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 = 0.0264048, antiderivative size = 91, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0016308, 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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Maple [A] time = 0.001, size = 60, normalized size = 0.7 \begin{align*}{\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}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.958375, size = 80, normalized size = 0.88 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.05527, size = 200, normalized size = 2.2 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.08129, size = 73, normalized size = 0.8 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15265, size = 80, normalized size = 0.88 \begin{align*} \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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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