Optimal. Leaf size=16 \[ \frac{3}{5} (-(3-x) x)^{5/3} \]
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Rubi [A] time = 0.006378, antiderivative size = 16, normalized size of antiderivative = 1., 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} \[ \frac{3}{5} (-(3-x) x)^{5/3} \]
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*}
Mathematica [A] time = 0.0031555, size = 13, normalized size = 0.81 \[ \frac{3}{5} ((x-3) x)^{5/3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 14, normalized size = 0.9 \begin{align*}{\frac{ \left ( -9+3\,x \right ) x}{5} \left ( \left ( -3+x \right ) x \right ) ^{{\frac{2}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01458, size = 12, normalized size = 0.75 \begin{align*} \frac{3}{5} \, \left ({\left (x - 3\right )} x\right )^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.66149, size = 31, normalized size = 1.94 \begin{align*} \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 10.0711, size = 10, normalized size = 0.62 \begin{align*} \frac{3 \left (x \left (x - 3\right )\right )^{\frac{5}{3}}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.18262, size = 15, normalized size = 0.94 \begin{align*} \frac{3}{5} \,{\left (x^{2} - 3 \, x\right )}^{\frac{5}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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