Optimal. Leaf size=27 \[ x^{-m} (e x)^m \text{Unintegrable}\left (x^m \text{csch}^2\left (a+b x^n\right ),x\right ) \]
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Rubi [A] time = 0.0377175, 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 = {} \[ \int (e x)^m \text{csch}^2\left (a+b x^n\right ) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int (e x)^m \text{csch}^2\left (a+b x^n\right ) \, dx &=\left (x^{-m} (e x)^m\right ) \int x^m \text{csch}^2\left (a+b x^n\right ) \, dx\\ \end{align*}
Mathematica [A] time = 24.3329, size = 0, normalized size = 0. \[ \int (e x)^m \text{csch}^2\left (a+b x^n\right ) \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.13, size = 0, normalized size = 0. \begin{align*} \int{\frac{ \left ( ex \right ) ^{m}}{ \left ( \sinh \left ( a+b{x}^{n} \right ) \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*} -4 \, e^{m}{\left (m - n + 1\right )} \int \frac{x^{m}}{4 \,{\left (b n x^{n} + b n e^{\left (b x^{n} + n \log \left (x\right ) + a\right )}\right )}}\,{d x} + 4 \, e^{m}{\left (m - n + 1\right )} \int -\frac{x^{m}}{4 \,{\left (b n x^{n} - b n e^{\left (b x^{n} + n \log \left (x\right ) + a\right )}\right )}}\,{d x} + \frac{2 \, e^{m} x x^{m}}{b n x^{n} - b n e^{\left (2 \, b x^{n} + n \log \left (x\right ) + 2 \, a\right )}} \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{\left (e x\right )^{m}}{\sinh \left (b x^{n} + a\right )^{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{\left (e x\right )^{m}}{\sinh ^{2}{\left (a + b x^{n} \right )}}\, 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{\left (e x\right )^{m}}{\sinh \left (b x^{n} + a\right )^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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