Optimal. Leaf size=15 \[ \frac {3}{5} \left (-3 x+x^2\right )^{5/3} \]
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Rubi [A]
time = 0.02, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.087, Rules used = {1645, 643}
\begin {gather*} \frac {3}{5} \left (x^2-3 x\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 643
Rule 1645
Rubi steps
\begin {align*} \int \frac {x \left (9-9 x+2 x^2\right )}{\sqrt [3]{-3 x+x^2}} \, dx &=\int (-3+2 x) \left (-3 x+x^2\right )^{2/3} \, dx\\ &=\frac {3}{5} \left (-3 x+x^2\right )^{5/3}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 13, normalized size = 0.87 \begin {gather*} \frac {3}{5} ((-3+x) x)^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 16, normalized size = 1.07
method | result | size |
trager | \(\frac {3 \left (x -3\right ) x \left (x^{2}-3 x \right )^{\frac {2}{3}}}{5}\) | \(16\) |
risch | \(\frac {3 \left (x -3\right )^{2} x^{2}}{5 \left (\left (x -3\right ) x \right )^{\frac {1}{3}}}\) | \(18\) |
gosper | \(\frac {3 \left (x -3\right )^{2} x^{2}}{5 \left (x^{2}-3 x \right )^{\frac {1}{3}}}\) | \(20\) |
meijerg | \(\frac {2 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (x -3\right )\right )^{\frac {1}{3}} x^{\frac {11}{3}} \hypergeom \left (\left [\frac {1}{3}, \frac {11}{3}\right ], \left [\frac {14}{3}\right ], \frac {x}{3}\right )}{11 \mathrm {signum}\left (x -3\right )^{\frac {1}{3}}}-\frac {9 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (x -3\right )\right )^{\frac {1}{3}} x^{\frac {8}{3}} \hypergeom \left (\left [\frac {1}{3}, \frac {8}{3}\right ], \left [\frac {11}{3}\right ], \frac {x}{3}\right )}{8 \mathrm {signum}\left (x -3\right )^{\frac {1}{3}}}+\frac {9 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (x -3\right )\right )^{\frac {1}{3}} x^{\frac {5}{3}} \hypergeom \left (\left [\frac {1}{3}, \frac {5}{3}\right ], \left [\frac {8}{3}\right ], \frac {x}{3}\right )}{5 \mathrm {signum}\left (x -3\right )^{\frac {1}{3}}}\) | \(95\) |
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 = 0.36, size = 11, normalized size = 0.73 \begin {gather*} \frac {3}{5} \, {\left (x^{2} - 3 \, x\right )}^{\frac {5}{3}} \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 {x \left (x - 3\right ) \left (2 x - 3\right )}{\sqrt [3]{x \left (x - 3\right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.66, size = 11, normalized size = 0.73 \begin {gather*} \frac {3}{5} \, {\left (x^{2} - 3 \, x\right )}^{\frac {5}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.68, size = 15, normalized size = 1.00 \begin {gather*} \frac {3\,x\,{\left (x^2-3\,x\right )}^{2/3}\,\left (x-3\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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