Optimal. Leaf size=80 \[ \frac {1}{20} (x+1)^{20}-\frac {8}{19} (x+1)^{19}+\frac {14}{9} (x+1)^{18}-\frac {56}{17} (x+1)^{17}+\frac {35}{8} (x+1)^{16}-\frac {56}{15} (x+1)^{15}+2 (x+1)^{14}-\frac {8}{13} (x+1)^{13}+\frac {1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.02, antiderivative size = 80, 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} \begin {gather*} \frac {1}{20} (x+1)^{20}-\frac {8}{19} (x+1)^{19}+\frac {14}{9} (x+1)^{18}-\frac {56}{17} (x+1)^{17}+\frac {35}{8} (x+1)^{16}-\frac {56}{15} (x+1)^{15}+2 (x+1)^{14}-\frac {8}{13} (x+1)^{13}+\frac {1}{12} (x+1)^{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int x^8 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^8 (1+x)^{11} \, dx\\ &=\int \left ((1+x)^{11}-8 (1+x)^{12}+28 (1+x)^{13}-56 (1+x)^{14}+70 (1+x)^{15}-56 (1+x)^{16}+28 (1+x)^{17}-8 (1+x)^{18}+(1+x)^{19}\right ) \, dx\\ &=\frac {1}{12} (1+x)^{12}-\frac {8}{13} (1+x)^{13}+2 (1+x)^{14}-\frac {56}{15} (1+x)^{15}+\frac {35}{8} (1+x)^{16}-\frac {56}{17} (1+x)^{17}+\frac {14}{9} (1+x)^{18}-\frac {8}{19} (1+x)^{19}+\frac {1}{20} (1+x)^{20}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 81, normalized size = 1.01 \begin {gather*} \frac {x^{20}}{20}+\frac {11 x^{19}}{19}+\frac {55 x^{18}}{18}+\frac {165 x^{17}}{17}+\frac {165 x^{16}}{8}+\frac {154 x^{15}}{5}+33 x^{14}+\frac {330 x^{13}}{13}+\frac {55 x^{12}}{4}+5 x^{11}+\frac {11 x^{10}}{10}+\frac {x^9}{9} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^8 (1+x) \left (1+2 x+x^2\right )^5 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.35, size = 61, normalized size = 0.76 \begin {gather*} \frac {1}{20} x^{20} + \frac {11}{19} x^{19} + \frac {55}{18} x^{18} + \frac {165}{17} x^{17} + \frac {165}{8} x^{16} + \frac {154}{5} x^{15} + 33 x^{14} + \frac {330}{13} x^{13} + \frac {55}{4} x^{12} + 5 x^{11} + \frac {11}{10} x^{10} + \frac {1}{9} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 61, normalized size = 0.76 \begin {gather*} \frac {1}{20} \, x^{20} + \frac {11}{19} \, x^{19} + \frac {55}{18} \, x^{18} + \frac {165}{17} \, x^{17} + \frac {165}{8} \, x^{16} + \frac {154}{5} \, x^{15} + 33 \, x^{14} + \frac {330}{13} \, x^{13} + \frac {55}{4} \, x^{12} + 5 \, x^{11} + \frac {11}{10} \, x^{10} + \frac {1}{9} \, x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 62, normalized size = 0.78 \begin {gather*} \frac {1}{20} x^{20}+\frac {11}{19} x^{19}+\frac {55}{18} x^{18}+\frac {165}{17} x^{17}+\frac {165}{8} x^{16}+\frac {154}{5} x^{15}+33 x^{14}+\frac {330}{13} x^{13}+\frac {55}{4} x^{12}+5 x^{11}+\frac {11}{10} x^{10}+\frac {1}{9} x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 61, normalized size = 0.76 \begin {gather*} \frac {1}{20} \, x^{20} + \frac {11}{19} \, x^{19} + \frac {55}{18} \, x^{18} + \frac {165}{17} \, x^{17} + \frac {165}{8} \, x^{16} + \frac {154}{5} \, x^{15} + 33 \, x^{14} + \frac {330}{13} \, x^{13} + \frac {55}{4} \, x^{12} + 5 \, x^{11} + \frac {11}{10} \, x^{10} + \frac {1}{9} \, x^{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 61, normalized size = 0.76 \begin {gather*} \frac {x^{20}}{20}+\frac {11\,x^{19}}{19}+\frac {55\,x^{18}}{18}+\frac {165\,x^{17}}{17}+\frac {165\,x^{16}}{8}+\frac {154\,x^{15}}{5}+33\,x^{14}+\frac {330\,x^{13}}{13}+\frac {55\,x^{12}}{4}+5\,x^{11}+\frac {11\,x^{10}}{10}+\frac {x^9}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 73, normalized size = 0.91 \begin {gather*} \frac {x^{20}}{20} + \frac {11 x^{19}}{19} + \frac {55 x^{18}}{18} + \frac {165 x^{17}}{17} + \frac {165 x^{16}}{8} + \frac {154 x^{15}}{5} + 33 x^{14} + \frac {330 x^{13}}{13} + \frac {55 x^{12}}{4} + 5 x^{11} + \frac {11 x^{10}}{10} + \frac {x^{9}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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