Optimal. Leaf size=8 \[ -\log (\sin (x)+\cos (x)) \]
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Rubi [A] time = 0.02, antiderivative size = 8, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.02, size = 8, normalized size = 1.00 \[ -\log (\sin (x)+\cos (x)) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 11, normalized size = 1.38 \[ -\frac {1}{2} \, \log \left (2 \, \cos \relax (x) \sin \relax (x) + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.98, size = 18, normalized size = 2.25 \[ \frac {1}{2} \, \log \left (\tan \relax (x)^{2} + 1\right ) - \log \left ({\left | \tan \relax (x) + 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 9, normalized size = 1.12 \[ -\ln \left (\cos \relax (x )+\sin \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 8, normalized size = 1.00 \[ -\log \left (\cos \relax (x) + \sin \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.42, size = 32, normalized size = 4.00 \[ -2\,\mathrm {atanh}\left (\frac {128\,\mathrm {tan}\left (\frac {x}{2}\right )+128}{16\,{\mathrm {tan}\left (\frac {x}{2}\right )}^2+32\,\mathrm {tan}\left (\frac {x}{2}\right )+48}-3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 8, normalized size = 1.00 \[ - \log {\left (\sin {\relax (x )} + \cos {\relax (x )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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