Optimal. Leaf size=16 \[ -\frac {\sqrt {x^6+2}}{6 x^3} \]
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Rubi [A] time = 0.00, antiderivative size = 16, normalized size of antiderivative = 1.00, 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} \[ -\frac {\sqrt {x^6+2}}{6 x^3} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin {align*} \int \frac {1}{x^4 \sqrt {2+x^6}} \, dx &=-\frac {\sqrt {2+x^6}}{6 x^3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 1.00 \[ -\frac {\sqrt {x^6+2}}{6 x^3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 16, normalized size = 1.00 \[ -\frac {x^{3} + \sqrt {x^{6} + 2}}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 20, normalized size = 1.25 \[ -\frac {\sqrt {\frac {2}{x^{6}} + 1}}{6 \, \mathrm {sgn}\relax (x)} + \frac {1}{6} \, \mathrm {sgn}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 0.81 \[ -\frac {\sqrt {x^{6}+2}}{6 x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.92, size = 12, normalized size = 0.75 \[ -\frac {\sqrt {x^{6} + 2}}{6 \, x^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 12, normalized size = 0.75 \[ -\frac {\sqrt {x^6+2}}{6\,x^3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.17, size = 12, normalized size = 0.75 \[ - \frac {\sqrt {1 + \frac {2}{x^{6}}}}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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