Optimal. Leaf size=3 \[ \log (\sin (x)) \]
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Rubi [B] time = 0.02, 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 31
Rule 2667
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*}
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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 = 0.97, 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 [B] time = 0.41, size = 11, normalized size = 3.67 \[ \frac {1}{2} \, \log \left (-\cos \left (2 \, x\right ) + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.02, size = 12, normalized size = 4.00 \[ \frac {\ln \left (1-\cos \left (2 x \right )\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.31, size = 9, normalized size = 3.00 \[ \frac {1}{2} \, \log \left (\cos \left (2 \, x\right ) - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 9, normalized size = 3.00 \[ \frac {\ln \left (-{\sin \relax (x)}^2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.11, size = 8, normalized size = 2.67 \[ \frac {\log {\left (\cos {\left (2 x \right )} - 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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