Optimal. Leaf size=16 \[ \frac{x^3}{6 \sqrt{x^6+2}} \]
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Rubi [A] time = 0.0030059, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {264} \[ \frac{x^3}{6 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{x^2}{\left (2+x^6\right )^{3/2}} \, dx &=\frac{x^3}{6 \sqrt{2+x^6}}\\ \end{align*}
Mathematica [A] time = 0.0024186, size = 16, normalized size = 1. \[ \frac{x^3}{6 \sqrt{x^6+2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*}{\frac{{x}^{3}}{6}{\frac{1}{\sqrt{{x}^{6}+2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0038, size = 16, normalized size = 1. \begin{align*} \frac{x^{3}}{6 \, \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.48822, size = 61, normalized size = 3.81 \begin{align*} \frac{x^{6} + \sqrt{x^{6} + 2} x^{3} + 2}{6 \,{\left (x^{6} + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.487208, size = 12, normalized size = 0.75 \begin{align*} \frac{x^{3}}{6 \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2325, size = 16, normalized size = 1. \begin{align*} \frac{x^{3}}{6 \, \sqrt{x^{6} + 2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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