Optimal. Leaf size=8 \[ \frac{\sinh \left (x^3\right )}{3} \]
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Rubi [A] time = 0.0114006, 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 = {5321, 2637} \[ \frac{\sinh \left (x^3\right )}{3} \]
Antiderivative was successfully verified.
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Rule 5321
Rule 2637
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*}
Mathematica [A] time = 0.0024136, size = 8, normalized size = 1. \[ \frac{\sinh \left (x^3\right )}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 7, normalized size = 0.9 \begin{align*}{\frac{\sinh \left ({x}^{3} \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11214, size = 8, normalized size = 1. \begin{align*} \frac{1}{3} \, \sinh \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74606, size = 20, normalized size = 2.5 \begin{align*} \frac{1}{3} \, \sinh \left (x^{3}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.333811, size = 5, normalized size = 0.62 \begin{align*} \frac{\sinh{\left (x^{3} \right )}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.29961, size = 20, normalized size = 2.5 \begin{align*} -\frac{1}{6} \, e^{\left (-x^{3}\right )} + \frac{1}{6} \, e^{\left (x^{3}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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