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 = 0.03, antiderivative size = 83, 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} \[ \frac {x^{22}}{22}+\frac {11 x^{21}}{21}+\frac {11 x^{20}}{4}+\frac {165 x^{19}}{19}+\frac {55 x^{18}}{3}+\frac {462 x^{17}}{17}+\frac {231 x^{16}}{8}+22 x^{15}+\frac {165 x^{14}}{14}+\frac {55 x^{13}}{13}+\frac {11 x^{12}}{12}+\frac {x^{11}}{11} \]
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*}
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Mathematica [A] time = 0.00, size = 83, normalized size = 1.00 \[ \frac {x^{22}}{22}+\frac {11 x^{21}}{21}+\frac {11 x^{20}}{4}+\frac {165 x^{19}}{19}+\frac {55 x^{18}}{3}+\frac {462 x^{17}}{17}+\frac {231 x^{16}}{8}+22 x^{15}+\frac {165 x^{14}}{14}+\frac {55 x^{13}}{13}+\frac {11 x^{12}}{12}+\frac {x^{11}}{11} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 61, normalized size = 0.73 \[ \frac {1}{22} x^{22} + \frac {11}{21} x^{21} + \frac {11}{4} x^{20} + \frac {165}{19} x^{19} + \frac {55}{3} x^{18} + \frac {462}{17} x^{17} + \frac {231}{8} x^{16} + 22 x^{15} + \frac {165}{14} x^{14} + \frac {55}{13} x^{13} + \frac {11}{12} x^{12} + \frac {1}{11} x^{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 61, normalized size = 0.73 \[ \frac {1}{22} \, x^{22} + \frac {11}{21} \, x^{21} + \frac {11}{4} \, x^{20} + \frac {165}{19} \, x^{19} + \frac {55}{3} \, x^{18} + \frac {462}{17} \, x^{17} + \frac {231}{8} \, x^{16} + 22 \, x^{15} + \frac {165}{14} \, x^{14} + \frac {55}{13} \, x^{13} + \frac {11}{12} \, x^{12} + \frac {1}{11} \, x^{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 62, normalized size = 0.75 \[ \frac {1}{22} x^{22}+\frac {11}{21} x^{21}+\frac {11}{4} x^{20}+\frac {165}{19} x^{19}+\frac {55}{3} x^{18}+\frac {462}{17} x^{17}+\frac {231}{8} x^{16}+22 x^{15}+\frac {165}{14} x^{14}+\frac {55}{13} x^{13}+\frac {11}{12} x^{12}+\frac {1}{11} x^{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.60, size = 61, normalized size = 0.73 \[ \frac {1}{22} \, x^{22} + \frac {11}{21} \, x^{21} + \frac {11}{4} \, x^{20} + \frac {165}{19} \, x^{19} + \frac {55}{3} \, x^{18} + \frac {462}{17} \, x^{17} + \frac {231}{8} \, x^{16} + 22 \, x^{15} + \frac {165}{14} \, x^{14} + \frac {55}{13} \, x^{13} + \frac {11}{12} \, x^{12} + \frac {1}{11} \, x^{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 61, normalized size = 0.73 \[ \frac {x^{22}}{22}+\frac {11\,x^{21}}{21}+\frac {11\,x^{20}}{4}+\frac {165\,x^{19}}{19}+\frac {55\,x^{18}}{3}+\frac {462\,x^{17}}{17}+\frac {231\,x^{16}}{8}+22\,x^{15}+\frac {165\,x^{14}}{14}+\frac {55\,x^{13}}{13}+\frac {11\,x^{12}}{12}+\frac {x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 75, normalized size = 0.90 \[ \frac {x^{22}}{22} + \frac {11 x^{21}}{21} + \frac {11 x^{20}}{4} + \frac {165 x^{19}}{19} + \frac {55 x^{18}}{3} + \frac {462 x^{17}}{17} + \frac {231 x^{16}}{8} + 22 x^{15} + \frac {165 x^{14}}{14} + \frac {55 x^{13}}{13} + \frac {11 x^{12}}{12} + \frac {x^{11}}{11} \]
Verification of antiderivative is not currently implemented for this CAS.
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