Optimal. Leaf size=121 \[ \frac {2}{51} \left (1-x^3\right )^{17/2}-\frac {14}{45} \left (1-x^3\right )^{15/2}+\frac {14}{13} \left (1-x^3\right )^{13/2}-\frac {74}{33} \left (1-x^3\right )^{11/2}+\frac {86}{27} \left (1-x^3\right )^{9/2}-\frac {22}{7} \left (1-x^3\right )^{7/2}+\frac {32}{15} \left (1-x^3\right )^{5/2}-\frac {8}{9} \left (1-x^3\right )^{3/2} \]
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Rubi [A] time = 0.11, antiderivative size = 121, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1821, 1620} \[ \frac {2}{51} \left (1-x^3\right )^{17/2}-\frac {14}{45} \left (1-x^3\right )^{15/2}+\frac {14}{13} \left (1-x^3\right )^{13/2}-\frac {74}{33} \left (1-x^3\right )^{11/2}+\frac {86}{27} \left (1-x^3\right )^{9/2}-\frac {22}{7} \left (1-x^3\right )^{7/2}+\frac {32}{15} \left (1-x^3\right )^{5/2}-\frac {8}{9} \left (1-x^3\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 1620
Rule 1821
Rubi steps
\begin {align*} \int x^5 \sqrt {1-x^3} \left (1+x^9\right )^2 \, dx &=\frac {1}{3} \operatorname {Subst}\left (\int \sqrt {1-x} x \left (1+x^3\right )^2 \, dx,x,x^3\right )\\ &=\frac {1}{3} \operatorname {Subst}\left (\int \left (4 \sqrt {1-x}-16 (1-x)^{3/2}+33 (1-x)^{5/2}-43 (1-x)^{7/2}+37 (1-x)^{9/2}-21 (1-x)^{11/2}+7 (1-x)^{13/2}-(1-x)^{15/2}\right ) \, dx,x,x^3\right )\\ &=-\frac {8}{9} \left (1-x^3\right )^{3/2}+\frac {32}{15} \left (1-x^3\right )^{5/2}-\frac {22}{7} \left (1-x^3\right )^{7/2}+\frac {86}{27} \left (1-x^3\right )^{9/2}-\frac {74}{33} \left (1-x^3\right )^{11/2}+\frac {14}{13} \left (1-x^3\right )^{13/2}-\frac {14}{45} \left (1-x^3\right )^{15/2}+\frac {2}{51} \left (1-x^3\right )^{17/2}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 57, normalized size = 0.47 \[ \frac {2 \sqrt {1-x^3} \left (45045 x^{24}-3003 x^{21}-3234 x^{18}+135702 x^{15}-19390 x^{12}-22160 x^9+126561 x^6-86507 x^3-173014\right )}{2297295} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 53, normalized size = 0.44 \[ \frac {2}{2297295} \, {\left (45045 \, x^{24} - 3003 \, x^{21} - 3234 \, x^{18} + 135702 \, x^{15} - 19390 \, x^{12} - 22160 \, x^{9} + 126561 \, x^{6} - 86507 \, x^{3} - 173014\right )} \sqrt {-x^{3} + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 138, normalized size = 1.14 \[ \frac {2}{51} \, {\left (x^{3} - 1\right )}^{8} \sqrt {-x^{3} + 1} + \frac {14}{45} \, {\left (x^{3} - 1\right )}^{7} \sqrt {-x^{3} + 1} + \frac {14}{13} \, {\left (x^{3} - 1\right )}^{6} \sqrt {-x^{3} + 1} + \frac {74}{33} \, {\left (x^{3} - 1\right )}^{5} \sqrt {-x^{3} + 1} + \frac {86}{27} \, {\left (x^{3} - 1\right )}^{4} \sqrt {-x^{3} + 1} + \frac {22}{7} \, {\left (x^{3} - 1\right )}^{3} \sqrt {-x^{3} + 1} + \frac {32}{15} \, {\left (x^{3} - 1\right )}^{2} \sqrt {-x^{3} + 1} - \frac {8}{9} \, {\left (-x^{3} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 58, normalized size = 0.48 \[ \frac {2 \sqrt {-x^{3}+1}\, \left (45045 x^{21}+42042 x^{18}+38808 x^{15}+174510 x^{12}+155120 x^{9}+132960 x^{6}+259521 x^{3}+173014\right ) \left (x -1\right ) \left (x^{2}+x +1\right )}{2297295} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.54, size = 89, normalized size = 0.74 \[ \frac {2}{51} \, {\left (-x^{3} + 1\right )}^{\frac {17}{2}} - \frac {14}{45} \, {\left (-x^{3} + 1\right )}^{\frac {15}{2}} + \frac {14}{13} \, {\left (-x^{3} + 1\right )}^{\frac {13}{2}} - \frac {74}{33} \, {\left (-x^{3} + 1\right )}^{\frac {11}{2}} + \frac {86}{27} \, {\left (-x^{3} + 1\right )}^{\frac {9}{2}} - \frac {22}{7} \, {\left (-x^{3} + 1\right )}^{\frac {7}{2}} + \frac {32}{15} \, {\left (-x^{3} + 1\right )}^{\frac {5}{2}} - \frac {8}{9} \, {\left (-x^{3} + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.27, size = 124, normalized size = 1.02 \[ \frac {84374\,x^6\,\sqrt {1-x^3}}{765765}-\frac {173014\,x^3\,\sqrt {1-x^3}}{2297295}-\frac {8864\,x^9\,\sqrt {1-x^3}}{459459}-\frac {1108\,x^{12}\,\sqrt {1-x^3}}{65637}+\frac {1436\,x^{15}\,\sqrt {1-x^3}}{12155}-\frac {28\,x^{18}\,\sqrt {1-x^3}}{9945}-\frac {2\,x^{21}\,\sqrt {1-x^3}}{765}+\frac {2\,x^{24}\,\sqrt {1-x^3}}{51}-\frac {346028\,\sqrt {1-x^3}}{2297295} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 12.71, size = 133, normalized size = 1.10 \[ \frac {2 x^{24} \sqrt {1 - x^{3}}}{51} - \frac {2 x^{21} \sqrt {1 - x^{3}}}{765} - \frac {28 x^{18} \sqrt {1 - x^{3}}}{9945} + \frac {1436 x^{15} \sqrt {1 - x^{3}}}{12155} - \frac {1108 x^{12} \sqrt {1 - x^{3}}}{65637} - \frac {8864 x^{9} \sqrt {1 - x^{3}}}{459459} + \frac {84374 x^{6} \sqrt {1 - x^{3}}}{765765} - \frac {173014 x^{3} \sqrt {1 - x^{3}}}{2297295} - \frac {346028 \sqrt {1 - x^{3}}}{2297295} \]
Verification of antiderivative is not currently implemented for this CAS.
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