Optimal. Leaf size=17 \[ \frac {6}{5} \left (-3 \sqrt {x}+x\right )^{5/3} \]
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Rubi [A]
time = 0.03, 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 = {2068, 1645,
643} \begin {gather*} \frac {6}{5} \left (x-3 \sqrt {x}\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 643
Rule 1645
Rule 2068
Rubi steps
\begin {align*} \int \frac {9-9 \sqrt {x}+2 x}{\sqrt [3]{-3 \sqrt {x}+x}} \, dx &=2 \text {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 \text {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 = 0.03, size = 17, normalized size = 1.00 \begin {gather*} \frac {6}{5} \left (-3 \sqrt {x}+x\right )^{5/3} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
2.
time = 0.56, size = 125, normalized size = 7.35
method | result | size |
meijerg | \(\frac {18 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (-1+\frac {\sqrt {x}}{3}\right )\right )^{\frac {1}{3}} x^{\frac {5}{6}} \hypergeom \left (\left [\frac {1}{3}, \frac {5}{3}\right ], \left [\frac {8}{3}\right ], \frac {\sqrt {x}}{3}\right )}{5 \mathrm {signum}\left (-1+\frac {\sqrt {x}}{3}\right )^{\frac {1}{3}}}+\frac {4 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (-1+\frac {\sqrt {x}}{3}\right )\right )^{\frac {1}{3}} x^{\frac {11}{6}} \hypergeom \left (\left [\frac {1}{3}, \frac {11}{3}\right ], \left [\frac {14}{3}\right ], \frac {\sqrt {x}}{3}\right )}{11 \mathrm {signum}\left (-1+\frac {\sqrt {x}}{3}\right )^{\frac {1}{3}}}-\frac {9 \,3^{\frac {2}{3}} \left (-\mathrm {signum}\left (-1+\frac {\sqrt {x}}{3}\right )\right )^{\frac {1}{3}} x^{\frac {4}{3}} \hypergeom \left (\left [\frac {1}{3}, \frac {8}{3}\right ], \left [\frac {11}{3}\right ], \frac {\sqrt {x}}{3}\right )}{4 \mathrm {signum}\left (-1+\frac {\sqrt {x}}{3}\right )^{\frac {1}{3}}}\) | \(125\) |
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 11, normalized size = 0.65 \begin {gather*} \frac {6}{5} \, {\left (x - 3 \, \sqrt {x}\right )}^{\frac {5}{3}} \end {gather*}
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 \begin {gather*} \int \frac {- 9 \sqrt {x} + 2 x + 9}{\sqrt [3]{- 3 \sqrt {x} + x}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.65, size = 11, normalized size = 0.65 \begin {gather*} \frac {6}{5} \, {\left (x - 3 \, \sqrt {x}\right )}^{\frac {5}{3}} \end {gather*}
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 \begin {gather*} \int \frac {2\,x-9\,\sqrt {x}+9}{{\left (x-3\,\sqrt {x}\right )}^{1/3}} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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