Optimal. Leaf size=17 \[ \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \]
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Rubi [A] time = 0.05, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {2043, 1631, 629} \[ \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \]
Antiderivative was successfully verified.
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Rule 629
Rule 1631
Rule 2043
Rubi steps
\begin {align*} \int \frac {9-9 \sqrt {x}+2 x}{\sqrt [3]{-3 \sqrt {x}+x}} \, dx &=2 \operatorname {Subst}\left (\int \frac {x \left (9-9 x+2 x^2\right )}{\sqrt [3]{-3 x+x^2}} \, dx,x,\sqrt {x}\right )\\ &=2 \operatorname {Subst}\left (\int (-3+2 x) \left (-3 x+x^2\right )^{2/3} \, dx,x,\sqrt {x}\right )\\ &=\frac {6}{5} \left (-3 \sqrt {x}+x\right )^{5/3}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 17, normalized size = 1.00 \[ \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 11, normalized size = 0.65 \[ \frac {6}{5} \, {\left (x - 3 \, \sqrt {x}\right )}^{\frac {5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 11, normalized size = 0.65 \[ \frac {6}{5} \, {\left (x - 3 \, \sqrt {x}\right )}^{\frac {5}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.11, size = 125, normalized size = 7.35 \[ \frac {4 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (\frac {\sqrt {x}}{3}-1\right )\right )^{\frac {1}{3}} x^{\frac {11}{6}} \hypergeom \left (\left [\frac {1}{3}, \frac {11}{3}\right ], \left [\frac {14}{3}\right ], \frac {\sqrt {x}}{3}\right )}{11 \mathrm {signum}\left (\frac {\sqrt {x}}{3}-1\right )^{\frac {1}{3}}}-\frac {9 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (\frac {\sqrt {x}}{3}-1\right )\right )^{\frac {1}{3}} x^{\frac {4}{3}} \hypergeom \left (\left [\frac {1}{3}, \frac {8}{3}\right ], \left [\frac {11}{3}\right ], \frac {\sqrt {x}}{3}\right )}{4 \mathrm {signum}\left (\frac {\sqrt {x}}{3}-1\right )^{\frac {1}{3}}}+\frac {18 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (\frac {\sqrt {x}}{3}-1\right )\right )^{\frac {1}{3}} x^{\frac {5}{6}} \hypergeom \left (\left [\frac {1}{3}, \frac {5}{3}\right ], \left [\frac {8}{3}\right ], \frac {\sqrt {x}}{3}\right )}{5 \mathrm {signum}\left (\frac {\sqrt {x}}{3}-1\right )^{\frac {1}{3}}} \]
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 \[ \int \frac {2 \, x - 9 \, \sqrt {x} + 9}{{\left (x - 3 \, \sqrt {x}\right )}^{\frac {1}{3}}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {2\,x-9\,\sqrt {x}+9}{{\left (x-3\,\sqrt {x}\right )}^{1/3}} \,d x \]
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 \[ \int \frac {- 9 \sqrt {x} + 2 x + 9}{\sqrt [3]{- 3 \sqrt {x} + x}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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