Optimal. Leaf size=8 \[ -\log (\sin (x)+\cos (x)) \]
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Rubi [A] time = 0.0225275, antiderivative size = 8, 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 = 0.0233293, size = 8, normalized size = 1. \[ -\log (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.029, size = 9, normalized size = 1.1 \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 = 0.953654, size = 11, normalized size = 1.38 \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 = 2.05828, size = 42, normalized size = 5.25 \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 = 0.129102, size = 8, normalized size = 1. \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 = 1.08499, size = 24, normalized size = 3. \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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