Optimal. Leaf size=6 \[ -\log (\log (\cos (x))) \]
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Rubi [A] time = 0.02, antiderivative size = 6, normalized size of antiderivative = 1.00, 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 29
Rule 2302
Rule 4339
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*}
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Mathematica [A] time = 0.01, size = 6, normalized size = 1.00 \[ -\log (\log (\cos (x))) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 6, normalized size = 1.00 \[ -\log \left (\log \left (\cos \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 7, normalized size = 1.17 \[ -\log \left ({\left | \log \left (\cos \relax (x)\right ) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 7, normalized size = 1.17 \[ -\ln \left (\ln \left (\cos \relax (x )\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 6, normalized size = 1.00 \[ -\log \left (\log \left (\cos \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 6, normalized size = 1.00 \[ -\ln \left (\ln \left (\cos \relax (x)\right )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\tan {\relax (x )}}{\log {\left (\cos {\relax (x )} \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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