Optimal. Leaf size=3 \[ \log (\sin (x)) \]
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Rubi [A] time = 0.001929, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3475} \[ \log (\sin (x)) \]
Antiderivative was successfully verified.
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Rule 3475
Rubi steps
\begin{align*} \int \cot (x) \, dx &=\log (\sin (x))\\ \end{align*}
Mathematica [A] time = 0.0020149, size = 3, normalized size = 1. \[ \log (\sin (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 4, normalized size = 1.3 \begin{align*} \ln \left ( \sin \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926513, size = 4, normalized size = 1.33 \begin{align*} \log \left (\sin \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.03097, size = 41, normalized size = 13.67 \begin{align*} \frac{1}{2} \, \log \left (-\frac{1}{2} \, \cos \left (2 \, x\right ) + \frac{1}{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.058282, size = 3, normalized size = 1. \begin{align*} \log{\left (\sin{\left (x \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.05605, size = 15, normalized size = 5. \begin{align*} \frac{1}{2} \, \log \left (-\cos \left (x\right )^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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