Optimal. Leaf size=28 \[ x^{-m} (e x)^m \text {Int}\left (x^m \text {csch}^2\left (a+b x^n\right ),x\right ) \]
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Rubi [A]
time = 0.03, 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 = {}
\begin {gather*} \int (e x)^m \text {csch}^2\left (a+b x^n\right ) \, dx \end {gather*}
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*}
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Mathematica [A]
time = 16.54, size = 0, normalized size = 0.00 \begin {gather*} \int (e x)^m \text {csch}^2\left (a+b x^n\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.52, size = 0, normalized size = 0.00 \[\int \frac {\left (e x \right )^{m}}{\sinh \left (a +b \,x^{n}\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (e x\right )^{m}}{\sinh ^{2}{\left (a + b x^{n} \right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [A]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\left (e\,x\right )}^m}{{\mathrm {sinh}\left (a+b\,x^n\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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