Optimal. Leaf size=10 \[ -\cos (x)-\log (\cos (x)) \]
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Rubi [A] time = 0.0049923, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.4, Rules used = {2638, 3475} \[ -\cos (x)-\log (\cos (x)) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3475
Rubi steps
\begin{align*} \int (\sin (x)+\tan (x)) \, dx &=\int \sin (x) \, dx+\int \tan (x) \, dx\\ &=-\cos (x)-\log (\cos (x))\\ \end{align*}
Mathematica [A] time = 0.0029032, size = 10, normalized size = 1. \[ -\cos (x)-\log (\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 1.1 \begin{align*} -\cos \left ( x \right ) -\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 = 0.982502, size = 11, normalized size = 1.1 \begin{align*} -\cos \left (x\right ) + \log \left (\sec \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.26663, size = 32, normalized size = 3.2 \begin{align*} -\cos \left (x\right ) - \log \left (-\cos \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.065387, size = 8, normalized size = 0.8 \begin{align*} - \log{\left (\cos{\left (x \right )} \right )} - \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12834, size = 15, normalized size = 1.5 \begin{align*} -\cos \left (x\right ) - \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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