Optimal. Leaf size=27 \[ \text {ArcSin}(\sin (x))+\log (\text {ArcSin}(\sin (x))) \left (-\text {ArcSin}(\sin (x))+x \sqrt {\cos ^2(x)} \sec (x)\right ) \]
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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}{\text {ArcSin}(\sin (x))} \, dx \end {gather*}
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 = 0.36, size = 28, normalized size = 1.04 \begin {gather*} -\text {ArcSin}(\sin (x)) (-1+\log (\text {ArcSin}(\sin (x))))+x \sqrt {\cos ^2(x)} \log (\text {ArcSin}(\sin (x))) \sec (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.10, size = 0, normalized size = 0.00 \[\int \frac {x}{\arcsin \left (\sin \left (x \right )\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.48, 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 = 3.30, size = 3, normalized size = 0.11 \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 {asin}{\left (\sin {\left (x \right )} \right )}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {x}{\mathrm {asin}\left (\sin \left (x\right )\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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