Optimal. Leaf size=7 \[ x \sin (x)+\cos (x) \]
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Rubi [A] time = 0.008778, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {3296, 2638} \[ x \sin (x)+\cos (x) \]
Antiderivative was successfully verified.
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Rule 3296
Rule 2638
Rubi steps
\begin{align*} \int x \cos (x) \, dx &=x \sin (x)-\int \sin (x) \, dx\\ &=\cos (x)+x \sin (x)\\ \end{align*}
Mathematica [A] time = 0.0017807, size = 7, normalized size = 1. \[ x \sin (x)+\cos (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 8, normalized size = 1.1 \begin{align*} \cos \left ( x \right ) +x\sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.938032, size = 9, normalized size = 1.29 \begin{align*} x \sin \left (x\right ) + \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.90055, size = 26, normalized size = 3.71 \begin{align*} x \sin \left (x\right ) + \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.164299, size = 7, normalized size = 1. \begin{align*} x \sin{\left (x \right )} + \cos{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04116, size = 9, normalized size = 1.29 \begin{align*} x \sin \left (x\right ) + \cos \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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