Optimal. Leaf size=27 \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{2 \sqrt{x^6+2}}{3} \]
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Rubi [A] time = 0.0109, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac{1}{9} \left (x^6+2\right )^{3/2}-\frac{2 \sqrt{x^6+2}}{3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{11}}{\sqrt{2+x^6}} \, dx &=\frac{1}{6} \operatorname{Subst}\left (\int \frac{x}{\sqrt{2+x}} \, dx,x,x^6\right )\\ &=\frac{1}{6} \operatorname{Subst}\left (\int \left (-\frac{2}{\sqrt{2+x}}+\sqrt{2+x}\right ) \, dx,x,x^6\right )\\ &=-\frac{2}{3} \sqrt{2+x^6}+\frac{1}{9} \left (2+x^6\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0048161, size = 18, normalized size = 0.67 \[ \frac{1}{9} \left (x^6-4\right ) \sqrt{x^6+2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 15, normalized size = 0.6 \begin{align*}{\frac{{x}^{6}-4}{9}\sqrt{{x}^{6}+2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.002, size = 26, normalized size = 0.96 \begin{align*} \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.44149, size = 39, normalized size = 1.44 \begin{align*} \frac{1}{9} \, \sqrt{x^{6} + 2}{\left (x^{6} - 4\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.13623, size = 24, normalized size = 0.89 \begin{align*} \frac{x^{6} \sqrt{x^{6} + 2}}{9} - \frac{4 \sqrt{x^{6} + 2}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.10393, size = 26, normalized size = 0.96 \begin{align*} \frac{1}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} - \frac{2}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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