Optimal. Leaf size=15 \[ \frac {3}{5} \left (x^2-3 x\right )^{5/3} \]
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Rubi [A] time = 0.03, 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 = {1631, 629} \[ \frac {3}{5} \left (x^2-3 x\right )^{5/3} \]
Antiderivative was successfully verified.
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Rule 629
Rule 1631
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 \[ \frac {3}{5} ((x-3) x)^{5/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 11, normalized size = 0.73 \[ \frac {3}{5} \, {\left (x^{2} - 3 \, x\right )}^{\frac {5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 11, normalized size = 0.73 \[ \frac {3}{5} \, {\left (x^{2} - 3 \, x\right )}^{\frac {5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 20, normalized size = 1.33 \[ \frac {3 \left (x -3\right )^{2} x^{2}}{5 \left (x^{2}-3 x \right )^{\frac {1}{3}}} \]
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 \[ \int \frac {{\left (2 \, x^{2} - 9 \, x + 9\right )} x}{{\left (x^{2} - 3 \, x\right )}^{\frac {1}{3}}}\,{d x} \]
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 \[ \frac {3\,x\,{\left (x^2-3\,x\right )}^{2/3}\,\left (x-3\right )}{5} \]
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 \[ \int \frac {x \left (x - 3\right ) \left (2 x - 3\right )}{\sqrt [3]{x \left (x - 3\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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