Optimal. Leaf size=6 \[ -\log (\log (\cos (x))) \]
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Rubi [A] time = 0.0215558, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {4339, 2302, 29} \[ -\log (\log (\cos (x))) \]
Antiderivative was successfully verified.
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Rule 4339
Rule 2302
Rule 29
Rubi steps
\begin{align*} \int \frac{\tan (x)}{\log (\cos (x))} \, dx &=-\operatorname{Subst}\left (\int \frac{1}{x \log (x)} \, dx,x,\cos (x)\right )\\ &=-\operatorname{Subst}\left (\int \frac{1}{x} \, dx,x,\log (\cos (x))\right )\\ &=-\log (\log (\cos (x)))\\ \end{align*}
Mathematica [A] time = 0.0083844, size = 6, normalized size = 1. \[ -\log (\log (\cos (x))) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 7, normalized size = 1.2 \begin{align*} -\ln \left ( \ln \left ( \cos \left ( x \right ) \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.998179, size = 8, normalized size = 1.33 \begin{align*} -\log \left (\log \left (\cos \left (x\right )\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.1658, size = 26, normalized size = 4.33 \begin{align*} -\log \left (\log \left (\cos \left (x\right )\right )\right ) \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{\tan{\left (x \right )}}{\log{\left (\cos{\left (x \right )} \right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.3045, size = 9, normalized size = 1.5 \begin{align*} -\log \left ({\left | \log \left (\cos \left (x\right )\right ) \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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