Optimal. Leaf size=6 \[ x-\cos (x) \]
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Rubi [A] time = 0.0106472, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {3161, 2638} \[ x-\cos (x) \]
Antiderivative was successfully verified.
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Rule 3161
Rule 2638
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*}
Mathematica [A] time = 0.0015746, size = 6, normalized size = 1. \[ x-\cos (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.031, size = 7, normalized size = 1.2 \begin{align*} x-\cos \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.952995, size = 8, normalized size = 1.33 \begin{align*} x - \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.31247, size = 16, normalized size = 2.67 \begin{align*} x - \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.80056, size = 3, normalized size = 0.5 \begin{align*} x - \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.11234, size = 19, normalized size = 3.17 \begin{align*} x - \frac{2}{\tan \left (\frac{1}{2} \, x\right )^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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