Optimal. Leaf size=55 \[ \frac {1}{17} (x+1)^{17}-\frac {5}{16} (x+1)^{16}+\frac {2}{3} (x+1)^{15}-\frac {5}{7} (x+1)^{14}+\frac {5}{13} (x+1)^{13}-\frac {1}{12} (x+1)^{12} \]
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Rubi [A] time = 0.02, antiderivative size = 55, 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}{17} (x+1)^{17}-\frac {5}{16} (x+1)^{16}+\frac {2}{3} (x+1)^{15}-\frac {5}{7} (x+1)^{14}+\frac {5}{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^5 (1+x) \left (1+2 x+x^2\right )^5 \, dx &=\int x^5 (1+x)^{11} \, dx\\ &=\int \left (-(1+x)^{11}+5 (1+x)^{12}-10 (1+x)^{13}+10 (1+x)^{14}-5 (1+x)^{15}+(1+x)^{16}\right ) \, dx\\ &=-\frac {1}{12} (1+x)^{12}+\frac {5}{13} (1+x)^{13}-\frac {5}{7} (1+x)^{14}+\frac {2}{3} (1+x)^{15}-\frac {5}{16} (1+x)^{16}+\frac {1}{17} (1+x)^{17}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 81, normalized size = 1.47 \begin {gather*} \frac {x^{17}}{17}+\frac {11 x^{16}}{16}+\frac {11 x^{15}}{3}+\frac {165 x^{14}}{14}+\frac {330 x^{13}}{13}+\frac {77 x^{12}}{2}+42 x^{11}+33 x^{10}+\frac {55 x^9}{3}+\frac {55 x^8}{8}+\frac {11 x^7}{7}+\frac {x^6}{6} \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^5 (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 = 1.11 \begin {gather*} \frac {1}{17} x^{17} + \frac {11}{16} x^{16} + \frac {11}{3} x^{15} + \frac {165}{14} x^{14} + \frac {330}{13} x^{13} + \frac {77}{2} x^{12} + 42 x^{11} + 33 x^{10} + \frac {55}{3} x^{9} + \frac {55}{8} x^{8} + \frac {11}{7} x^{7} + \frac {1}{6} x^{6} \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 = 1.11 \begin {gather*} \frac {1}{17} \, x^{17} + \frac {11}{16} \, x^{16} + \frac {11}{3} \, x^{15} + \frac {165}{14} \, x^{14} + \frac {330}{13} \, x^{13} + \frac {77}{2} \, x^{12} + 42 \, x^{11} + 33 \, x^{10} + \frac {55}{3} \, x^{9} + \frac {55}{8} \, x^{8} + \frac {11}{7} \, x^{7} + \frac {1}{6} \, x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 62, normalized size = 1.13 \begin {gather*} \frac {1}{17} x^{17}+\frac {11}{16} x^{16}+\frac {11}{3} x^{15}+\frac {165}{14} x^{14}+\frac {330}{13} x^{13}+\frac {77}{2} x^{12}+42 x^{11}+33 x^{10}+\frac {55}{3} x^{9}+\frac {55}{8} x^{8}+\frac {11}{7} x^{7}+\frac {1}{6} x^{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.66, size = 61, normalized size = 1.11 \begin {gather*} \frac {1}{17} \, x^{17} + \frac {11}{16} \, x^{16} + \frac {11}{3} \, x^{15} + \frac {165}{14} \, x^{14} + \frac {330}{13} \, x^{13} + \frac {77}{2} \, x^{12} + 42 \, x^{11} + 33 \, x^{10} + \frac {55}{3} \, x^{9} + \frac {55}{8} \, x^{8} + \frac {11}{7} \, x^{7} + \frac {1}{6} \, x^{6} \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 = 1.11 \begin {gather*} \frac {x^{17}}{17}+\frac {11\,x^{16}}{16}+\frac {11\,x^{15}}{3}+\frac {165\,x^{14}}{14}+\frac {330\,x^{13}}{13}+\frac {77\,x^{12}}{2}+42\,x^{11}+33\,x^{10}+\frac {55\,x^9}{3}+\frac {55\,x^8}{8}+\frac {11\,x^7}{7}+\frac {x^6}{6} \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 = 1.33 \begin {gather*} \frac {x^{17}}{17} + \frac {11 x^{16}}{16} + \frac {11 x^{15}}{3} + \frac {165 x^{14}}{14} + \frac {330 x^{13}}{13} + \frac {77 x^{12}}{2} + 42 x^{11} + 33 x^{10} + \frac {55 x^{9}}{3} + \frac {55 x^{8}}{8} + \frac {11 x^{7}}{7} + \frac {x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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