Optimal. Leaf size=11 \[ \sin (x) \log (\sin (x))-\sin (x) \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2637, 2554} \[ \sin (x) \log (\sin (x))-\sin (x) \]
Antiderivative was successfully verified.
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Rule 2554
Rule 2637
Rubi steps
\begin {align*} \int \cos (x) \log (\sin (x)) \, dx &=\log (\sin (x)) \sin (x)-\int \cos (x) \, dx\\ &=-\sin (x)+\log (\sin (x)) \sin (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ \sin (x) \log (\sin (x))-\sin (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 11, normalized size = 1.00 \[ \log \left (\sin \relax (x)\right ) \sin \relax (x) - \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 11, normalized size = 1.00 \[ \log \left (\sin \relax (x)\right ) \sin \relax (x) - \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.19, size = 12, normalized size = 1.09 \[ \ln \left (\sin \relax (x )\right ) \sin \relax (x )-\sin \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 11, normalized size = 1.00 \[ \log \left (\sin \relax (x)\right ) \sin \relax (x) - \sin \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.41, size = 8, normalized size = 0.73 \[ \sin \relax (x)\,\left (\ln \left (\sin \relax (x)\right )-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.87, size = 10, normalized size = 0.91 \[ \log {\left (\sin {\relax (x )} \right )} \sin {\relax (x )} - \sin {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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