Optimal. Leaf size=74 \[ -\frac {1}{11 x^{11}}-\frac {11}{10 x^{10}}-\frac {55}{9 x^9}-\frac {165}{8 x^8}-\frac {330}{7 x^7}-\frac {77}{x^6}-\frac {462}{5 x^5}-\frac {165}{2 x^4}-\frac {55}{x^3}-\frac {55}{2 x^2}-\frac {11}{x}+\log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 74, 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 {55}{2 x^2}-\frac {55}{x^3}-\frac {165}{2 x^4}-\frac {462}{5 x^5}-\frac {77}{x^6}-\frac {330}{7 x^7}-\frac {165}{8 x^8}-\frac {55}{9 x^9}-\frac {11}{10 x^{10}}-\frac {1}{11 x^{11}}-\frac {11}{x}+\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^{12}} \, dx &=\int \frac {(1+x)^{11}}{x^{12}} \, dx\\ &=\int \left (\frac {1}{x^{12}}+\frac {11}{x^{11}}+\frac {55}{x^{10}}+\frac {165}{x^9}+\frac {330}{x^8}+\frac {462}{x^7}+\frac {462}{x^6}+\frac {330}{x^5}+\frac {165}{x^4}+\frac {55}{x^3}+\frac {11}{x^2}+\frac {1}{x}\right ) \, dx\\ &=-\frac {1}{11 x^{11}}-\frac {11}{10 x^{10}}-\frac {55}{9 x^9}-\frac {165}{8 x^8}-\frac {330}{7 x^7}-\frac {77}{x^6}-\frac {462}{5 x^5}-\frac {165}{2 x^4}-\frac {55}{x^3}-\frac {55}{2 x^2}-\frac {11}{x}+\log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 74, normalized size = 1.00 \begin {gather*} -\frac {1}{11 x^{11}}-\frac {11}{10 x^{10}}-\frac {55}{9 x^9}-\frac {165}{8 x^8}-\frac {330}{7 x^7}-\frac {77}{x^6}-\frac {462}{5 x^5}-\frac {165}{2 x^4}-\frac {55}{x^3}-\frac {55}{2 x^2}-\frac {11}{x}+\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^{12}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 62, normalized size = 0.84 \begin {gather*} \frac {27720 \, x^{11} \log \relax (x) - 304920 \, x^{10} - 762300 \, x^{9} - 1524600 \, x^{8} - 2286900 \, x^{7} - 2561328 \, x^{6} - 2134440 \, x^{5} - 1306800 \, x^{4} - 571725 \, x^{3} - 169400 \, x^{2} - 30492 \, x - 2520}{27720 \, x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 59, normalized size = 0.80 \begin {gather*} -\frac {304920 \, x^{10} + 762300 \, x^{9} + 1524600 \, x^{8} + 2286900 \, x^{7} + 2561328 \, x^{6} + 2134440 \, x^{5} + 1306800 \, x^{4} + 571725 \, x^{3} + 169400 \, x^{2} + 30492 \, x + 2520}{27720 \, x^{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 = 59, normalized size = 0.80 \begin {gather*} \ln \relax (x )-\frac {11}{x}-\frac {55}{2 x^{2}}-\frac {55}{x^{3}}-\frac {165}{2 x^{4}}-\frac {462}{5 x^{5}}-\frac {77}{x^{6}}-\frac {330}{7 x^{7}}-\frac {165}{8 x^{8}}-\frac {55}{9 x^{9}}-\frac {11}{10 x^{10}}-\frac {1}{11 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.58, size = 58, normalized size = 0.78 \begin {gather*} -\frac {304920 \, x^{10} + 762300 \, x^{9} + 1524600 \, x^{8} + 2286900 \, x^{7} + 2561328 \, x^{6} + 2134440 \, x^{5} + 1306800 \, x^{4} + 571725 \, x^{3} + 169400 \, x^{2} + 30492 \, x + 2520}{27720 \, x^{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 = 58, normalized size = 0.78 \begin {gather*} \ln \relax (x)-\frac {11\,x^{10}+\frac {55\,x^9}{2}+55\,x^8+\frac {165\,x^7}{2}+\frac {462\,x^6}{5}+77\,x^5+\frac {330\,x^4}{7}+\frac {165\,x^3}{8}+\frac {55\,x^2}{9}+\frac {11\,x}{10}+\frac {1}{11}}{x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 60, normalized size = 0.81 \begin {gather*} \log {\relax (x )} + \frac {- 304920 x^{10} - 762300 x^{9} - 1524600 x^{8} - 2286900 x^{7} - 2561328 x^{6} - 2134440 x^{5} - 1306800 x^{4} - 571725 x^{3} - 169400 x^{2} - 30492 x - 2520}{27720 x^{11}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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