Optimal. Leaf size=33 \[ \frac {\sqrt {x^6+2}}{18 x^3}-\frac {\sqrt {x^6+2}}{18 x^9} \]
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Rubi [A] time = 0.01, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {271, 264} \[ \frac {\sqrt {x^6+2}}{18 x^3}-\frac {\sqrt {x^6+2}}{18 x^9} \]
Antiderivative was successfully verified.
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Rule 264
Rule 271
Rubi steps
\begin {align*} \int \frac {1}{x^{10} \sqrt {2+x^6}} \, dx &=-\frac {\sqrt {2+x^6}}{18 x^9}-\frac {1}{3} \int \frac {1}{x^4 \sqrt {2+x^6}} \, dx\\ &=-\frac {\sqrt {2+x^6}}{18 x^9}+\frac {\sqrt {2+x^6}}{18 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 21, normalized size = 0.64 \[ \frac {\left (x^6-1\right ) \sqrt {x^6+2}}{18 x^9} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 22, normalized size = 0.67 \[ \frac {x^{9} + \sqrt {x^{6} + 2} {\left (x^{6} - 1\right )}}{18 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 0.55 \[ \frac {\sqrt {x^{6}+2}\, \left (x^{6}-1\right )}{18 x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.99, size = 25, normalized size = 0.76 \[ \frac {\sqrt {x^{6} + 2}}{12 \, x^{3}} - \frac {{\left (x^{6} + 2\right )}^{\frac {3}{2}}}{36 \, x^{9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.17, size = 17, normalized size = 0.52 \[ \frac {\left (x^6-1\right )\,\sqrt {x^6+2}}{18\,x^9} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.98, size = 26, normalized size = 0.79 \[ \frac {\sqrt {1 + \frac {2}{x^{6}}}}{18} - \frac {\sqrt {1 + \frac {2}{x^{6}}}}{18 x^{6}} \]
Verification of antiderivative is not currently implemented for this CAS.
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