Optimal. Leaf size=6 \[ x-\cos (x) \]
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Rubi [A] time = 0.01, antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3161, 2638} \[ x-\cos (x) \]
Antiderivative was successfully verified.
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Rule 2638
Rule 3161
Rubi steps
\begin {align*} \int \cos (x) (\sec (x)+\tan (x)) \, dx &=\int (1+\sin (x)) \, dx\\ &=x+\int \sin (x) \, dx\\ &=x-\cos (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 6, normalized size = 1.00 \[ x-\cos (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 6, normalized size = 1.00 \[ x - \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.13, size = 14, normalized size = 2.33 \[ x - \frac {2}{\tan \left (\frac {1}{2} \, x\right )^{2} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 7, normalized size = 1.17 \[ x -\cos \relax (x ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 6, normalized size = 1.00 \[ x - \cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.95, size = 6, normalized size = 1.00 \[ x-\cos \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.13, size = 3, normalized size = 0.50 \[ x - \cos {\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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