Optimal. Leaf size=6 \[ 4 \sin \left (x^3\right ) \]
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Rubi [A] time = 0.0091064, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333, Rules used = {12, 3380, 2637} \[ 4 \sin \left (x^3\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int 12 x^2 \cos \left (x^3\right ) \, dx &=12 \int x^2 \cos \left (x^3\right ) \, dx\\ &=4 \operatorname{Subst}\left (\int \cos (x) \, dx,x,x^3\right )\\ &=4 \sin \left (x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0016396, size = 6, normalized size = 1. \[ 4 \sin \left (x^3\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 7, normalized size = 1.2 \begin{align*} 4\,\sin \left ({x}^{3} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.962417, size = 8, normalized size = 1.33 \begin{align*} 4 \, \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.03581, size = 16, normalized size = 2.67 \begin{align*} 4 \, \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.296115, size = 5, normalized size = 0.83 \begin{align*} 4 \sin{\left (x^{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06525, size = 8, normalized size = 1.33 \begin{align*} 4 \, \sin \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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