Optimal. Leaf size=8 \[ \sin (x)-x \cos (x) \]
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Rubi [A] time = 0.0085667, antiderivative size = 8, 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, 2637} \[ \sin (x)-x \cos (x) \]
Antiderivative was successfully verified.
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Rule 3296
Rule 2637
Rubi steps
\begin{align*} \int x \sin (x) \, dx &=-x \cos (x)+\int \cos (x) \, dx\\ &=-x \cos (x)+\sin (x)\\ \end{align*}
Mathematica [A] time = 0.0020667, size = 8, normalized size = 1. \[ \sin (x)-x \cos (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 9, normalized size = 1.1 \begin{align*} -x\cos \left ( x \right ) +\sin \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.933074, size = 11, normalized size = 1.38 \begin{align*} -x \cos \left (x\right ) + \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.90965, size = 27, normalized size = 3.38 \begin{align*} -x \cos \left (x\right ) + \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.166954, size = 7, normalized size = 0.88 \begin{align*} - x \cos{\left (x \right )} + \sin{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04858, size = 11, normalized size = 1.38 \begin{align*} -x \cos \left (x\right ) + \sin \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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