Optimal. Leaf size=91 \[ \frac {1}{21} (x+1)^{21}-\frac {9}{20} (x+1)^{20}+\frac {36}{19} (x+1)^{19}-\frac {14}{3} (x+1)^{18}+\frac {126}{17} (x+1)^{17}-\frac {63}{8} (x+1)^{16}+\frac {28}{5} (x+1)^{15}-\frac {18}{7} (x+1)^{14}+\frac {9}{13} (x+1)^{13}-\frac {1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.03, antiderivative size = 91, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {27, 43} \[ \frac {1}{21} (x+1)^{21}-\frac {9}{20} (x+1)^{20}+\frac {36}{19} (x+1)^{19}-\frac {14}{3} (x+1)^{18}+\frac {126}{17} (x+1)^{17}-\frac {63}{8} (x+1)^{16}+\frac {28}{5} (x+1)^{15}-\frac {18}{7} (x+1)^{14}+\frac {9}{13} (x+1)^{13}-\frac {1}{12} (x+1)^{12} \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int x^9 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^9 (1+x)^{11} \, dx\\ &=\int \left (-(1+x)^{11}+9 (1+x)^{12}-36 (1+x)^{13}+84 (1+x)^{14}-126 (1+x)^{15}+126 (1+x)^{16}-84 (1+x)^{17}+36 (1+x)^{18}-9 (1+x)^{19}+(1+x)^{20}\right ) \, dx\\ &=-\frac {1}{12} (1+x)^{12}+\frac {9}{13} (1+x)^{13}-\frac {18}{7} (1+x)^{14}+\frac {28}{5} (1+x)^{15}-\frac {63}{8} (1+x)^{16}+\frac {126}{17} (1+x)^{17}-\frac {14}{3} (1+x)^{18}+\frac {36}{19} (1+x)^{19}-\frac {9}{20} (1+x)^{20}+\frac {1}{21} (1+x)^{21}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 81, normalized size = 0.89 \[ \frac {x^{21}}{21}+\frac {11 x^{20}}{20}+\frac {55 x^{19}}{19}+\frac {55 x^{18}}{6}+\frac {330 x^{17}}{17}+\frac {231 x^{16}}{8}+\frac {154 x^{15}}{5}+\frac {165 x^{14}}{7}+\frac {165 x^{13}}{13}+\frac {55 x^{12}}{12}+x^{11}+\frac {x^{10}}{10} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 59, normalized size = 0.65 \[ \frac {1}{21} x^{21} + \frac {11}{20} x^{20} + \frac {55}{19} x^{19} + \frac {55}{6} x^{18} + \frac {330}{17} x^{17} + \frac {231}{8} x^{16} + \frac {154}{5} x^{15} + \frac {165}{7} x^{14} + \frac {165}{13} x^{13} + \frac {55}{12} x^{12} + x^{11} + \frac {1}{10} x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 59, normalized size = 0.65 \[ \frac {1}{21} \, x^{21} + \frac {11}{20} \, x^{20} + \frac {55}{19} \, x^{19} + \frac {55}{6} \, x^{18} + \frac {330}{17} \, x^{17} + \frac {231}{8} \, x^{16} + \frac {154}{5} \, x^{15} + \frac {165}{7} \, x^{14} + \frac {165}{13} \, x^{13} + \frac {55}{12} \, x^{12} + x^{11} + \frac {1}{10} \, x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 60, normalized size = 0.66 \[ \frac {1}{21} x^{21}+\frac {11}{20} x^{20}+\frac {55}{19} x^{19}+\frac {55}{6} x^{18}+\frac {330}{17} x^{17}+\frac {231}{8} x^{16}+\frac {154}{5} x^{15}+\frac {165}{7} x^{14}+\frac {165}{13} x^{13}+\frac {55}{12} x^{12}+x^{11}+\frac {1}{10} x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 59, normalized size = 0.65 \[ \frac {1}{21} \, x^{21} + \frac {11}{20} \, x^{20} + \frac {55}{19} \, x^{19} + \frac {55}{6} \, x^{18} + \frac {330}{17} \, x^{17} + \frac {231}{8} \, x^{16} + \frac {154}{5} \, x^{15} + \frac {165}{7} \, x^{14} + \frac {165}{13} \, x^{13} + \frac {55}{12} \, x^{12} + x^{11} + \frac {1}{10} \, x^{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 59, normalized size = 0.65 \[ \frac {x^{21}}{21}+\frac {11\,x^{20}}{20}+\frac {55\,x^{19}}{19}+\frac {55\,x^{18}}{6}+\frac {330\,x^{17}}{17}+\frac {231\,x^{16}}{8}+\frac {154\,x^{15}}{5}+\frac {165\,x^{14}}{7}+\frac {165\,x^{13}}{13}+\frac {55\,x^{12}}{12}+x^{11}+\frac {x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 73, normalized size = 0.80 \[ \frac {x^{21}}{21} + \frac {11 x^{20}}{20} + \frac {55 x^{19}}{19} + \frac {55 x^{18}}{6} + \frac {330 x^{17}}{17} + \frac {231 x^{16}}{8} + \frac {154 x^{15}}{5} + \frac {165 x^{14}}{7} + \frac {165 x^{13}}{13} + \frac {55 x^{12}}{12} + x^{11} + \frac {x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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