Optimal. Leaf size=83 \[ \frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11} \]
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Rubi [A] time = 0.0261487, antiderivative size = 83, 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} \[ \frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11} \]
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin{align*} \int x^{10} (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^{10} (1+x)^{11} \, dx\\ &=\int \left (x^{10}+11 x^{11}+55 x^{12}+165 x^{13}+330 x^{14}+462 x^{15}+462 x^{16}+330 x^{17}+165 x^{18}+55 x^{19}+11 x^{20}+x^{21}\right ) \, dx\\ &=\frac{x^{11}}{11}+\frac{11 x^{12}}{12}+\frac{55 x^{13}}{13}+\frac{165 x^{14}}{14}+22 x^{15}+\frac{231 x^{16}}{8}+\frac{462 x^{17}}{17}+\frac{55 x^{18}}{3}+\frac{165 x^{19}}{19}+\frac{11 x^{20}}{4}+\frac{11 x^{21}}{21}+\frac{x^{22}}{22}\\ \end{align*}
Mathematica [A] time = 0.001611, size = 83, normalized size = 1. \[ \frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 62, normalized size = 0.8 \begin{align*}{\frac{{x}^{11}}{11}}+{\frac{11\,{x}^{12}}{12}}+{\frac{55\,{x}^{13}}{13}}+{\frac{165\,{x}^{14}}{14}}+22\,{x}^{15}+{\frac{231\,{x}^{16}}{8}}+{\frac{462\,{x}^{17}}{17}}+{\frac{55\,{x}^{18}}{3}}+{\frac{165\,{x}^{19}}{19}}+{\frac{11\,{x}^{20}}{4}}+{\frac{11\,{x}^{21}}{21}}+{\frac{{x}^{22}}{22}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00509, size = 82, normalized size = 0.99 \begin{align*} \frac{1}{22} \, x^{22} + \frac{11}{21} \, x^{21} + \frac{11}{4} \, x^{20} + \frac{165}{19} \, x^{19} + \frac{55}{3} \, x^{18} + \frac{462}{17} \, x^{17} + \frac{231}{8} \, x^{16} + 22 \, x^{15} + \frac{165}{14} \, x^{14} + \frac{55}{13} \, x^{13} + \frac{11}{12} \, x^{12} + \frac{1}{11} \, x^{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.11117, size = 204, normalized size = 2.46 \begin{align*} \frac{1}{22} x^{22} + \frac{11}{21} x^{21} + \frac{11}{4} x^{20} + \frac{165}{19} x^{19} + \frac{55}{3} x^{18} + \frac{462}{17} x^{17} + \frac{231}{8} x^{16} + 22 x^{15} + \frac{165}{14} x^{14} + \frac{55}{13} x^{13} + \frac{11}{12} x^{12} + \frac{1}{11} x^{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.092665, size = 75, normalized size = 0.9 \begin{align*} \frac{x^{22}}{22} + \frac{11 x^{21}}{21} + \frac{11 x^{20}}{4} + \frac{165 x^{19}}{19} + \frac{55 x^{18}}{3} + \frac{462 x^{17}}{17} + \frac{231 x^{16}}{8} + 22 x^{15} + \frac{165 x^{14}}{14} + \frac{55 x^{13}}{13} + \frac{11 x^{12}}{12} + \frac{x^{11}}{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.153, size = 82, normalized size = 0.99 \begin{align*} \frac{1}{22} \, x^{22} + \frac{11}{21} \, x^{21} + \frac{11}{4} \, x^{20} + \frac{165}{19} \, x^{19} + \frac{55}{3} \, x^{18} + \frac{462}{17} \, x^{17} + \frac{231}{8} \, x^{16} + 22 \, x^{15} + \frac{165}{14} \, x^{14} + \frac{55}{13} \, x^{13} + \frac{11}{12} \, x^{12} + \frac{1}{11} \, x^{11} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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