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 = 0.43, size = 16, normalized size = 5.33 \[ \frac {1}{2} \, \log \left (\frac {\tan \relax (x)^{2}}{\tan \relax (x)^{2} + 1}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.13, size = 17, normalized size = 5.67 \[ -\frac {1}{2} \, \log \left (\tan \relax (x)^{2} + 1\right ) + \frac {1}{2} \, \log \left (\tan \relax (x)^{2}\right ) \]
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 = 0.42, 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 = 0.20, size = 13, normalized size = 4.33 \[ \ln \left (\mathrm {tan}\relax (x)\right )-\frac {\ln \left ({\mathrm {tan}\relax (x)}^2+1\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, 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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