Optimal. Leaf size=8 \[ \frac {\sin \left (x^4\right )}{4} \]
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Rubi [A] time = 0.01, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3380, 2637} \[ \frac {\sin \left (x^4\right )}{4} \]
Antiderivative was successfully verified.
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Rule 2637
Rule 3380
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*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {\sin \left (x^4\right )}{4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 6, normalized size = 0.75 \[ \frac {1}{4} \, \sin \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 6, normalized size = 0.75 \[ \frac {1}{4} \, \sin \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 7, normalized size = 0.88 \[ \frac {\sin \left (x^{4}\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.31, size = 6, normalized size = 0.75 \[ \frac {1}{4} \, \sin \left (x^{4}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 6, normalized size = 0.75 \[ \frac {\sin \left (x^4\right )}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 5, normalized size = 0.62 \[ \frac {\sin {\left (x^{4} \right )}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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