Optimal. Leaf size=27 \[ \sinh ^{-1}(\sinh (x))+\log \left (\sinh ^{-1}(\sinh (x))\right ) \left (x \sqrt{\cosh ^2(x)} \text{sech}(x)-\sinh ^{-1}(\sinh (x))\right ) \]
[Out]
________________________________________________________________________________________
Rubi [F] time = 0.0393858, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{x}{\sinh ^{-1}(\sinh (x))} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin{align*} \int \frac{x}{\sinh ^{-1}(\sinh (x))} \, dx &=\int \frac{x}{\sinh ^{-1}(\sinh (x))} \, dx\\ \end{align*}
Mathematica [A] time = 0.519165, size = 28, normalized size = 1.04 \[ x \sqrt{\cosh ^2(x)} \text{sech}(x) \log \left (\sinh ^{-1}(\sinh (x))\right )-\sinh ^{-1}(\sinh (x)) \left (\log \left (\sinh ^{-1}(\sinh (x))\right )-1\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [F] time = 0.041, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{{\it Arcsinh} \left ( \sinh \left ( x \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.81796, size = 1, normalized size = 0.04 \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 2.20826, size = 4, normalized size = 0.15 \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{x}{\operatorname{asinh}{\left (\sinh{\left (x \right )} \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.35227, size = 1, normalized size = 0.04 \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]