Optimal. Leaf size=10 \[ \cos (x)-\cos (x) \log (\cos (x)) \]
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Rubi [A] time = 0.0078169, antiderivative size = 10, 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 = {2638, 2554} \[ \cos (x)-\cos (x) \log (\cos (x)) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 2554
Rubi steps
\begin{align*} \int \log (\cos (x)) \sin (x) \, dx &=-\cos (x) \log (\cos (x))-\int \sin (x) \, dx\\ &=\cos (x)-\cos (x) \log (\cos (x))\\ \end{align*}
Mathematica [A] time = 0.007417, size = 10, normalized size = 1. \[ \cos (x)-\cos (x) \log (\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 11, normalized size = 1.1 \begin{align*} \cos \left ( x \right ) -\cos \left ( x \right ) \ln \left ( \cos \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.993473, size = 14, normalized size = 1.4 \begin{align*} -\cos \left (x\right ) \log \left (\cos \left (x\right )\right ) + \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.2622, size = 41, normalized size = 4.1 \begin{align*} -\cos \left (x\right ) \log \left (\cos \left (x\right )\right ) + \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.947031, size = 10, normalized size = 1. \begin{align*} - \log{\left (\cos{\left (x \right )} \right )} \cos{\left (x \right )} + \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19456, size = 14, normalized size = 1.4 \begin{align*} -\cos \left (x\right ) \log \left (\cos \left (x\right )\right ) + \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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