Optimal. Leaf size=10 \[ \frac{1}{12} \sin \left (4 x^3\right ) \]
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Rubi [A] time = 0.0121073, 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 = {3380, 2637} \[ \frac{1}{12} \sin \left (4 x^3\right ) \]
Antiderivative was successfully verified.
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Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int x^2 \cos \left (4 x^3\right ) \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int \cos (4 x) \, dx,x,x^3\right )\\ &=\frac{1}{12} \sin \left (4 x^3\right )\\ \end{align*}
Mathematica [A] time = 0.003212, size = 10, normalized size = 1. \[ \frac{1}{12} \sin \left (4 x^3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 9, normalized size = 0.9 \begin{align*}{\frac{\sin \left ( 4\,{x}^{3} \right ) }{12}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.967451, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{12} \, \sin \left (4 \, x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99023, size = 23, normalized size = 2.3 \begin{align*} \frac{1}{12} \, \sin \left (4 \, x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.293403, size = 7, normalized size = 0.7 \begin{align*} \frac{\sin{\left (4 x^{3} \right )}}{12} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.1051, size = 11, normalized size = 1.1 \begin{align*} \frac{1}{12} \, \sin \left (4 \, x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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