Optimal. Leaf size=9 \[ \frac{1}{2} \log ^2(\cosh (x)) \]
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Rubi [A] time = 0.0154075, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 3, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3475, 4341, 2301} \[ \frac{1}{2} \log ^2(\cosh (x)) \]
Antiderivative was successfully verified.
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Rule 3475
Rule 4341
Rule 2301
Rubi steps
\begin{align*} \int \log (\cosh (x)) \tanh (x) \, dx &=\operatorname{Subst}\left (\int \frac{\log (x)}{x} \, dx,x,\cosh (x)\right )\\ &=\frac{1}{2} \log ^2(\cosh (x))\\ \end{align*}
Mathematica [A] time = 0.003558, size = 9, normalized size = 1. \[ \frac{1}{2} \log ^2(\cosh (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 8, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( \cosh \left ( x \right ) \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.941918, size = 9, normalized size = 1. \begin{align*} \frac{1}{2} \, \log \left (\cosh \left (x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.39197, size = 27, normalized size = 3. \begin{align*} \frac{1}{2} \, \log \left (\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 (\cosh{\left (x \right )} \right )} \tanh{\left (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 \log \left (\cosh \left (x\right )\right ) \tanh \left (x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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