Optimal. Leaf size=6 \[ \sin \left (x^3+7\right ) \]
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Rubi [A] time = 0.0128978, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273, Rules used = {12, 3380, 2637} \[ \sin \left (x^3+7\right ) \]
Antiderivative was successfully verified.
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Rule 12
Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int 3 x^2 \cos \left (7+x^3\right ) \, dx &=3 \int x^2 \cos \left (7+x^3\right ) \, dx\\ &=\operatorname{Subst}\left (\int \cos (7+x) \, dx,x,x^3\right )\\ &=\sin \left (7+x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0035533, size = 6, normalized size = 1. \[ \sin \left (x^3+7\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 7, normalized size = 1.2 \begin{align*} \sin \left ({x}^{3}+7 \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963454, size = 8, normalized size = 1.33 \begin{align*} \sin \left (x^{3} + 7\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.02274, size = 19, normalized size = 3.17 \begin{align*} \sin \left (x^{3} + 7\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.302243, size = 5, normalized size = 0.83 \begin{align*} \sin{\left (x^{3} + 7 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09105, size = 8, normalized size = 1.33 \begin{align*} \sin \left (x^{3} + 7\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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