Optimal. Leaf size=4 \[ \cosh ^x(x) \]
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Rubi [A] time = 0.14, antiderivative size = 4, normalized size of antiderivative = 1.00, 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 2553
Rule 6742
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*}
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Mathematica [A] time = 0.08, size = 4, normalized size = 1.00 \[ \cosh ^x(x) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.41, size = 13, normalized size = 3.25 \[ \cosh \left (x \log \left (\cosh \relax (x)\right )\right ) + \sinh \left (x \log \left (\cosh \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (x \tanh \relax (x) + \log \left (\cosh \relax (x)\right )\right )} \cosh \relax (x)^{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 5, normalized size = 1.25 \[ \cosh ^{x}\relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.62, size = 21, normalized size = 5.25 \[ e^{\left (-x^{2} - x \log \relax (2) + x \log \left (e^{\left (2 \, x\right )} + 1\right )\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.95, size = 4, normalized size = 1.00 \[ {\mathrm {cosh}\relax (x)}^x \]
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 \[ \int \left (x \tanh {\relax (x )} + \log {\left (\cosh {\relax (x )} \right )}\right ) \cosh ^{x}{\relax (x )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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