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 = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, 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 43
Rule 266
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*}
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Mathematica [A] time = 0.01, 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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fricas [A] time = 0.81, size = 14, normalized size = 0.52 \[ \frac {1}{9} \, \sqrt {x^{6} + 2} {\left (x^{6} - 4\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 19, normalized size = 0.70 \[ \frac {1}{9} \, {\left (x^{6} + 2\right )}^{\frac {3}{2}} - \frac {2}{3} \, \sqrt {x^{6} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ \frac {\sqrt {x^{6}+2}\, \left (x^{6}-4\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.99, size = 19, normalized size = 0.70 \[ \frac {1}{9} \, {\left (x^{6} + 2\right )}^{\frac {3}{2}} - \frac {2}{3} \, \sqrt {x^{6} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.16, size = 14, normalized size = 0.52 \[ \frac {\sqrt {x^6+2}\,\left (x^6-4\right )}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.38, size = 24, normalized size = 0.89 \[ \frac {x^{6} \sqrt {x^{6} + 2}}{9} - \frac {4 \sqrt {x^{6} + 2}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
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