Optimal. Leaf size=3 \[ \log (\sin (x)) \]
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Rubi [A] time = 0.00, antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, 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*}
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Mathematica [A] time = 0.00, size = 3, normalized size = 1.00 \[ \log (\sin (x)) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.44, size = 11, normalized size = 3.67 \[ \frac {1}{2} \, \log \left (-\frac {1}{2} \, \cos \left (2 \, x\right ) + \frac {1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 4, normalized size = 1.33 \[ \log \left ({\left | \sin \relax (x) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 4, normalized size = 1.33 \[ \ln \left (\sin \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 3, normalized size = 1.00 \[ \log \left (\sin \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 3, normalized size = 1.00 \[ \ln \left (\sin \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 3, normalized size = 1.00 \[ \log {\left (\sin {\relax (x )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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