Optimal. Leaf size=70 \[ -\frac {1}{10 x^{10}}-\frac {11}{9 x^9}-\frac {55}{8 x^8}-\frac {165}{7 x^7}-\frac {55}{x^6}-\frac {462}{5 x^5}-\frac {231}{2 x^4}-\frac {110}{x^3}-\frac {165}{2 x^2}+x-\frac {55}{x}+11 \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 70, 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 {165}{2 x^2}-\frac {110}{x^3}-\frac {231}{2 x^4}-\frac {462}{5 x^5}-\frac {55}{x^6}-\frac {165}{7 x^7}-\frac {55}{8 x^8}-\frac {11}{9 x^9}-\frac {1}{10 x^{10}}+x-\frac {55}{x}+11 \log (x) \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^{11}} \, dx &=\int \frac {(1+x)^{11}}{x^{11}} \, dx\\ &=\int \left (1+\frac {1}{x^{11}}+\frac {11}{x^{10}}+\frac {55}{x^9}+\frac {165}{x^8}+\frac {330}{x^7}+\frac {462}{x^6}+\frac {462}{x^5}+\frac {330}{x^4}+\frac {165}{x^3}+\frac {55}{x^2}+\frac {11}{x}\right ) \, dx\\ &=-\frac {1}{10 x^{10}}-\frac {11}{9 x^9}-\frac {55}{8 x^8}-\frac {165}{7 x^7}-\frac {55}{x^6}-\frac {462}{5 x^5}-\frac {231}{2 x^4}-\frac {110}{x^3}-\frac {165}{2 x^2}-\frac {55}{x}+x+11 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 70, normalized size = 1.00 \begin {gather*} -\frac {1}{10 x^{10}}-\frac {11}{9 x^9}-\frac {55}{8 x^8}-\frac {165}{7 x^7}-\frac {55}{x^6}-\frac {462}{5 x^5}-\frac {231}{2 x^4}-\frac {110}{x^3}-\frac {165}{2 x^2}+x-\frac {55}{x}+11 \log (x) \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^{11}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.40, size = 62, normalized size = 0.89 \begin {gather*} \frac {2520 \, x^{11} + 27720 \, x^{10} \log \relax (x) - 138600 \, x^{9} - 207900 \, x^{8} - 277200 \, x^{7} - 291060 \, x^{6} - 232848 \, x^{5} - 138600 \, x^{4} - 59400 \, x^{3} - 17325 \, x^{2} - 3080 \, x - 252}{2520 \, x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 57, normalized size = 0.81 \begin {gather*} x - \frac {138600 \, x^{9} + 207900 \, x^{8} + 277200 \, x^{7} + 291060 \, x^{6} + 232848 \, x^{5} + 138600 \, x^{4} + 59400 \, x^{3} + 17325 \, x^{2} + 3080 \, x + 252}{2520 \, x^{10}} + 11 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 57, normalized size = 0.81 \begin {gather*} x +11 \ln \relax (x )-\frac {55}{x}-\frac {165}{2 x^{2}}-\frac {110}{x^{3}}-\frac {231}{2 x^{4}}-\frac {462}{5 x^{5}}-\frac {55}{x^{6}}-\frac {165}{7 x^{7}}-\frac {55}{8 x^{8}}-\frac {11}{9 x^{9}}-\frac {1}{10 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 56, normalized size = 0.80 \begin {gather*} x - \frac {138600 \, x^{9} + 207900 \, x^{8} + 277200 \, x^{7} + 291060 \, x^{6} + 232848 \, x^{5} + 138600 \, x^{4} + 59400 \, x^{3} + 17325 \, x^{2} + 3080 \, x + 252}{2520 \, x^{10}} + 11 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.08, size = 62, normalized size = 0.89 \begin {gather*} -\frac {\frac {11\,x}{9}-11\,x^{10}\,\ln \relax (x)+\frac {55\,x^2}{8}+\frac {165\,x^3}{7}+55\,x^4+\frac {462\,x^5}{5}+\frac {231\,x^6}{2}+110\,x^7+\frac {165\,x^8}{2}+55\,x^9-x^{11}+\frac {1}{10}}{x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 58, normalized size = 0.83 \begin {gather*} x + 11 \log {\relax (x )} + \frac {- 138600 x^{9} - 207900 x^{8} - 277200 x^{7} - 291060 x^{6} - 232848 x^{5} - 138600 x^{4} - 59400 x^{3} - 17325 x^{2} - 3080 x - 252}{2520 x^{10}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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