Optimal. Leaf size=16 \[ \frac {3}{5} (-((3-x) x))^{5/3} \]
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Rubi [A] time = 0.01, 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 = {1588} \begin {gather*} \frac {3}{5} (-(3-x) x)^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 1588
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} ((x-3) x)^{5/3} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [A] time = 0.01, size = 13, normalized size = 0.81 \begin {gather*} \frac {3}{5} ((x-3) x)^{5/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, 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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giac [A] time = 0.15, 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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maple [A] time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} \frac {3 \left (x -3\right ) \left (\left (x -3\right ) x \right )^{\frac {2}{3}} x}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, 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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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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sympy [A] time = 4.25, 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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