Optimal. Leaf size=8 \[ \frac{\sin \left (x^4\right )}{4} \]
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Rubi [A] time = 0.0094394, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {3380, 2637} \[ \frac{\sin \left (x^4\right )}{4} \]
Antiderivative was successfully verified.
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Rule 3380
Rule 2637
Rubi steps
\begin{align*} \int x^3 \cos \left (x^4\right ) \, dx &=\frac{1}{4} \operatorname{Subst}\left (\int \cos (x) \, dx,x,x^4\right )\\ &=\frac{\sin \left (x^4\right )}{4}\\ \end{align*}
Mathematica [A] time = 0.001593, size = 8, normalized size = 1. \[ \frac{\sin \left (x^4\right )}{4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 7, normalized size = 0.9 \begin{align*}{\frac{\sin \left ({x}^{4} \right ) }{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.982466, size = 8, normalized size = 1. \begin{align*} \frac{1}{4} \, \sin \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.94804, size = 19, normalized size = 2.38 \begin{align*} \frac{1}{4} \, \sin \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.538404, size = 5, normalized size = 0.62 \begin{align*} \frac{\sin{\left (x^{4} \right )}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0835, size = 8, normalized size = 1. \begin{align*} \frac{1}{4} \, \sin \left (x^{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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