Optimal. Leaf size=20 \[ \frac{1}{3} x^3 \sin \left (x^3\right )+\frac{\cos \left (x^3\right )}{3} \]
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Rubi [A] time = 0.0160509, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375, Rules used = {3380, 3296, 2638} \[ \frac{1}{3} x^3 \sin \left (x^3\right )+\frac{\cos \left (x^3\right )}{3} \]
Antiderivative was successfully verified.
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Rule 3380
Rule 3296
Rule 2638
Rubi steps
\begin{align*} \int x^5 \cos \left (x^3\right ) \, dx &=\frac{1}{3} \operatorname{Subst}\left (\int x \cos (x) \, dx,x,x^3\right )\\ &=\frac{1}{3} x^3 \sin \left (x^3\right )-\frac{1}{3} \operatorname{Subst}\left (\int \sin (x) \, dx,x,x^3\right )\\ &=\frac{\cos \left (x^3\right )}{3}+\frac{1}{3} x^3 \sin \left (x^3\right )\\ \end{align*}
Mathematica [A] time = 0.0087507, size = 20, normalized size = 1. \[ \frac{1}{3} x^3 \sin \left (x^3\right )+\frac{\cos \left (x^3\right )}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 17, normalized size = 0.9 \begin{align*}{\frac{\cos \left ({x}^{3} \right ) }{3}}+{\frac{{x}^{3}\sin \left ({x}^{3} \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.939193, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{3} \, x^{3} \sin \left (x^{3}\right ) + \frac{1}{3} \, \cos \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.30663, size = 45, normalized size = 2.25 \begin{align*} \frac{1}{3} \, x^{3} \sin \left (x^{3}\right ) + \frac{1}{3} \, \cos \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.85221, size = 15, normalized size = 0.75 \begin{align*} \frac{x^{3} \sin{\left (x^{3} \right )}}{3} + \frac{\cos{\left (x^{3} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06456, size = 22, normalized size = 1.1 \begin{align*} \frac{1}{3} \, x^{3} \sin \left (x^{3}\right ) + \frac{1}{3} \, \cos \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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