Optimal. Leaf size=83 \[ -\frac {1}{21 x^{21}}-\frac {11}{20 x^{20}}-\frac {55}{19 x^{19}}-\frac {55}{6 x^{18}}-\frac {330}{17 x^{17}}-\frac {231}{8 x^{16}}-\frac {154}{5 x^{15}}-\frac {165}{7 x^{14}}-\frac {165}{13 x^{13}}-\frac {55}{12 x^{12}}-\frac {1}{x^{11}}-\frac {1}{10 x^{10}} \]
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Rubi [A] time = 0.02, 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 {1}{10 x^{10}}-\frac {1}{x^{11}}-\frac {55}{12 x^{12}}-\frac {165}{13 x^{13}}-\frac {165}{7 x^{14}}-\frac {154}{5 x^{15}}-\frac {231}{8 x^{16}}-\frac {330}{17 x^{17}}-\frac {55}{6 x^{18}}-\frac {55}{19 x^{19}}-\frac {11}{20 x^{20}}-\frac {1}{21 x^{21}} \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^{22}} \, dx &=\int \frac {(1+x)^{11}}{x^{22}} \, dx\\ &=\int \left (\frac {1}{x^{22}}+\frac {11}{x^{21}}+\frac {55}{x^{20}}+\frac {165}{x^{19}}+\frac {330}{x^{18}}+\frac {462}{x^{17}}+\frac {462}{x^{16}}+\frac {330}{x^{15}}+\frac {165}{x^{14}}+\frac {55}{x^{13}}+\frac {11}{x^{12}}+\frac {1}{x^{11}}\right ) \, dx\\ &=-\frac {1}{21 x^{21}}-\frac {11}{20 x^{20}}-\frac {55}{19 x^{19}}-\frac {55}{6 x^{18}}-\frac {330}{17 x^{17}}-\frac {231}{8 x^{16}}-\frac {154}{5 x^{15}}-\frac {165}{7 x^{14}}-\frac {165}{13 x^{13}}-\frac {55}{12 x^{12}}-\frac {1}{x^{11}}-\frac {1}{10 x^{10}}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 83, normalized size = 1.00 \begin {gather*} -\frac {1}{21 x^{21}}-\frac {11}{20 x^{20}}-\frac {55}{19 x^{19}}-\frac {55}{6 x^{18}}-\frac {330}{17 x^{17}}-\frac {231}{8 x^{16}}-\frac {154}{5 x^{15}}-\frac {165}{7 x^{14}}-\frac {165}{13 x^{13}}-\frac {55}{12 x^{12}}-\frac {1}{x^{11}}-\frac {1}{10 x^{10}} \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^{22}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 60, normalized size = 0.72 \begin {gather*} -\frac {352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 60, normalized size = 0.72 \begin {gather*} -\frac {352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \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 = 0.75 \begin {gather*} -\frac {1}{10 x^{10}}-\frac {1}{x^{11}}-\frac {55}{12 x^{12}}-\frac {165}{13 x^{13}}-\frac {165}{7 x^{14}}-\frac {154}{5 x^{15}}-\frac {231}{8 x^{16}}-\frac {330}{17 x^{17}}-\frac {55}{6 x^{18}}-\frac {55}{19 x^{19}}-\frac {11}{20 x^{20}}-\frac {1}{21 x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 60, normalized size = 0.72 \begin {gather*} -\frac {352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.07, size = 58, normalized size = 0.70 \begin {gather*} -\frac {\frac {x^{11}}{10}+x^{10}+\frac {55\,x^9}{12}+\frac {165\,x^8}{13}+\frac {165\,x^7}{7}+\frac {154\,x^6}{5}+\frac {231\,x^5}{8}+\frac {330\,x^4}{17}+\frac {55\,x^3}{6}+\frac {55\,x^2}{19}+\frac {11\,x}{20}+\frac {1}{21}}{x^{21}} \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 = 0.73 \begin {gather*} \frac {- 352716 x^{11} - 3527160 x^{10} - 16166150 x^{9} - 44767800 x^{8} - 83140200 x^{7} - 108636528 x^{6} - 101846745 x^{5} - 68468400 x^{4} - 32332300 x^{3} - 10210200 x^{2} - 1939938 x - 167960}{3527160 x^{21}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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