Optimal. Leaf size=14 \[ \frac{1}{7} \sin ^{\frac{7}{4}}\left (2 x^2\right ) \]
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Rubi [A] time = 0.0131242, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {3441} \[ \frac{1}{7} \sin ^{\frac{7}{4}}\left (2 x^2\right ) \]
Antiderivative was successfully verified.
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Rule 3441
Rubi steps
\begin{align*} \int x \cos \left (2 x^2\right ) \sin ^{\frac{3}{4}}\left (2 x^2\right ) \, dx &=\frac{1}{7} \sin ^{\frac{7}{4}}\left (2 x^2\right )\\ \end{align*}
Mathematica [A] time = 0.0065822, size = 14, normalized size = 1. \[ \frac{1}{7} \sin ^{\frac{7}{4}}\left (2 x^2\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 11, normalized size = 0.8 \begin{align*}{\frac{1}{7} \left ( \sin \left ( 2\,{x}^{2} \right ) \right ) ^{{\frac{7}{4}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.953281, size = 14, normalized size = 1. \begin{align*} \frac{1}{7} \, \sin \left (2 \, x^{2}\right )^{\frac{7}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.15446, size = 30, normalized size = 2.14 \begin{align*} \frac{1}{7} \, \sin \left (2 \, x^{2}\right )^{\frac{7}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 120.493, size = 10, normalized size = 0.71 \begin{align*} \frac{\sin ^{\frac{7}{4}}{\left (2 x^{2} \right )}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09325, size = 14, normalized size = 1. \begin{align*} \frac{1}{7} \, \sin \left (2 \, x^{2}\right )^{\frac{7}{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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