Optimal. Leaf size=10 \[ \frac{1}{4} \sin ^2\left (x^2\right ) \]
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Rubi [A] time = 0.0071152, antiderivative size = 10, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {3441} \[ \frac{1}{4} \sin ^2\left (x^2\right ) \]
Antiderivative was successfully verified.
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Rule 3441
Rubi steps
\begin{align*} \int x \cos \left (x^2\right ) \sin \left (x^2\right ) \, dx &=\frac{1}{4} \sin ^2\left (x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0024186, size = 10, normalized size = 1. \[ -\frac{1}{4} \cos ^2\left (x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 9, normalized size = 0.9 \begin{align*} -{\frac{ \left ( \cos \left ({x}^{2} \right ) \right ) ^{2}}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.959578, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{4} \, \cos \left (x^{2}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.517447, size = 23, normalized size = 2.3 \begin{align*} -\frac{1}{4} \, \cos \left (x^{2}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.301366, size = 7, normalized size = 0.7 \begin{align*} \frac{\sin ^{2}{\left (x^{2} \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10867, size = 11, normalized size = 1.1 \begin{align*} -\frac{1}{4} \, \cos \left (x^{2}\right )^{2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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