + (b*c*e^2*x*(1 - c^2*x^2))/(8*d^3*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2)) - (a + b*acosh(c*x))/(2*d^3*x^2) - (e*(a + b*acosh(c*x)))/(4*d^2*(d + e*x^2)^2) - (e*(a + b*acosh(c*x)))/(d^3*(d + e*x^2)) - (3*e*(a + b*acosh(c*x))^2)/(b*d^4) + (b*c*e*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(d^(7/2)*sqrt(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*c*e*(2*c^2*d + e)*sqrt(-1 + c^2*x^2)*atanh((sqrt(c^2*d + e)*x)/(sqrt(d)*sqrt(-1 + c^2*x^2))))/(8*d^(7/2)*(c^2*d + e)^(3/2)*sqrt(-1 + c*x)*sqrt(1 + c*x)) - (3*e*(a + b*acosh(c*x))*log(1 + ℯ^(-2*acosh(c*x))))/d^4 + (3*e*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^4) + (3*e*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^4) + (3*e*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^4) + (3*e*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^4) + (3*b*e*PolyLog(2, -ℯ^(-2*acosh(c*x))))/(2*d^4) + (3*b*e*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(2*d^4) + (3*b*e*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*d^4) + (3*b*e*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(2*d^4) + (3*b*e*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*d^4)]

    @test_int [(x^4*(a + b*acosh(c*x)))/(d + e*x^2)^3, x, 80, -((b*c*sqrt(-d)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*e^2*(c^2*d + e)*(sqrt(-d) - sqrt(e)*x))) - (b*c*sqrt(-d)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*e^2*(c^2*d + e)*(sqrt(-d) + sqrt(e)*x)) - (sqrt(-d)*(a + b*acosh(c*x)))/(16*e^(5/2)*(sqrt(-d) - sqrt(e)*x)^2) + (5*(a + b*acosh(c*x)))/(16*e^(5/2)*(sqrt(-d) - sqrt(e)*x)) + (sqrt(-d)*(a + b*acosh(c*x)))/(16*e^(5/2)*(sqrt(-d) + sqrt(e)*x)^2) - (5*(a + b*acosh(c*x)))/(16*e^(5/2)*(sqrt(-d) + sqrt(e)*x)) - (b*c^3*d*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(8*(c*sqrt(-d) - sqrt(e))^(3/2)*(c*sqrt(-d) + sqrt(e))^(3/2)*e^(5/2)) - (5*b*c*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(8*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(5/2)) + (b*c^3*d*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(8*(c*sqrt(-d) - sqrt(e))^(3/2)*(c*sqrt(-d) + sqrt(e))^(3/2)*e^(5/2)) + (5*b*c*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(8*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(5/2)) + (3*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*sqrt(-d)*e^(5/2)) - (3*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*sqrt(-d)*e^(5/2)) + (3*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*sqrt(-d)*e^(5/2)) - (3*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*sqrt(-d)*e^(5/2)) - (3*b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(16*sqrt(-d)*e^(5/2)) + (3*b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*sqrt(-d)*e^(5/2)) - (3*b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(16*sqrt(-d)*e^(5/2)) + (3*b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*sqrt(-d)*e^(5/2))]
    @test_int [(x^2*(a + b*acosh(c*x)))/(d + e*x^2)^3, x, 62, -((b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*sqrt(-d)*e*(c^2*d + e)*(sqrt(-d) - sqrt(e)*x))) - (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*sqrt(-d)*e*(c^2*d + e)*(sqrt(-d) + sqrt(e)*x)) - (a + b*acosh(c*x))/(16*sqrt(-d)*e^(3/2)*(sqrt(-d) - sqrt(e)*x)^2) - (a + b*acosh(c*x))/(16*d*e^(3/2)*(sqrt(-d) - sqrt(e)*x)) + (a + b*acosh(c*x))/(16*sqrt(-d)*e^(3/2)*(sqrt(-d) + sqrt(e)*x)^2) + (a + b*acosh(c*x))/(16*d*e^(3/2)*(sqrt(-d) + sqrt(e)*x)) + (b*c^3*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(8*(c*sqrt(-d) - sqrt(e))^(3/2)*(c*sqrt(-d) + sqrt(e))^(3/2)*e^(3/2)) + (b*c*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(8*d*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(3/2)) - (b*c^3*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(8*(c*sqrt(-d) - sqrt(e))^(3/2)*(c*sqrt(-d) + sqrt(e))^(3/2)*e^(3/2)) - (b*c*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(8*d*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*e^(3/2)) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*(-d)^(3/2)*e^(3/2)) - ((a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*(-d)^(3/2)*e^(3/2)) + ((a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*(-d)^(3/2)*e^(3/2)) + (b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(16*(-d)^(3/2)*e^(3/2)) - (b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*(-d)^(3/2)*e^(3/2))]
    @test_int [(a + b*acosh(c*x))/(d + e*x^2)^3, x, 34, -((b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*(-d)^(3/2)*(c^2*d + e)*(sqrt(-d) - sqrt(e)*x))) - (b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(16*(-d)^(3/2)*(c^2*d + e)*(sqrt(-d) + sqrt(e)*x)) - (a + b*acosh(c*x))/(16*(-d)^(3/2)*sqrt(e)*(sqrt(-d) - sqrt(e)*x)^2) - (3*(a + b*acosh(c*x)))/(16*d^2*sqrt(e)*(sqrt(-d) - sqrt(e)*x)) + (a + b*acosh(c*x))/(16*(-d)^(3/2)*sqrt(e)*(sqrt(-d) + sqrt(e)*x)^2) + (3*(a + b*acosh(c*x)))/(16*d^2*sqrt(e)*(sqrt(-d) + sqrt(e)*x)) - (b*c^3*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(8*d*(c*sqrt(-d) - sqrt(e))^(3/2)*(c*sqrt(-d) + sqrt(e))^(3/2)*sqrt(e)) + (3*b*c*atanh((sqrt(c*sqrt(-d) - sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) + sqrt(e))*sqrt(-1 + c*x))))/(8*d^2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*sqrt(e)) + (b*c^3*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(8*d*(c*sqrt(-d) - sqrt(e))^(3/2)*(c*sqrt(-d) + sqrt(e))^(3/2)*sqrt(e)) - (3*b*c*atanh((sqrt(c*sqrt(-d) + sqrt(e))*sqrt(1 + c*x))/(sqrt(c*sqrt(-d) - sqrt(e))*sqrt(-1 + c*x))))/(8*d^2*sqrt(c*sqrt(-d) - sqrt(e))*sqrt(c*sqrt(-d) + sqrt(e))*sqrt(e)) + (3*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*(-d)^(5/2)*sqrt(e)) - (3*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*(-d)^(5/2)*sqrt(e)) + (3*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*(-d)^(5/2)*sqrt(e)) - (3*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*(-d)^(5/2)*sqrt(e)) - (3*b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(16*(-d)^(5/2)*sqrt(e)) + (3*b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(16*(-d)^(5/2)*sqrt(e)) - (3*b*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(16*(-d)^(5/2)*sqrt(e)) + (3*b*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(16*(-d)^(5/2)*sqrt(e))]
    #= [(a + b*acosh(c*x))/(x^2*(d + e*x^2)^3), x, 102, (b*c*e*sqrt(1 - c^2*x^2))/(16*(-d)^(5/2)*(c^2*d + e)*(sqrt(-d) - sqrt(e)*x)) + (b*c*e*sqrt(1 - c^2*x^2))/(16*(-d)^(5/2)*(c^2*d + e)*(sqrt(-d) + sqrt(e)*x)) - (a + b*acosh(c*x))/(d^3*x) - (sqrt(e)*(a + b*acosh(c*x)))/(16*(-d)^(5/2)*(sqrt(-d) - sqrt(e)*x)^2) + (7*sqrt(e)*(a + b*acosh(c*x)))/(16*d^3*(sqrt(-d) - sqrt(e)*x)) + (sqrt(e)*(a + b*acosh(c*x)))/(16*(-d)^(5/2)*(sqrt(-d) + sqrt(e)*x)^2) - (7*sqrt(e)*(a + b*acosh(c*x)))/(16*d^3*(sqrt(-d) + sqrt(e)*x)) - (b*c^3*sqrt(e)*atanh((sqrt(e) - c^2*sqrt(-d)*x)/(sqrt(c^2*d + e)*sqrt(1 - c^2*x^2))))/(16*d^2*(c^2*d + e)^(3/2)) - (7*b*c*sqrt(e)*atanh((sqrt(e) - c^2*sqrt(-d)*x)/(sqrt(c^2*d + e)*sqrt(1 - c^2*x^2))))/(16*d^3*sqrt(c^2*d + e)) - (b*c^3*sqrt(e)*atanh((sqrt(e) + c^2*sqrt(-d)*x)/(sqrt(c^2*d + e)*sqrt(1 - c^2*x^2))))/(16*d^2*(c^2*d + e)^(3/2)) - (7*b*c*sqrt(e)*atanh((sqrt(e) + c^2*sqrt(-d)*x)/(sqrt(c^2*d + e)*sqrt(1 - c^2*x^2))))/(16*d^3*sqrt(c^2*d + e)) - (b*c*atanh(sqrt(1 - c^2*x^2)))/d^3 + (15*sqrt(e)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) - sqrt(c^2*d + e))))/(16*(-d)^(7/2)) - (15*sqrt(e)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) - sqrt(c^2*d + e))))/(16*(-d)^(7/2)) + (15*sqrt(e)*(a + b*acosh(c*x))*log(1 - (sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) + sqrt(c^2*d + e))))/(16*(-d)^(7/2)) - (15*sqrt(e)*(a + b*acosh(c*x))*log(1 + (sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) + sqrt(c^2*d + e))))/(16*(-d)^(7/2)) + (15*im*b*sqrt(e)*PolyLog(2, -((sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) - sqrt(c^2*d + e)))))/(16*(-d)^(7/2)) - (15*im*b*sqrt(e)*PolyLog(2, (sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) - sqrt(c^2*d + e))))/(16*(-d)^(7/2)) + (15*im*b*sqrt(e)*PolyLog(2, -((sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) + sqrt(c^2*d + e)))))/(16*(-d)^(7/2)) - (15*im*b*sqrt(e)*PolyLog(2, (sqrt(e)*ℯ^(im*acosh(c*x)))/(im*c*sqrt(-d) + sqrt(c^2*d + e))))/(16*(-d)^(7/2))] =#

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

    @test_int [sqrt(d + e*x^2)*(a + b*acosh(c*x)), x, 0, Unintegrable(sqrt(d + e*x^2)*(a + b*acosh(c*x)), x)]
    @test_int [(a + b*acosh(c*x))/sqrt(d + e*x^2), x, 0, Unintegrable((a + b*acosh(c*x))/sqrt(d + e*x^2), x)]
    @test_int [(a + b*acosh(c*x))/(d + e*x^2)^(3/2), x, 7, (x*(a + b*acosh(c*x)))/(d*sqrt(d + e*x^2)) - (b*sqrt(-1 + c^2*x^2)*atanh((sqrt(e)*sqrt(-1 + c^2*x^2))/(c*sqrt(d + e*x^2))))/(d*sqrt(e)*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(a + b*acosh(c*x))/(d + e*x^2)^(5/2), x, 8, -((b*c*sqrt(-1 + c*x)*sqrt(1 + c*x))/(3*d*(c^2*d + e)*sqrt(d + e*x^2))) + (x*(a + b*acosh(c*x)))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*acosh(c*x)))/(3*d^2*sqrt(d + e*x^2)) + (2*b*sqrt(1 - c^2*x^2)*atan((sqrt(e)*sqrt(1 - c^2*x^2))/(c*sqrt(d + e*x^2))))/(3*d^2*sqrt(e)*sqrt(-1 + c*x)*sqrt(1 + c*x)), (b*c*(1 - c^2*x^2))/(3*d*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(d + e*x^2)) + (x*(a + b*acosh(c*x)))/(3*d*(d + e*x^2)^(3/2)) + (2*x*(a + b*acosh(c*x)))/(3*d^2*sqrt(d + e*x^2)) - (2*b*sqrt(-1 + c^2*x^2)*atanh((sqrt(e)*sqrt(-1 + c^2*x^2))/(c*sqrt(d + e*x^2))))/(3*d^2*sqrt(e)*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(a + b*acosh(c*x))/(d + e*x^2)^(7/2), x, 9, (b*c*(1 - c^2*x^2))/(15*d*(c^2*d + e)*sqrt(-1 + c*x)*sqrt(1 + c*x)*(d + e*x^2)^(3/2)) + (2*b*c*(3*c^2*d + 2*e)*(1 - c^2*x^2))/(15*d^2*(c^2*d + e)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(d + e*x^2)) + (x*(a + b*acosh(c*x)))/(5*d*(d + e*x^2)^(5/2)) + (4*x*(a + b*acosh(c*x)))/(15*d^2*(d + e*x^2)^(3/2)) + (8*x*(a + b*acosh(c*x)))/(15*d^3*sqrt(d + e*x^2)) - (8*b*sqrt(-1 + c^2*x^2)*atanh((sqrt(e)*sqrt(-1 + c^2*x^2))/(c*sqrt(d + e*x^2))))/(15*d^3*sqrt(e)*sqrt(-1 + c*x)*sqrt(1 + c*x))]

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

    @test_int [(f*x)^m*(d + e*x^2)^3*(a + b*acosh(c*x)), x, 8, If(13>=8, (b*e*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4))*(f*x)^(2 + m)*(1 - c^2*x^2))/(c^5*f^2*(3 + m)^2*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*(3*c^2*d*(7 + m)^2 + e*(30 + 11*m + m^2))*(f*x)^(4 + m)*(1 - c^2*x^2))/(c^3*f^4*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^3*(f*x)^(6 + m)*(1 - c^2*x^2))/(c*f^6*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^3*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*acosh(c*x)))/(f^7*(7 + m)) - (b*((c^6*d^3*(3 + m)*(5 + m)*(7 + m))/(1 + m) + (e*(2 + m)*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4)))/((3 + m)*(5 + m)*(7 + m)))*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(c^5*f^2*(2 + m)*(3 + m)*(5 + m)*(7 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)), (b*e*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4))*(f*x)^(2 + m)*(1 - c^2*x^2))/(c^5*f^2*(3 + m)^2*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*(3*c^2*d*(7 + m)^2 + e*(30 + 11*m + m^2))*(f*x)^(4 + m)*(1 - c^2*x^2))/(c^3*f^4*(5 + m)^2*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^3*(f*x)^(6 + m)*(1 - c^2*x^2))/(c*f^6*(7 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^3*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) + (3*d^2*e*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (3*d*e^2*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) + (e^3*(f*x)^(7 + m)*(a + b*acosh(c*x)))/(f^7*(7 + m)) - (b*((c^6*d^3*(3 + m)*(5 + m)*(7 + m))/(1 + m) + (e*(2 + m)*(3*c^2*d*e*(7 + m)^2*(12 + 7*m + m^2) + 3*c^4*d^2*(35 + 12*m + m^2)^2 + e^2*(360 + 342*m + 119*m^2 + 18*m^3 + m^4)))/(105 + 71*m + 15*m^2 + m^3))*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(c^5*f^2*(2 + m)*(3 + m)*(5 + m)*(7 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x)))]
    @test_int [(f*x)^m*(d + e*x^2)^2*(a + b*acosh(c*x)), x, 7, (b*e*(2*c^2*d*(5 + m)^2 + e*(12 + 7*m + m^2))*(f*x)^(2 + m)*(1 - c^2*x^2))/(c^3*f^2*(3 + m)^2*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (b*e^2*(f*x)^(4 + m)*(1 - c^2*x^2))/(c*f^4*(5 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x)) + (d^2*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) + (2*d*e*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) + (e^2*(f*x)^(5 + m)*(a + b*acosh(c*x)))/(f^5*(5 + m)) - (b*((c^4*d^2*(3 + m)*(5 + m))/(1 + m) + (e*(2 + m)*(2*c^2*d*(5 + m)^2 + e*(12 + 7*m + m^2)))/((3 + m)*(5 + m)))*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(c^3*f^2*(2 + m)*(3 + m)*(5 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(f*x)^m*(d + e*x^2)^1*(a + b*acosh(c*x)), x, 5, -((b*e*(f*x)^(2 + m)*sqrt(-1 + c*x)*sqrt(1 + c*x))/(c*f^2*(3 + m)^2)) + (d*(f*x)^(1 + m)*(a + b*acosh(c*x)))/(f*(1 + m)) + (e*(f*x)^(3 + m)*(a + b*acosh(c*x)))/(f^3*(3 + m)) - (b*(e*(1 + m)*(2 + m) + c^2*d*(3 + m)^2)*(f*x)^(2 + m)*sqrt(1 - c^2*x^2)*HypergeometricFunctions._₂F₁(1/2, (2 + m)/2, (4 + m)/2, c^2*x^2))/(c*f^2*(1 + m)*(2 + m)*(3 + m)^2*sqrt(-1 + c*x)*sqrt(1 + c*x))]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d + e*x^2)^1, x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x)))/(d + e*x^2), x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d + e*x^2)^2, x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x)))/(d + e*x^2)^2, x)]
    @test_int [(f*x)^m*(a + b*acosh(c*x))/(d + e*x^2)^3, x, 0, Unintegrable(((f*x)^m*(a + b*acosh(c*x)))/(d + e*x^2)^3, x)]

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

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

    @test_int [(d + e*x^2)^3*(a + b*acosh(c*x))^2, x, 26, 2*b^2*d^3*x + (4*b^2*d^2*e*x)/(3*c^2) + (16*b^2*d*e^2*x)/(25*c^4) + (32*b^2*e^3*x)/(245*c^6) + (2*b^2*d^2*e*x^3)/9 + (8*b^2*d*e^2*x^3)/(75*c^2) + (16*b^2*e^3*x^3)/(735*c^4) + (6*b^2*d*e^2*x^5)/125 + (12*b^2*e^3*x^5)/(1225*c^2) + (2*b^2*e^3*x^7)/343 - (2*b*d^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (4*b*d^2*e*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c^3) - (16*b*d*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(25*c^5) - (32*b*e^3*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(245*c^7) - (2*b*d^2*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(3*c) - (8*b*d*e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(25*c^3) - (16*b*e^3*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(245*c^5) - (6*b*d*e^2*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(25*c) - (12*b*e^3*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(245*c^3) - (2*b*e^3*x^6*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(49*c) + d^3*x*(a + b*acosh(c*x))^2 + d^2*e*x^3*(a + b*acosh(c*x))^2 + (3*d*e^2*x^5*(a + b*acosh(c*x))^2)/5 + (e^3*x^7*(a + b*acosh(c*x))^2)/7]
    @test_int [(d + e*x^2)^2*(a + b*acosh(c*x))^2, x, 17, 2*b^2*d^2*x + (8*b^2*d*e*x)/(9*c^2) + (16*b^2*e^2*x)/(75*c^4) + (4*b^2*d*e*x^3)/27 + (8*b^2*e^2*x^3)/(225*c^2) + (2*b^2*e^2*x^5)/125 - (2*b*d^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (8*b*d*e*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c^3) - (16*b*e^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(75*c^5) - (4*b*d*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c) - (8*b*e^2*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(75*c^3) - (2*b*e^2*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(25*c) + d^2*x*(a + b*acosh(c*x))^2 + (2*d*e*x^3*(a + b*acosh(c*x))^2)/3 + (e^2*x^5*(a + b*acosh(c*x))^2)/5]
    @test_int [(d + e*x^2)*(a + b*acosh(c*x))^2, x, 10, 2*b^2*d*x + (4*b^2*e*x)/(9*c^2) + (2*b^2*e*x^3)/27 - (2*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c - (4*b*e*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c^3) - (2*b*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/(9*c) + d*x*(a + b*acosh(c*x))^2 + (e*x^3*(a + b*acosh(c*x))^2)/3]
    @test_int [(a + b*acosh(c*x))^2, x, 3, 2*b^2*x - (2*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*(a + b*acosh(c*x)))/c + x*(a + b*acosh(c*x))^2]
    @test_int [(a + b*acosh(c*x))^2/(d + e*x^2), x, 22, ((a + b*acosh(c*x))^2*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*acosh(c*x))^2*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) + ((a + b*acosh(c*x))^2*log(1 - (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - ((a + b*acosh(c*x))^2*log(1 + (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(2*sqrt(-d)*sqrt(e)) - (b*(a + b*acosh(c*x))*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(sqrt(-d)*sqrt(e)) + (b*(a + b*acosh(c*x))*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(sqrt(-d)*sqrt(e)) - (b*(a + b*acosh(c*x))*PolyLog(2, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(sqrt(-d)*sqrt(e)) + (b*(a + b*acosh(c*x))*PolyLog(2, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(sqrt(-d)*sqrt(e)) + (b^2*PolyLog(3, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e)))))/(sqrt(-d)*sqrt(e)) - (b^2*PolyLog(3, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) - sqrt((-c^2)*d - e))))/(sqrt(-d)*sqrt(e)) + (b^2*PolyLog(3, -((sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e)))))/(sqrt(-d)*sqrt(e)) - (b^2*PolyLog(3, (sqrt(e)*ℯ^acosh(c*x))/(c*sqrt(-d) + sqrt((-c^2)*d - e))))/(sqrt(-d)*sqrt(e))]

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

    @test_int [sqrt(d + e*x^2)*(a + b*acosh(c*x))^2, x, 0, Unintegrable(sqrt(d + e*x^2)*(a + b*acosh(c*x))^2, x)]
    @test_int [(a + b*acosh(c*x))^2/sqrt(d + e*x^2), x, 0, Unintegrable((a + b*acosh(c*x))^2/sqrt(d + e*x^2), x)]
    @test_int [(a + b*acosh(c*x))^2/(d + e*x^2)^(3/2), x, 0, Unintegrable((a + b*acosh(c*x))^2/(d + e*x^2)^(3/2), x)]
    @test_int [(a + b*acosh(c*x))^2/(d + e*x^2)^(5/2), x, 0, Unintegrable((a + b*acosh(c*x))^2/(d + e*x^2)^(5/2), x)]

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

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

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

    @test_int [(d + e*x^2)^2/(a + b*acosh(c*x)), x, 27, -((d^2*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(b*c)) - (d*e*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(2*b*c^3) - (e^2*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(8*b*c^5) - (d*e*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(2*b*c^3) - (3*e^2*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(16*b*c^5) - (e^2*CoshIntegral((5*(a + b*acosh(c*x)))/b)*sinh((5*a)/b))/(16*b*c^5) + (d^2*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b*c) + (d*e*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(2*b*c^3) + (e^2*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b*c^5) + (d*e*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(2*b*c^3) + (3*e^2*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b*c^5) + (e^2*cosh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b*c^5)]
    @test_int [(d + e*x^2)^1/(a + b*acosh(c*x)), x, 15, -(((4*c^2*d + e)*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(4*b*c^3)) - (e*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(4*b*c^3) + ((4*c^2*d + e)*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b*c^3) + (e*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*c^3), -((d*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(b*c)) - (e*CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(4*b*c^3) - (e*CoshIntegral((3*(a + b*acosh(c*x)))/b)*sinh((3*a)/b))/(4*b*c^3) + (d*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b*c) + (e*cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b*c^3) + (e*cosh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b*c^3)]
    @test_int [(d + e*x^2)^0/(a + b*acosh(c*x)), x, 4, -((CoshIntegral((a + b*acosh(c*x))/b)*sinh(a/b))/(b*c)) + (cosh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b*c)]
    @test_int [1/((d + e*x^2)^1*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [1/((d + e*x^2)^2*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^2*(a + b*acosh(c*x))), x)]

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

    @test_int [sqrt(d + e*x^2)/(a + b*acosh(c*x)), x, 0, Unintegrable(sqrt(d + e*x^2)/(a + b*acosh(c*x)), x)]
    @test_int [1/(sqrt(d + e*x^2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/(sqrt(d + e*x^2)*(a + b*acosh(c*x))), x)]
    @test_int [1/((d + e*x^2)^(3/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^(3/2)*(a + b*acosh(c*x))), x)]
    @test_int [1/((d + e*x^2)^(5/2)*(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^(5/2)*(a + b*acosh(c*x))), x)]

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

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

    @test_int [(d + e*x^2)^2/(a + b*acosh(c*x))^2, x, 26, -((d^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x)))) - (2*d*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x))) - (e^2*x^4*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x))) + (d^2*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b^2*c) + (d*e*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(2*b^2*c^3) + (e^2*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(8*b^2*c^5) + (3*d*e*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(2*b^2*c^3) + (9*e^2*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(16*b^2*c^5) + (5*e^2*cosh((5*a)/b)*CoshIntegral((5*(a + b*acosh(c*x)))/b))/(16*b^2*c^5) - (d^2*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*c) - (d*e*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(2*b^2*c^3) - (e^2*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(8*b^2*c^5) - (3*d*e*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(2*b^2*c^3) - (9*e^2*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(16*b^2*c^5) - (5*e^2*sinh((5*a)/b)*SinhIntegral((5*(a + b*acosh(c*x)))/b))/(16*b^2*c^5)]
    @test_int [(d + e*x^2)^1/(a + b*acosh(c*x))^2, x, 15, -((d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x)))) - (e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x))) + (d*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b^2*c) + (e*cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(4*b^2*c^3) + (3*e*cosh((3*a)/b)*CoshIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*c^3) - (d*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*c) - (e*sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(4*b^2*c^3) - (3*e*sinh((3*a)/b)*SinhIntegral((3*(a + b*acosh(c*x)))/b))/(4*b^2*c^3)]
    @test_int [(d + e*x^2)^0/(a + b*acosh(c*x))^2, x, 5, -((sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*(a + b*acosh(c*x)))) + (cosh(a/b)*CoshIntegral((a + b*acosh(c*x))/b))/(b^2*c) - (sinh(a/b)*SinhIntegral((a + b*acosh(c*x))/b))/(b^2*c)]
    @test_int [1/((d + e*x^2)^1*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)*(a + b*acosh(c*x))^2), x)]
    @test_int [1/((d + e*x^2)^2*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)^2*(a + b*acosh(c*x))^2), x)]

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

    @test_int [sqrt(d + e*x^2)/(a + b*acosh(c*x))^2, x, 0, Unintegrable(sqrt(d + e*x^2)/(a + b*acosh(c*x))^2, x)]
    @test_int [1/(sqrt(d + e*x^2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/(sqrt(d + e*x^2)*(a + b*acosh(c*x))^2), x)]
    @test_int [1/((d + e*x^2)^(3/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)^(3/2)*(a + b*acosh(c*x))^2), x)]
    @test_int [1/((d + e*x^2)^(5/2)*(a + b*acosh(c*x))^2), x, 0, Unintegrable(1/((d + e*x^2)^(5/2)*(a + b*acosh(c*x))^2), x)]

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

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

    #= ::Subsubsection::Closed:: =#
    #=n>0=#

    @test_int [(d + e*x^2)^2*sqrt(a + b*acosh(c*x)), x, 42, d^2*x*sqrt(a + b*acosh(c*x)) + (2*d*e*x^3*sqrt(a + b*acosh(c*x)))/3 + (e^2*x^5*sqrt(a + b*acosh(c*x)))/5 - (sqrt(b)*d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*c) - (sqrt(b)*d*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*c^3) - (sqrt(b)*e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(32*c^5) - (sqrt(b)*d*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(24*c^3) - (sqrt(b)*e^2*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(64*c^5) - (sqrt(b)*e^2*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(320*c^5) - (sqrt(b)*d^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*c*ℯ^(a/b)) - (sqrt(b)*d*e*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*c^3*ℯ^(a/b)) - (sqrt(b)*e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(32*c^5*ℯ^(a/b)) - (sqrt(b)*d*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(24*c^3*ℯ^((3*a)/b)) - (sqrt(b)*e^2*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(64*c^5*ℯ^((3*a)/b)) - (sqrt(b)*e^2*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(320*c^5*ℯ^((5*a)/b))]
    @test_int [(d + e*x^2)*sqrt(a + b*acosh(c*x)), x, 23, d*x*sqrt(a + b*acosh(c*x)) + (e*x^3*sqrt(a + b*acosh(c*x)))/3 - (sqrt(b)*d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*c) - (sqrt(b)*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(16*c^3) - (sqrt(b)*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(48*c^3) - (sqrt(b)*d*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*c*ℯ^(a/b)) - (sqrt(b)*e*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(16*c^3*ℯ^(a/b)) - (sqrt(b)*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(48*c^3*ℯ^((3*a)/b))]
    @test_int [sqrt(a + b*acosh(c*x)), x, 7, x*sqrt(a + b*acosh(c*x)) - (sqrt(b)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*c) - (sqrt(b)*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*c*ℯ^(a/b))]
    @test_int [sqrt(a + b*acosh(c*x))/(d + e*x^2), x, 0, Unintegrable(sqrt(a + b*acosh(c*x))/(d + e*x^2), x)]
    @test_int [sqrt(a + b*acosh(c*x))/(d + e*x^2)^2, x, 0, Unintegrable(sqrt(a + b*acosh(c*x))/(d + e*x^2)^2, x)]

    @test_int [(d + e*x^2)*(a + b*acosh(c*x))^(3/2), x, 32, (-3*b*d*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x)))/(2*c) - (b*e*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x)))/(3*c^3) - (b*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x)))/(6*c) + d*x*(a + b*acosh(c*x))^(3/2) + (e*x^3*(a + b*acosh(c*x))^(3/2))/3 - (3*b^(3/2)*d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*c) - (3*b^(3/2)*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(32*c^3) - (b^(3/2)*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(96*c^3) + (3*b^(3/2)*d*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*c*ℯ^(a/b)) + (3*b^(3/2)*e*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(32*c^3*ℯ^(a/b)) + (b^(3/2)*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(96*c^3*ℯ^((3*a)/b))]
    @test_int [(a + b*acosh(c*x))^(3/2), x, 8, (-3*b*sqrt(-1 + c*x)*sqrt(1 + c*x)*sqrt(a + b*acosh(c*x)))/(2*c) + x*(a + b*acosh(c*x))^(3/2) - (3*b^(3/2)*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*c) + (3*b^(3/2)*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*c*ℯ^(a/b))]
    @test_int [(a + b*acosh(c*x))^(3/2)/(d + e*x^2), x, 0, Unintegrable((a + b*acosh(c*x))^(3/2)/(d + e*x^2), x)]
    @test_int [(a + b*acosh(c*x))^(3/2)/(d + e*x^2)^2, x, 0, Unintegrable((a + b*acosh(c*x))^(3/2)/(d + e*x^2)^2, x)]

    #= ::Subsubsection::Closed:: =#
    #=n<0=#

    @test_int [(d + e*x^2)^2/sqrt(a + b*acosh(c*x)), x, 39, -(d^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(2*sqrt(b)*c) - (d*e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*sqrt(b)*c^3) - (e^2*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(16*sqrt(b)*c^5) - (d*e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*sqrt(b)*c^3) - (e^2*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5) - (e^2*ℯ^((5*a)/b)*sqrt(pi/5)*erf((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5) + (d^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(2*sqrt(b)*c*ℯ^(a/b)) + (d*e*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*sqrt(b)*c^3*ℯ^(a/b)) + (e^2*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(16*sqrt(b)*c^5*ℯ^(a/b)) + (d*e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*sqrt(b)*c^3*ℯ^((3*a)/b)) + (e^2*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5*ℯ^((3*a)/b)) + (e^2*sqrt(pi/5)*erfi((sqrt(5)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(32*sqrt(b)*c^5*ℯ^((5*a)/b))]
    @test_int [(d + e*x^2)/sqrt(a + b*acosh(c*x)), x, 21, -(d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(2*sqrt(b)*c) - (e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*sqrt(b)*c^3) - (e*ℯ^((3*a)/b)*sqrt(pi/3)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(8*sqrt(b)*c^3) + (d*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(2*sqrt(b)*c*ℯ^(a/b)) + (e*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(8*sqrt(b)*c^3*ℯ^(a/b)) + (e*sqrt(pi/3)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(8*sqrt(b)*c^3*ℯ^((3*a)/b))]
    @test_int [1/sqrt(a + b*acosh(c*x)), x, 6, -(ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(2*sqrt(b)*c) + (sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(2*sqrt(b)*c*ℯ^(a/b))]
    @test_int [1/((d + e*x^2)*sqrt(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)*sqrt(a + b*acosh(c*x))), x)]
    @test_int [1/((d + e*x^2)^2*sqrt(a + b*acosh(c*x))), x, 0, Unintegrable(1/((d + e*x^2)^2*sqrt(a + b*acosh(c*x))), x)]

    @test_int [(d + e*x^2)/(a + b*acosh(c*x))^(3/2), x, 21, (-2*d*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*sqrt(a + b*acosh(c*x))) - (2*e*x^2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*sqrt(a + b*acosh(c*x))) + (d*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(b^(3/2)*c) + (e*ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*b^(3/2)*c^3) + (e*ℯ^((3*a)/b)*sqrt(3*pi)*erf((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^3) + (d*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(b^(3/2)*c*ℯ^(a/b)) + (e*sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(4*b^(3/2)*c^3*ℯ^(a/b)) + (e*sqrt(3*pi)*erfi((sqrt(3)*sqrt(a + b*acosh(c*x)))/sqrt(b)))/(4*b^(3/2)*c^3*ℯ^((3*a)/b))]
    @test_int [(a + b*acosh(c*x))^(-3/2), x, 7, (-2*sqrt(-1 + c*x)*sqrt(1 + c*x))/(b*c*sqrt(a + b*acosh(c*x))) + (ℯ^(a/b)*sqrt(pi)*erf(sqrt(a + b*acosh(c*x))/sqrt(b)))/(b^(3/2)*c) + (sqrt(pi)*erfi(sqrt(a + b*acosh(c*x))/sqrt(b)))/(b^(3/2)*c*ℯ^(a/b))]
    @test_int [1/((d + e*x^2)*(a + b*acosh(c*x))^(3/2)), x, 0, Unintegrable(1/((d + e*x^2)*(a + b*acosh(c*x))^(3/2)), x)]
    @test_int [1/((d + e*x^2)^2*(a + b*acosh(c*x))^(3/2)), x, 0, Unintegrable(1/((d + e*x^2)^2*(a + b*acosh(c*x))^(3/2)), x)]
    end

max_stars_repo_path: test/7 Inverse hyperbolic functions/7.2 Inverse hyperbolic cosine/7.2.4 (f x)^m (d+e x^2)^p (a+b arccosh(c x))^n.jl