Optimal. Leaf size=83 \[ \frac {x^{23}}{23}+\frac {x^{22}}{2}+\frac {55 x^{21}}{21}+\frac {33 x^{20}}{4}+\frac {330 x^{19}}{19}+\frac {77 x^{18}}{3}+\frac {462 x^{17}}{17}+\frac {165 x^{16}}{8}+11 x^{15}+\frac {55 x^{14}}{14}+\frac {11 x^{13}}{13}+\frac {x^{12}}{12} \]
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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} \begin {gather*} \frac {x^{23}}{23}+\frac {x^{22}}{2}+\frac {55 x^{21}}{21}+\frac {33 x^{20}}{4}+\frac {330 x^{19}}{19}+\frac {77 x^{18}}{3}+\frac {462 x^{17}}{17}+\frac {165 x^{16}}{8}+11 x^{15}+\frac {55 x^{14}}{14}+\frac {11 x^{13}}{13}+\frac {x^{12}}{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int x^{11} (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^{11} (1+x)^{11} \, dx\\ &=\int \left (x^{11}+11 x^{12}+55 x^{13}+165 x^{14}+330 x^{15}+462 x^{16}+462 x^{17}+330 x^{18}+165 x^{19}+55 x^{20}+11 x^{21}+x^{22}\right ) \, dx\\ &=\frac {x^{12}}{12}+\frac {11 x^{13}}{13}+\frac {55 x^{14}}{14}+11 x^{15}+\frac {165 x^{16}}{8}+\frac {462 x^{17}}{17}+\frac {77 x^{18}}{3}+\frac {330 x^{19}}{19}+\frac {33 x^{20}}{4}+\frac {55 x^{21}}{21}+\frac {x^{22}}{2}+\frac {x^{23}}{23}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 83, normalized size = 1.00 \begin {gather*} \frac {x^{23}}{23}+\frac {x^{22}}{2}+\frac {55 x^{21}}{21}+\frac {33 x^{20}}{4}+\frac {330 x^{19}}{19}+\frac {77 x^{18}}{3}+\frac {462 x^{17}}{17}+\frac {165 x^{16}}{8}+11 x^{15}+\frac {55 x^{14}}{14}+\frac {11 x^{13}}{13}+\frac {x^{12}}{12} \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^{11} (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 = 0.36, size = 61, normalized size = 0.73 \begin {gather*} \frac {1}{23} x^{23} + \frac {1}{2} x^{22} + \frac {55}{21} x^{21} + \frac {33}{4} x^{20} + \frac {330}{19} x^{19} + \frac {77}{3} x^{18} + \frac {462}{17} x^{17} + \frac {165}{8} x^{16} + 11 x^{15} + \frac {55}{14} x^{14} + \frac {11}{13} x^{13} + \frac {1}{12} x^{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 61, normalized size = 0.73 \begin {gather*} \frac {1}{23} \, x^{23} + \frac {1}{2} \, x^{22} + \frac {55}{21} \, x^{21} + \frac {33}{4} \, x^{20} + \frac {330}{19} \, x^{19} + \frac {77}{3} \, x^{18} + \frac {462}{17} \, x^{17} + \frac {165}{8} \, x^{16} + 11 \, x^{15} + \frac {55}{14} \, x^{14} + \frac {11}{13} \, x^{13} + \frac {1}{12} \, x^{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 62, normalized size = 0.75 \begin {gather*} \frac {1}{23} x^{23}+\frac {1}{2} x^{22}+\frac {55}{21} x^{21}+\frac {33}{4} x^{20}+\frac {330}{19} x^{19}+\frac {77}{3} x^{18}+\frac {462}{17} x^{17}+\frac {165}{8} x^{16}+11 x^{15}+\frac {55}{14} x^{14}+\frac {11}{13} x^{13}+\frac {1}{12} x^{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 61, normalized size = 0.73 \begin {gather*} \frac {1}{23} \, x^{23} + \frac {1}{2} \, x^{22} + \frac {55}{21} \, x^{21} + \frac {33}{4} \, x^{20} + \frac {330}{19} \, x^{19} + \frac {77}{3} \, x^{18} + \frac {462}{17} \, x^{17} + \frac {165}{8} \, x^{16} + 11 \, x^{15} + \frac {55}{14} \, x^{14} + \frac {11}{13} \, x^{13} + \frac {1}{12} \, x^{12} \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 = 0.73 \begin {gather*} \frac {x^{23}}{23}+\frac {x^{22}}{2}+\frac {55\,x^{21}}{21}+\frac {33\,x^{20}}{4}+\frac {330\,x^{19}}{19}+\frac {77\,x^{18}}{3}+\frac {462\,x^{17}}{17}+\frac {165\,x^{16}}{8}+11\,x^{15}+\frac {55\,x^{14}}{14}+\frac {11\,x^{13}}{13}+\frac {x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 73, normalized size = 0.88 \begin {gather*} \frac {x^{23}}{23} + \frac {x^{22}}{2} + \frac {55 x^{21}}{21} + \frac {33 x^{20}}{4} + \frac {330 x^{19}}{19} + \frac {77 x^{18}}{3} + \frac {462 x^{17}}{17} + \frac {165 x^{16}}{8} + 11 x^{15} + \frac {55 x^{14}}{14} + \frac {11 x^{13}}{13} + \frac {x^{12}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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