Optimal. Leaf size=20 \[ \frac {3 \left (-x^2+x^3\right )^{2/3}}{2 x^2} \]
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Rubi [A]
time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {2039}
\begin {gather*} \frac {3 \left (x^3-x^2\right )^{2/3}}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 2039
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt [3]{-x^2+x^3}} \, dx &=\frac {3 \left (-x^2+x^3\right )^{2/3}}{2 x^2}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 0.90 \begin {gather*} \frac {3 (-1+x)}{2 \sqrt [3]{(-1+x) x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.30, size = 15, normalized size = 0.75
method | result | size |
risch | \(\frac {-\frac {3}{2}+\frac {3 x}{2}}{\left (\left (-1+x \right ) x^{2}\right )^{\frac {1}{3}}}\) | \(15\) |
gosper | \(\frac {-\frac {3}{2}+\frac {3 x}{2}}{\left (x^{3}-x^{2}\right )^{\frac {1}{3}}}\) | \(17\) |
trager | \(\frac {3 \left (x^{3}-x^{2}\right )^{\frac {2}{3}}}{2 x^{2}}\) | \(17\) |
meijerg | \(-\frac {3 \left (-\mathrm {signum}\left (-1+x \right )\right )^{\frac {1}{3}} \left (1-x \right )^{\frac {2}{3}}}{2 \mathrm {signum}\left (-1+x \right )^{\frac {1}{3}} x^{\frac {2}{3}}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 16, normalized size = 0.80 \begin {gather*} \frac {3 \, {\left (x^{3} - x^{2}\right )}^{\frac {2}{3}}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \sqrt [3]{x^{2} \left (x - 1\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.55 \begin {gather*} \frac {3}{2} \, {\left (-\frac {1}{x} + 1\right )}^{\frac {2}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.20, size = 16, normalized size = 0.80 \begin {gather*} \frac {3\,{\left (x^3-x^2\right )}^{2/3}}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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