Optimal. Leaf size=10 \[ -\cos \left (\frac{x^2}{2}\right ) \]
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Rubi [A] time = 0.0077483, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {3379, 2638} \[ -\cos \left (\frac{x^2}{2}\right ) \]
Antiderivative was successfully verified.
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Rule 3379
Rule 2638
Rubi steps
\begin{align*} \int x \sin \left (\frac{x^2}{2}\right ) \, dx &=\frac{1}{2} \operatorname{Subst}\left (\int \sin \left (\frac{x}{2}\right ) \, dx,x,x^2\right )\\ &=-\cos \left (\frac{x^2}{2}\right )\\ \end{align*}
Mathematica [A] time = 0.0104019, size = 10, normalized size = 1. \[ -\cos \left (\frac{x^2}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.9 \begin{align*} -\cos \left ({\frac{{x}^{2}}{2}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956508, size = 11, normalized size = 1.1 \begin{align*} -\cos \left (\frac{1}{2} \, x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.8549, size = 20, normalized size = 2. \begin{align*} -\cos \left (\frac{1}{2} \, x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.163217, size = 7, normalized size = 0.7 \begin{align*} - \cos{\left (\frac{x^{2}}{2} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.08726, size = 11, normalized size = 1.1 \begin{align*} -\cos \left (\frac{1}{2} \, x^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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