Optimal. Leaf size=9 \[ \frac {1}{4} \log ^2(\tanh (x)) \]
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Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, 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*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ \frac {1}{4} \log ^2(\tanh (x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 12, normalized size = 1.33 \[ \frac {1}{4} \, \log \left (\frac {\sinh \relax (x)}{\cosh \relax (x)}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 20, normalized size = 2.22 \[ \frac {1}{4} \, \log \left (\frac {e^{\left (2 \, x\right )} - 1}{e^{\left (2 \, x\right )} + 1}\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 8, normalized size = 0.89 \[ \frac {\ln \left (\tanh \relax (x )\right )^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 7, normalized size = 0.78 \[ \frac {1}{4} \, \log \left (\tanh \relax (x)\right )^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.67, size = 21, normalized size = 2.33 \[ \frac {{\left (\ln \left ({\mathrm {e}}^{2\,x}-1\right )-\ln \left ({\mathrm {e}}^{2\,x}+1\right )\right )}^2}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \log {\left (\tanh {\relax (x )} \right )} \operatorname {csch}{\left (2 x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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