Optimal. Leaf size=13 \[ \frac {2}{3} \sqrt {-1+x^3} \]
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Rubi [A]
time = 0.00, antiderivative size = 13, 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 = {267}
\begin {gather*} \frac {2 \sqrt {x^3-1}}{3} \end {gather*}
Antiderivative was successfully verified.
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Rule 267
Rubi steps
\begin {align*} \int \frac {x^2}{\sqrt {-1+x^3}} \, dx &=\frac {2}{3} \sqrt {-1+x^3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 1.00 \begin {gather*} \frac {2}{3} \sqrt {-1+x^3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.16, size = 10, normalized size = 0.77
method | result | size |
derivativedivides | \(\frac {2 \sqrt {x^{3}-1}}{3}\) | \(10\) |
default | \(\frac {2 \sqrt {x^{3}-1}}{3}\) | \(10\) |
trager | \(\frac {2 \sqrt {x^{3}-1}}{3}\) | \(10\) |
risch | \(\frac {2 \sqrt {x^{3}-1}}{3}\) | \(10\) |
elliptic | \(\frac {2 \sqrt {x^{3}-1}}{3}\) | \(10\) |
gosper | \(\frac {2 \left (x -1\right ) \left (x^{2}+x +1\right )}{3 \sqrt {x^{3}-1}}\) | \(19\) |
meijerg | \(-\frac {\sqrt {-\mathrm {signum}\left (x^{3}-1\right )}\, \left (-2 \sqrt {\pi }+2 \sqrt {\pi }\, \sqrt {-x^{3}+1}\right )}{3 \sqrt {\pi }\, \sqrt {\mathrm {signum}\left (x^{3}-1\right )}}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{3} \, \sqrt {x^{3} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{3} \, \sqrt {x^{3} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 10, normalized size = 0.77 \begin {gather*} \frac {2 \sqrt {x^{3} - 1}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.05, size = 9, normalized size = 0.69 \begin {gather*} \frac {2}{3} \, \sqrt {x^{3} - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 9, normalized size = 0.69 \begin {gather*} \frac {2\,\sqrt {x^3-1}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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