Optimal. Leaf size=11 \[ \sin (x) \log (\sin (x))-\sin (x) \]
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Rubi [A] time = 0.0093442, antiderivative size = 11, normalized size of antiderivative = 1., 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 2637
Rule 2554
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*}
Mathematica [A] time = 0.0025112, size = 11, normalized size = 1. \[ \sin (x) \log (\sin (x))-\sin (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 12, normalized size = 1.1 \begin{align*} -\sin \left ( x \right ) +\ln \left ( \sin \left ( x \right ) \right ) \sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00768, size = 15, normalized size = 1.36 \begin{align*} \log \left (\sin \left (x\right )\right ) \sin \left (x\right ) - \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.12528, size = 39, normalized size = 3.55 \begin{align*} \log \left (\sin \left (x\right )\right ) \sin \left (x\right ) - \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.946213, size = 10, normalized size = 0.91 \begin{align*} \log{\left (\sin{\left (x \right )} \right )} \sin{\left (x \right )} - \sin{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17447, size = 15, normalized size = 1.36 \begin{align*} \log \left (\sin \left (x\right )\right ) \sin \left (x\right ) - \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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