Optimal. Leaf size=4 \[ \cosh ^x(x) \]
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Rubi [A] time = 0.139696, antiderivative size = 4, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {6742, 2553} \[ \cosh ^x(x) \]
Antiderivative was successfully verified.
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Rule 6742
Rule 2553
Rubi steps
\begin{align*} \int \cosh ^x(x) (\log (\cosh (x))+x \tanh (x)) \, dx &=\int \left (\cosh ^x(x) \log (\cosh (x))+x \cosh ^{-1+x}(x) \sinh (x)\right ) \, dx\\ &=\int \cosh ^x(x) \log (\cosh (x)) \, dx+\int x \cosh ^{-1+x}(x) \sinh (x) \, dx\\ &=\cosh ^x(x)\\ \end{align*}
Mathematica [A] time = 0.0707959, size = 4, normalized size = 1. \[ \cosh ^x(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.02, size = 5, normalized size = 1.3 \begin{align*} \left ( \cosh \left ( x \right ) \right ) ^{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 2.23277, size = 28, normalized size = 7. \begin{align*} e^{\left (-x^{2} - x \log \left (2\right ) + x \log \left (e^{\left (2 \, x\right )} + 1\right )\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.07264, size = 61, normalized size = 15.25 \begin{align*} \cosh \left (x \log \left (\cosh \left (x\right )\right )\right ) + \sinh \left (x \log \left (\cosh \left (x\right )\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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{\left (x \tanh \left (x\right ) + \log \left (\cosh \left (x\right )\right )\right )} \cosh \left (x\right )^{x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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