Optimal. Leaf size=70 \[ -\frac{165}{2 x^2}-\frac{110}{x^3}-\frac{231}{2 x^4}-\frac{462}{5 x^5}-\frac{55}{x^6}-\frac{165}{7 x^7}-\frac{55}{8 x^8}-\frac{11}{9 x^9}-\frac{1}{10 x^{10}}+x-\frac{55}{x}+11 \log (x) \]
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Rubi [A] time = 0.020874, antiderivative size = 70, normalized size of antiderivative = 1., 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} \[ -\frac{165}{2 x^2}-\frac{110}{x^3}-\frac{231}{2 x^4}-\frac{462}{5 x^5}-\frac{55}{x^6}-\frac{165}{7 x^7}-\frac{55}{8 x^8}-\frac{11}{9 x^9}-\frac{1}{10 x^{10}}+x-\frac{55}{x}+11 \log (x) \]
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*}
Mathematica [A] time = 0.0031841, size = 70, normalized size = 1. \[ -\frac{165}{2 x^2}-\frac{110}{x^3}-\frac{231}{2 x^4}-\frac{462}{5 x^5}-\frac{55}{x^6}-\frac{165}{7 x^7}-\frac{55}{8 x^8}-\frac{11}{9 x^9}-\frac{1}{10 x^{10}}+x-\frac{55}{x}+11 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.009, size = 57, normalized size = 0.8 \begin{align*} -{\frac{1}{10\,{x}^{10}}}-{\frac{11}{9\,{x}^{9}}}-{\frac{55}{8\,{x}^{8}}}-{\frac{165}{7\,{x}^{7}}}-55\,{x}^{-6}-{\frac{462}{5\,{x}^{5}}}-{\frac{231}{2\,{x}^{4}}}-110\,{x}^{-3}-{\frac{165}{2\,{x}^{2}}}-55\,{x}^{-1}+x+11\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12422, size = 76, normalized size = 1.09 \begin{align*} 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 (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.26603, size = 219, normalized size = 3.13 \begin{align*} \frac{2520 \, x^{11} + 27720 \, x^{10} \log \left (x\right ) - 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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.162543, size = 56, normalized size = 0.8 \begin{align*} x + 11 \log{\left (x \right )} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11274, size = 77, normalized size = 1.1 \begin{align*} 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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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