Optimal. Leaf size=9 \[ \frac{1}{4} \log ^2(\tanh (x)) \]
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Rubi [A] time = 0.0243586, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {3770, 6686} \[ \frac{1}{4} \log ^2(\tanh (x)) \]
Antiderivative was successfully verified.
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Rule 3770
Rule 6686
Rubi steps
\begin{align*} \int \text{csch}(2 x) \log (\tanh (x)) \, dx &=\frac{1}{4} \log ^2(\tanh (x))\\ \end{align*}
Mathematica [A] time = 0.0090192, size = 9, normalized size = 1. \[ \frac{1}{4} \log ^2(\tanh (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.015, size = 8, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( \tanh \left ( x \right ) \right ) \right ) ^{2}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01263, size = 9, normalized size = 1. \begin{align*} \frac{1}{4} \, \log \left (\tanh \left (x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.11135, size = 38, normalized size = 4.22 \begin{align*} \frac{1}{4} \, \log \left (\frac{\sinh \left (x\right )}{\cosh \left (x\right )}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \log{\left (\tanh{\left (x \right )} \right )} \operatorname{csch}{\left (2 x \right )}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \operatorname{csch}\left (2 \, x\right ) \log \left (\tanh \left (x\right )\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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