Optimal. Leaf size=5 \[ -\log (\cos (x)) \]
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Rubi [A] time = 0.0020498, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 2, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3475} \[ -\log (\cos (x)) \]
Antiderivative was successfully verified.
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Rule 3475
Rubi steps
\begin{align*} \int \tan (x) \, dx &=-\log (\cos (x))\\ \end{align*}
Mathematica [A] time = 0.0022787, size = 5, normalized size = 1. \[ -\log (\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 6, normalized size = 1.2 \begin{align*} -\ln \left ( \cos \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.928878, size = 4, normalized size = 0.8 \begin{align*} \log \left (\sec \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.00598, size = 38, normalized size = 7.6 \begin{align*} -\frac{1}{2} \, \log \left (\frac{1}{\tan \left (x\right )^{2} + 1}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.05756, size = 5, normalized size = 1. \begin{align*} - \log{\left (\cos{\left (x \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.05968, size = 8, normalized size = 1.6 \begin{align*} -\log \left ({\left | \cos \left (x\right ) \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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