Optimal. Leaf size=3 \[ \log (\sin (x)) \]
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Rubi [B] time = 0.0216338, antiderivative size = 13, normalized size of antiderivative = 4.33, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.133, Rules used = {2667, 31} \[ \frac{1}{2} \log (1-\cos (2 x)) \]
Antiderivative was successfully verified.
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Rule 2667
Rule 31
Rubi steps
\begin{align*} \int \frac{\sin (2 x)}{1-\cos (2 x)} \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \frac{1}{1+x} \, dx,x,-\cos (2 x)\right )\\ &=\frac{1}{2} \log (1-\cos (2 x))\\ \end{align*}
Mathematica [A] time = 0.0042299, size = 3, normalized size = 1. \[ \log (\sin (x)) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.033, size = 12, normalized size = 4. \begin{align*}{\frac{\ln \left ( 1-\cos \left ( 2\,x \right ) \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] time = 1.12463, size = 12, normalized size = 4. \begin{align*} \frac{1}{2} \, \log \left (\cos \left (2 \, x\right ) - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.60334, 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 [B] time = 0.143573, size = 8, normalized size = 2.67 \begin{align*} \frac{\log{\left (\cos{\left (2 x \right )} - 1 \right )}}{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.16883, size = 15, normalized size = 5. \begin{align*} \frac{1}{2} \, \log \left (-\cos \left (2 \, x\right ) + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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