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 = 0.04, 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 = {} \[ \int \frac {x}{\sin ^{-1}(\sin (x))} \, dx \]
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*}
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Mathematica [A] time = 0.65, 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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fricas [A] time = 0.43, size = 3, normalized size = 0.11 \[ -x \]
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 \[ \mathit {sage}_{0} x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.20, size = 0, normalized size = 0.00 \[ \int \frac {x}{\arcsin \left (\sin \relax (x )\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 1, normalized size = 0.04 \[ x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x}{\mathrm {asin}\left (\sin \relax (x)\right )} \,d x \]
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 \[ \int \frac {x}{\operatorname {asin}{\left (\sin {\relax (x )} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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