Optimal. Leaf size=8 \[ \frac {\sinh \left (x^3\right )}{3} \]
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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 = {5321, 2637} \[ \frac {\sinh \left (x^3\right )}{3} \]
Antiderivative was successfully verified.
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Rule 2637
Rule 5321
Rubi steps
\begin {align*} \int x^2 \cosh \left (x^3\right ) \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \cosh (x) \, dx,x,x^3\right )\\ &=\frac {\sinh \left (x^3\right )}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \[ \frac {\sinh \left (x^3\right )}{3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, \sinh \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.11, size = 15, normalized size = 1.88 \[ -\frac {1}{6} \, e^{\left (-x^{3}\right )} + \frac {1}{6} \, e^{\left (x^{3}\right )} \]
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 \[ \frac {\sinh \left (x^{3}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.30, size = 6, normalized size = 0.75 \[ \frac {1}{3} \, \sinh \left (x^{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.88, size = 6, normalized size = 0.75 \[ \frac {\mathrm {sinh}\left (x^3\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 5, normalized size = 0.62 \[ \frac {\sinh {\left (x^{3} \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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