Optimal. Leaf size=5 \[ -\log (\cos (x)) \]
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Rubi [B] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 2.20, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {2667, 31} \[ -\frac {1}{2} \log (\cos (2 x)+1) \]
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 &=-\left (\frac {1}{2} \operatorname {Subst}\left (\int \frac {1}{1+x} \, dx,x,\cos (2 x)\right )\right )\\ &=-\frac {1}{2} \log (1+\cos (2 x))\\ \end {align*}
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Mathematica [A] time = 0.00, size = 5, normalized size = 1.00 \[ -\log (\cos (x)) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.88, size = 11, normalized size = 2.20 \[ -\frac {1}{2} \, \log \left (\frac {1}{2} \, \cos \left (2 \, x\right ) + \frac {1}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 9, normalized size = 1.80 \[ -\frac {1}{2} \, \log \left (\cos \left (2 \, x\right ) + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 2.00 \[ -\frac {\ln \left (1+\cos \left (2 x \right )\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 9, normalized size = 1.80 \[ -\frac {1}{2} \, \log \left (\cos \left (2 \, x\right ) + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.26, size = 7, normalized size = 1.40 \[ -\frac {\ln \left ({\cos \relax (x)}^2\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 10, normalized size = 2.00 \[ - \frac {\log {\left (\cos {\left (2 x \right )} + 1 \right )}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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