Optimal. Leaf size=16 \[ -\frac{\sqrt{x^6+2}}{6 x^3} \]
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Rubi [A] time = 0.0030968, antiderivative size = 16, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0022609, size = 16, normalized size = 1. \[ -\frac{\sqrt{x^6+2}}{6 x^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 13, normalized size = 0.8 \begin{align*} -{\frac{1}{6\,{x}^{3}}\sqrt{{x}^{6}+2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01833, size = 16, normalized size = 1. \begin{align*} -\frac{\sqrt{x^{6} + 2}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.57111, size = 43, normalized size = 2.69 \begin{align*} -\frac{x^{3} + \sqrt{x^{6} + 2}}{6 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.588745, size = 12, normalized size = 0.75 \begin{align*} - \frac{\sqrt{1 + \frac{2}{x^{6}}}}{6} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19195, size = 27, normalized size = 1.69 \begin{align*} -\frac{\sqrt{\frac{2}{x^{6}} + 1}}{6 \, \mathrm{sgn}\left (x\right )} + \frac{1}{6} \, \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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