Optimal. Leaf size=81 \[ -\frac {1}{20 x^{20}}-\frac {11}{19 x^{19}}-\frac {55}{18 x^{18}}-\frac {165}{17 x^{17}}-\frac {165}{8 x^{16}}-\frac {154}{5 x^{15}}-\frac {33}{x^{14}}-\frac {330}{13 x^{13}}-\frac {55}{4 x^{12}}-\frac {5}{x^{11}}-\frac {11}{10 x^{10}}-\frac {1}{9 x^9} \]
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Rubi [A] time = 0.02, antiderivative size = 81, 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}{9 x^9}-\frac {11}{10 x^{10}}-\frac {5}{x^{11}}-\frac {55}{4 x^{12}}-\frac {330}{13 x^{13}}-\frac {33}{x^{14}}-\frac {154}{5 x^{15}}-\frac {165}{8 x^{16}}-\frac {165}{17 x^{17}}-\frac {55}{18 x^{18}}-\frac {11}{19 x^{19}}-\frac {1}{20 x^{20}} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 43
Rubi steps
\begin {align*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{21}} \, dx &=\int \frac {(1+x)^{11}}{x^{21}} \, dx\\ &=\int \left (\frac {1}{x^{21}}+\frac {11}{x^{20}}+\frac {55}{x^{19}}+\frac {165}{x^{18}}+\frac {330}{x^{17}}+\frac {462}{x^{16}}+\frac {462}{x^{15}}+\frac {330}{x^{14}}+\frac {165}{x^{13}}+\frac {55}{x^{12}}+\frac {11}{x^{11}}+\frac {1}{x^{10}}\right ) \, dx\\ &=-\frac {1}{20 x^{20}}-\frac {11}{19 x^{19}}-\frac {55}{18 x^{18}}-\frac {165}{17 x^{17}}-\frac {165}{8 x^{16}}-\frac {154}{5 x^{15}}-\frac {33}{x^{14}}-\frac {330}{13 x^{13}}-\frac {55}{4 x^{12}}-\frac {5}{x^{11}}-\frac {11}{10 x^{10}}-\frac {1}{9 x^9}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 81, normalized size = 1.00 \begin {gather*} -\frac {1}{20 x^{20}}-\frac {11}{19 x^{19}}-\frac {55}{18 x^{18}}-\frac {165}{17 x^{17}}-\frac {165}{8 x^{16}}-\frac {154}{5 x^{15}}-\frac {33}{x^{14}}-\frac {330}{13 x^{13}}-\frac {55}{4 x^{12}}-\frac {5}{x^{11}}-\frac {11}{10 x^{10}}-\frac {1}{9 x^9} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^{21}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 60, normalized size = 0.74 \begin {gather*} -\frac {167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 60, normalized size = 0.74 \begin {gather*} -\frac {167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 62, normalized size = 0.77 \begin {gather*} -\frac {1}{9 x^{9}}-\frac {11}{10 x^{10}}-\frac {5}{x^{11}}-\frac {55}{4 x^{12}}-\frac {330}{13 x^{13}}-\frac {33}{x^{14}}-\frac {154}{5 x^{15}}-\frac {165}{8 x^{16}}-\frac {165}{17 x^{17}}-\frac {55}{18 x^{18}}-\frac {11}{19 x^{19}}-\frac {1}{20 x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 60, normalized size = 0.74 \begin {gather*} -\frac {167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 60, normalized size = 0.74 \begin {gather*} -\frac {\frac {x^{11}}{9}+\frac {11\,x^{10}}{10}+5\,x^9+\frac {55\,x^8}{4}+\frac {330\,x^7}{13}+33\,x^6+\frac {154\,x^5}{5}+\frac {165\,x^4}{8}+\frac {165\,x^3}{17}+\frac {55\,x^2}{18}+\frac {11\,x}{19}+\frac {1}{20}}{x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 61, normalized size = 0.75 \begin {gather*} \frac {- 167960 x^{11} - 1662804 x^{10} - 7558200 x^{9} - 20785050 x^{8} - 38372400 x^{7} - 49884120 x^{6} - 46558512 x^{5} - 31177575 x^{4} - 14671800 x^{3} - 4618900 x^{2} - 875160 x - 75582}{1511640 x^{20}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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