Optimal. Leaf size=16 \[ \frac {x^3}{6 \sqrt {2+x^6}} \]
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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 = {270}
\begin {gather*} \frac {x^3}{6 \sqrt {x^6+2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 270
Rubi steps
\begin {align*} \int \frac {x^2}{\left (2+x^6\right )^{3/2}} \, dx &=\frac {x^3}{6 \sqrt {2+x^6}}\\ \end {align*}
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Mathematica [A]
time = 0.11, size = 16, normalized size = 1.00 \begin {gather*} \frac {x^3}{6 \sqrt {2+x^6}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.18, size = 13, normalized size = 0.81
method | result | size |
gosper | \(\frac {x^{3}}{6 \sqrt {x^{6}+2}}\) | \(13\) |
trager | \(\frac {x^{3}}{6 \sqrt {x^{6}+2}}\) | \(13\) |
risch | \(\frac {x^{3}}{6 \sqrt {x^{6}+2}}\) | \(13\) |
meijerg | \(\frac {\sqrt {2}\, x^{3}}{12 \sqrt {1+\frac {x^{6}}{2}}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 12, normalized size = 0.75 \begin {gather*} \frac {x^{3}}{6 \, \sqrt {x^{6} + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 25 vs.
\(2 (12) = 24\).
time = 0.36, size = 25, normalized size = 1.56 \begin {gather*} \frac {x^{6} + \sqrt {x^{6} + 2} x^{3} + 2}{6 \, {\left (x^{6} + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.28, size = 12, normalized size = 0.75 \begin {gather*} \frac {x^{3}}{6 \sqrt {x^{6} + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.00, size = 12, normalized size = 0.75 \begin {gather*} \frac {x^{3}}{6 \, \sqrt {x^{6} + 2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.14, size = 12, normalized size = 0.75 \begin {gather*} \frac {x^3}{6\,\sqrt {x^6+2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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