Optimal. Leaf size=6 \[ \log (\sin (x)+\cos (x)) \]
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Rubi [A] time = 0.0225762, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067, Rules used = {3133} \[ \log (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
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Rule 3133
Rubi steps
\begin{align*} \int \frac{\cos (x)-\sin (x)}{\cos (x)+\sin (x)} \, dx &=\log (\cos (x)+\sin (x))\\ \end{align*}
Mathematica [A] time = 0.0262814, size = 6, normalized size = 1. \[ \log (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.022, size = 7, normalized size = 1.2 \begin{align*} \ln \left ( \cos \left ( x \right ) +\sin \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.989582, size = 8, normalized size = 1.33 \begin{align*} \log \left (\cos \left (x\right ) + \sin \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.88883, size = 41, normalized size = 6.83 \begin{align*} \frac{1}{2} \, \log \left (2 \, \cos \left (x\right ) \sin \left (x\right ) + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.138288, size = 7, normalized size = 1.17 \begin{align*} \log{\left (\sin{\left (x \right )} + \cos{\left (x \right )} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.14849, size = 22, normalized size = 3.67 \begin{align*} -\frac{1}{2} \, \log \left (\tan \left (x\right )^{2} + 1\right ) + \log \left ({\left | \tan \left (x\right ) + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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