3.37 \(\int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx\)

Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {csch}^3(a+b x)}{(c+d x)^2},x\right ) \]

[Out]

Unintegrable(csch(b*x+a)^3/(d*x+c)^2,x)

________________________________________________________________________________________

Rubi [A]  time = 0.04, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Csch[a + b*x]^3/(c + d*x)^2,x]

[Out]

Defer[Int][Csch[a + b*x]^3/(c + d*x)^2, x]

Rubi steps

\begin {align*} \int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx &=\int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]  time = 74.37, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^3(a+b x)}{(c+d x)^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Csch[a + b*x]^3/(c + d*x)^2,x]

[Out]

Integrate[Csch[a + b*x]^3/(c + d*x)^2, x]

________________________________________________________________________________________

fricas [A]  time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (b x + a\right )^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c)^2,x, algorithm="fricas")

[Out]

integral(csch(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)

________________________________________________________________________________________

giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c)^2,x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

maple [A]  time = 1.07, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (b x +a \right )^{3}}{\left (d x +c \right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(csch(b*x+a)^3/(d*x+c)^2,x)

[Out]

int(csch(b*x+a)^3/(d*x+c)^2,x)

________________________________________________________________________________________

maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ -\frac {{\left (b d x e^{\left (3 \, a\right )} + {\left (b c - 2 \, d\right )} e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} + {\left (b d x e^{a} + {\left (b c + 2 \, d\right )} e^{a}\right )} e^{\left (b x\right )}}{b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3} + {\left (b^{2} d^{3} x^{3} e^{\left (4 \, a\right )} + 3 \, b^{2} c d^{2} x^{2} e^{\left (4 \, a\right )} + 3 \, b^{2} c^{2} d x e^{\left (4 \, a\right )} + b^{2} c^{3} e^{\left (4 \, a\right )}\right )} e^{\left (4 \, b x\right )} - 2 \, {\left (b^{2} d^{3} x^{3} e^{\left (2 \, a\right )} + 3 \, b^{2} c d^{2} x^{2} e^{\left (2 \, a\right )} + 3 \, b^{2} c^{2} d x e^{\left (2 \, a\right )} + b^{2} c^{3} e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} - 8 \, \int \frac {b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 6 \, d^{2}}{16 \, {\left (b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4} + {\left (b^{2} d^{4} x^{4} e^{a} + 4 \, b^{2} c d^{3} x^{3} e^{a} + 6 \, b^{2} c^{2} d^{2} x^{2} e^{a} + 4 \, b^{2} c^{3} d x e^{a} + b^{2} c^{4} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} - 8 \, \int -\frac {b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 6 \, d^{2}}{16 \, {\left (b^{2} d^{4} x^{4} + 4 \, b^{2} c d^{3} x^{3} + 6 \, b^{2} c^{2} d^{2} x^{2} + 4 \, b^{2} c^{3} d x + b^{2} c^{4} - {\left (b^{2} d^{4} x^{4} e^{a} + 4 \, b^{2} c d^{3} x^{3} e^{a} + 6 \, b^{2} c^{2} d^{2} x^{2} e^{a} + 4 \, b^{2} c^{3} d x e^{a} + b^{2} c^{4} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)^3/(d*x+c)^2,x, algorithm="maxima")

[Out]

-((b*d*x*e^(3*a) + (b*c - 2*d)*e^(3*a))*e^(3*b*x) + (b*d*x*e^a + (b*c + 2*d)*e^a)*e^(b*x))/(b^2*d^3*x^3 + 3*b^
2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3 + (b^2*d^3*x^3*e^(4*a) + 3*b^2*c*d^2*x^2*e^(4*a) + 3*b^2*c^2*d*x*e^(4*a)
+ b^2*c^3*e^(4*a))*e^(4*b*x) - 2*(b^2*d^3*x^3*e^(2*a) + 3*b^2*c*d^2*x^2*e^(2*a) + 3*b^2*c^2*d*x*e^(2*a) + b^2
*c^3*e^(2*a))*e^(2*b*x)) - 8*integrate(1/16*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 6*d^2)/(b^2*d^4*x^4 + 4*b^2
*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 + (b^2*d^4*x^4*e^a + 4*b^2*c*d^3*x^3*e^a + 6*b^2*c^2*
d^2*x^2*e^a + 4*b^2*c^3*d*x*e^a + b^2*c^4*e^a)*e^(b*x)), x) - 8*integrate(-1/16*(b^2*d^2*x^2 + 2*b^2*c*d*x + b
^2*c^2 - 6*d^2)/(b^2*d^4*x^4 + 4*b^2*c*d^3*x^3 + 6*b^2*c^2*d^2*x^2 + 4*b^2*c^3*d*x + b^2*c^4 - (b^2*d^4*x^4*e^
a + 4*b^2*c*d^3*x^3*e^a + 6*b^2*c^2*d^2*x^2*e^a + 4*b^2*c^3*d*x*e^a + b^2*c^4*e^a)*e^(b*x)), x)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \frac {1}{{\mathrm {sinh}\left (a+b\,x\right )}^3\,{\left (c+d\,x\right )}^2} \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(sinh(a + b*x)^3*(c + d*x)^2),x)

[Out]

int(1/(sinh(a + b*x)^3*(c + d*x)^2), x)

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\operatorname {csch}^{3}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(csch(b*x+a)**3/(d*x+c)**2,x)

[Out]

Integral(csch(a + b*x)**3/(c + d*x)**2, x)

________________________________________________________________________________________