Optimal. Leaf size=27 \[ \sinh ^{-1}(\sinh (x))+\log \left (\sinh ^{-1}(\sinh (x))\right ) \left (-\sinh ^{-1}(\sinh (x))+x \sqrt {\cosh ^2(x)} \text {sech}(x)\right ) \]
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Rubi [F]
time = 0.03, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {x}{\sinh ^{-1}(\sinh (x))} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x}{\sinh ^{-1}(\sinh (x))} \, dx &=\int \frac {x}{\sinh ^{-1}(\sinh (x))} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.36, size = 28, normalized size = 1.04 \begin {gather*} -\sinh ^{-1}(\sinh (x)) \left (-1+\log \left (\sinh ^{-1}(\sinh (x))\right )\right )+x \sqrt {\cosh ^2(x)} \log \left (\sinh ^{-1}(\sinh (x))\right ) \text {sech}(x) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.82, size = 0, normalized size = 0.00 \[\int \frac {x}{\arcsinh \left (\sinh \left (x \right )\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.49, size = 1, normalized size = 0.04 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 1, normalized size = 0.04 \begin {gather*} x \end {gather*}
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 \begin {gather*} \int \frac {x}{\operatorname {asinh}{\left (\sinh {\left (x \right )} \right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 1, normalized size = 0.04 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.22, size = 1, normalized size = 0.04 \begin {gather*} x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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