Optimal. Leaf size=33 \[ \text{Unintegrable}\left (\frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right ) \]
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Rubi [A] time = 0.0744917, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx &=\int \frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx\\ \end{align*}
Mathematica [F] time = 180.001, size = 0, normalized size = 0. \[ \text{\$Aborted} \]
Verification is Not applicable to the result.
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Maple [A] time = 1.329, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (dx+c\right ) \right ) ^{2}}{ \left ( fx+e \right ) ^{2} \left ( a+ia\sinh \left ( dx+c \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -4 i \, f \int \frac{1}{-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3} +{\left (a d f^{3} x^{3} e^{c} + 3 \, a d e f^{2} x^{2} e^{c} + 3 \, a d e^{2} f x e^{c} + a d e^{3} e^{c}\right )} e^{\left (d x\right )}}\,{d x} - \frac{4 \,{\left (i \, e^{\left (2 \, d x + 2 \, c\right )} + e^{\left (d x + c\right )} - 2 i\right )}}{2 i \, a d f^{2} x^{2} + 4 i \, a d e f x + 2 i \, a d e^{2} + 2 \,{\left (a d f^{2} x^{2} e^{\left (3 \, c\right )} + 2 \, a d e f x e^{\left (3 \, c\right )} + a d e^{2} e^{\left (3 \, c\right )}\right )} e^{\left (3 \, d x\right )} +{\left (-2 i \, a d f^{2} x^{2} e^{\left (2 \, c\right )} - 4 i \, a d e f x e^{\left (2 \, c\right )} - 2 i \, a d e^{2} e^{\left (2 \, c\right )}\right )} e^{\left (2 \, d x\right )} - 2 \,{\left (a d f^{2} x^{2} e^{c} + 2 \, a d e f x e^{c} + a d e^{2} e^{c}\right )} e^{\left (d x\right )}} - 4 \, \int -\frac{i \, d f x + i \, d e + 2 \, f}{4 \,{\left (a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3} -{\left (a d f^{3} x^{3} e^{c} + 3 \, a d e f^{2} x^{2} e^{c} + 3 \, a d e^{2} f x e^{c} + a d e^{3} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} - 4 \, \int \frac{i \, d f x + i \, d e - 2 \, f}{4 \,{\left (a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3} +{\left (a d f^{3} x^{3} e^{c} + 3 \, a d e f^{2} x^{2} e^{c} + 3 \, a d e^{2} f x e^{c} + a d e^{3} e^{c}\right )} e^{\left (d x\right )}\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{{\left (i \, a d f^{2} x^{2} + 2 i \, a d e f x + i \, a d e^{2} +{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (3 \, d x + 3 \, c\right )} +{\left (-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2}\right )} e^{\left (2 \, d x + 2 \, c\right )} -{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (d x + c\right )}\right )}{\rm integral}\left (\frac{{\left (-2 i \, d f x - 2 i \, d e - 4 i \, f\right )} e^{\left (2 \, d x + 2 \, c\right )} - 2 \,{\left (d f x + d e + 2 \, f\right )} e^{\left (d x + c\right )} + 8 i \, f}{i \, a d f^{3} x^{3} + 3 i \, a d e f^{2} x^{2} + 3 i \, a d e^{2} f x + i \, a d e^{3} +{\left (a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right )} e^{\left (3 \, d x + 3 \, c\right )} +{\left (-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3}\right )} e^{\left (2 \, d x + 2 \, c\right )} -{\left (a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right )} e^{\left (d x + c\right )}}, x\right ) - 2 i \, e^{\left (2 \, d x + 2 \, c\right )} - 2 \, e^{\left (d x + c\right )} + 4 i}{i \, a d f^{2} x^{2} + 2 i \, a d e f x + i \, a d e^{2} +{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (3 \, d x + 3 \, c\right )} +{\left (-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2}\right )} e^{\left (2 \, d x + 2 \, c\right )} -{\left (a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right )} e^{\left (d x + c\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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