Optimal. Leaf size=40 \[ \frac{1}{15} \left (x^6+2\right )^{5/2}-\frac{4}{9} \left (x^6+2\right )^{3/2}+\frac{4 \sqrt{x^6+2}}{3} \]
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Rubi [A] time = 0.0147073, antiderivative size = 40, 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} \[ \frac{1}{15} \left (x^6+2\right )^{5/2}-\frac{4}{9} \left (x^6+2\right )^{3/2}+\frac{4 \sqrt{x^6+2}}{3} \]
Antiderivative was successfully verified.
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Rule 266
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{17}}{\sqrt{2+x^6}} \, dx &=\frac{1}{6} \operatorname{Subst}\left (\int \frac{x^2}{\sqrt{2+x}} \, dx,x,x^6\right )\\ &=\frac{1}{6} \operatorname{Subst}\left (\int \left (\frac{4}{\sqrt{2+x}}-4 \sqrt{2+x}+(2+x)^{3/2}\right ) \, dx,x,x^6\right )\\ &=\frac{4 \sqrt{2+x^6}}{3}-\frac{4}{9} \left (2+x^6\right )^{3/2}+\frac{1}{15} \left (2+x^6\right )^{5/2}\\ \end{align*}
Mathematica [A] time = 0.0065846, size = 25, normalized size = 0.62 \[ \frac{1}{45} \sqrt{x^6+2} \left (3 x^{12}-8 x^6+32\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 22, normalized size = 0.6 \begin{align*}{\frac{3\,{x}^{12}-8\,{x}^{6}+32}{45}\sqrt{{x}^{6}+2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.991476, size = 38, normalized size = 0.95 \begin{align*} \frac{1}{15} \,{\left (x^{6} + 2\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.47841, size = 57, normalized size = 1.42 \begin{align*} \frac{1}{45} \,{\left (3 \, x^{12} - 8 \, x^{6} + 32\right )} \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 4.3443, size = 39, normalized size = 0.98 \begin{align*} \frac{x^{12} \sqrt{x^{6} + 2}}{15} - \frac{8 x^{6} \sqrt{x^{6} + 2}}{45} + \frac{32 \sqrt{x^{6} + 2}}{45} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.16345, size = 38, normalized size = 0.95 \begin{align*} \frac{1}{15} \,{\left (x^{6} + 2\right )}^{\frac{5}{2}} - \frac{4}{9} \,{\left (x^{6} + 2\right )}^{\frac{3}{2}} + \frac{4}{3} \, \sqrt{x^{6} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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