Optimal. Leaf size=27 \[ \sin ^{-1}(\sin (x))+\log \left (\sin ^{-1}(\sin (x))\right ) \left (x \sqrt{\cos ^2(x)} \sec (x)-\sin ^{-1}(\sin (x))\right ) \]
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Rubi [F] time = 0.0387074, 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 = {} \[ \int \frac{x}{\sin ^{-1}(\sin (x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{x}{\sin ^{-1}(\sin (x))} \, dx &=\int \frac{x}{\sin ^{-1}(\sin (x))} \, dx\\ \end{align*}
Mathematica [A] time = 0.526656, size = 28, normalized size = 1.04 \[ x \sqrt{\cos ^2(x)} \sec (x) \log \left (\sin ^{-1}(\sin (x))\right )-\sin ^{-1}(\sin (x)) \left (\log \left (\sin ^{-1}(\sin (x))\right )-1\right ) \]
Antiderivative was successfully verified.
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Maple [F] time = 0.073, size = 0, normalized size = 0. \begin{align*} \int{\frac{x}{\arcsin \left ( \sin \left ( x \right ) \right ) }}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.51935, size = 1, normalized size = 0.04 \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7056, size = 5, normalized size = 0.19 \begin{align*} -x \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 \frac{x}{\operatorname{asin}{\left (\sin{\left (x \right )} \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15805, size = 1, normalized size = 0.04 \begin{align*} x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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