Optimal. Leaf size=16 \[ \frac {3}{5} (-((3-x) x))^{5/3} \]
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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 = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {1602}
\begin {gather*} \frac {3}{5} (-((3-x) x))^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1602
Rubi steps
\begin {align*} \int ((-3+x) x)^{2/3} (-3+2 x) \, dx &=\frac {3}{5} (-(3-x) x)^{5/3}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 13, normalized size = 0.81 \begin {gather*} \frac {3}{5} ((-3+x) x)^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 10, normalized size = 0.62
method | result | size |
derivativedivides | \(\frac {3 \left (\left (x -3\right ) x \right )^{\frac {5}{3}}}{5}\) | \(10\) |
default | \(\frac {3 \left (\left (x -3\right ) x \right )^{\frac {5}{3}}}{5}\) | \(10\) |
gosper | \(\frac {3 \left (x -3\right ) x \left (\left (x -3\right ) x \right )^{\frac {2}{3}}}{5}\) | \(14\) |
trager | \(\frac {3 \left (x -3\right ) x \left (x^{2}-3 x \right )^{\frac {2}{3}}}{5}\) | \(16\) |
risch | \(\frac {3 \left (x -3\right )^{2} x^{2}}{5 \left (\left (x -3\right ) x \right )^{\frac {1}{3}}}\) | \(18\) |
meijerg | \(-\frac {9 \,3^{\frac {2}{3}} \mathrm {signum}\left (x -3\right )^{\frac {2}{3}} x^{\frac {5}{3}} \hypergeom \left (\left [-\frac {2}{3}, \frac {5}{3}\right ], \left [\frac {8}{3}\right ], \frac {x}{3}\right )}{5 \left (-\mathrm {signum}\left (x -3\right )\right )^{\frac {2}{3}}}+\frac {3 \,3^{\frac {2}{3}} \mathrm {signum}\left (x -3\right )^{\frac {2}{3}} x^{\frac {8}{3}} \hypergeom \left (\left [-\frac {2}{3}, \frac {8}{3}\right ], \left [\frac {11}{3}\right ], \frac {x}{3}\right )}{4 \left (-\mathrm {signum}\left (x -3\right )\right )^{\frac {2}{3}}}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 9, normalized size = 0.56 \begin {gather*} \frac {3}{5} \, \left ({\left (x - 3\right )} x\right )^{\frac {5}{3}} \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 = 0.69 \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 [A]
time = 3.34, size = 10, normalized size = 0.62 \begin {gather*} \frac {3 \left (x \left (x - 3\right )\right )^{\frac {5}{3}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.62, size = 11, normalized size = 0.69 \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 = 3.66, size = 13, normalized size = 0.81 \begin {gather*} \frac {3\,x\,{\left (x\,\left (x-3\right )\right )}^{2/3}\,\left (x-3\right )}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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