Optimal. Leaf size=9 \[ \frac{1}{2} \log ^2(\tan (x)) \]
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Rubi [A] time = 0.0232566, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {2620, 29, 6686} \[ \frac{1}{2} \log ^2(\tan (x)) \]
Antiderivative was successfully verified.
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Rule 2620
Rule 29
Rule 6686
Rubi steps
\begin{align*} \int \csc (x) \log (\tan (x)) \sec (x) \, dx &=\frac{1}{2} \log ^2(\tan (x))\\ \end{align*}
Mathematica [A] time = 0.0052715, size = 9, normalized size = 1. \[ \frac{1}{2} \log ^2(\tan (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.02, size = 8, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( \tan \left ( x \right ) \right ) \right ) ^{2}}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.932059, size = 9, normalized size = 1. \begin{align*} \frac{1}{2} \, \log \left (\tan \left (x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.03166, size = 35, normalized size = 3.89 \begin{align*} \frac{1}{2} \, \log \left (\frac{\sin \left (x\right )}{\cos \left (x\right )}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\log{\left (\tan{\left (x \right )} \right )}}{\sin{\left (x \right )} \cos{\left (x \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05607, size = 9, normalized size = 1. \begin{align*} \frac{1}{2} \, \log \left (\tan \left (x\right )\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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