Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\text{csch}^3(a+b x)}{(c+d x)^2},x\right ) \]
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Rubi [A] time = 0.0372557, 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 = {} \[ \int \frac{\text{csch}^3(a+b x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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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 = 79.6001, size = 0, normalized size = 0. \[ \int \frac{\text{csch}^3(a+b x)}{(c+d x)^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.81, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ({\rm csch} \left (bx+a\right ) \right ) ^{3}}{ \left ( dx+c \right ) ^{2}}}\, 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*} -\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} \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*}{\rm integral}\left (\frac{\operatorname{csch}\left (b x + a\right )^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{csch}^{3}{\left (a + b x \right )}}{\left (c + d x\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\operatorname{csch}\left (b x + a\right )^{3}}{{\left (d x + c\right )}^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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