Optimal. Leaf size=70 \[ \frac{x^2}{2}-\frac{165}{x^2}-\frac{154}{x^3}-\frac{231}{2 x^4}-\frac{66}{x^5}-\frac{55}{2 x^6}-\frac{55}{7 x^7}-\frac{11}{8 x^8}-\frac{1}{9 x^9}+11 x-\frac{165}{x}+55 \log (x) \]
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Rubi [A] time = 0.0221587, 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} \[ \frac{x^2}{2}-\frac{165}{x^2}-\frac{154}{x^3}-\frac{231}{2 x^4}-\frac{66}{x^5}-\frac{55}{2 x^6}-\frac{55}{7 x^7}-\frac{11}{8 x^8}-\frac{1}{9 x^9}+11 x-\frac{165}{x}+55 \log (x) \]
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^{10}} \, dx &=\int \frac{(1+x)^{11}}{x^{10}} \, dx\\ &=\int \left (11+\frac{1}{x^{10}}+\frac{11}{x^9}+\frac{55}{x^8}+\frac{165}{x^7}+\frac{330}{x^6}+\frac{462}{x^5}+\frac{462}{x^4}+\frac{330}{x^3}+\frac{165}{x^2}+\frac{55}{x}+x\right ) \, dx\\ &=-\frac{1}{9 x^9}-\frac{11}{8 x^8}-\frac{55}{7 x^7}-\frac{55}{2 x^6}-\frac{66}{x^5}-\frac{231}{2 x^4}-\frac{154}{x^3}-\frac{165}{x^2}-\frac{165}{x}+11 x+\frac{x^2}{2}+55 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0025497, size = 70, normalized size = 1. \[ \frac{x^2}{2}-\frac{165}{x^2}-\frac{154}{x^3}-\frac{231}{2 x^4}-\frac{66}{x^5}-\frac{55}{2 x^6}-\frac{55}{7 x^7}-\frac{11}{8 x^8}-\frac{1}{9 x^9}+11 x-\frac{165}{x}+55 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 59, normalized size = 0.8 \begin{align*} -{\frac{1}{9\,{x}^{9}}}-{\frac{11}{8\,{x}^{8}}}-{\frac{55}{7\,{x}^{7}}}-{\frac{55}{2\,{x}^{6}}}-66\,{x}^{-5}-{\frac{231}{2\,{x}^{4}}}-154\,{x}^{-3}-165\,{x}^{-2}-165\,{x}^{-1}+11\,x+{\frac{{x}^{2}}{2}}+55\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06099, size = 78, normalized size = 1.11 \begin{align*} \frac{1}{2} \, x^{2} + 11 \, x - \frac{83160 \, x^{8} + 83160 \, x^{7} + 77616 \, x^{6} + 58212 \, x^{5} + 33264 \, x^{4} + 13860 \, x^{3} + 3960 \, x^{2} + 693 \, x + 56}{504 \, x^{9}} + 55 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.28418, size = 201, normalized size = 2.87 \begin{align*} \frac{252 \, x^{11} + 5544 \, x^{10} + 27720 \, x^{9} \log \left (x\right ) - 83160 \, x^{8} - 83160 \, x^{7} - 77616 \, x^{6} - 58212 \, x^{5} - 33264 \, x^{4} - 13860 \, x^{3} - 3960 \, x^{2} - 693 \, x - 56}{504 \, x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.156132, size = 58, normalized size = 0.83 \begin{align*} \frac{x^{2}}{2} + 11 x + 55 \log{\left (x \right )} - \frac{83160 x^{8} + 83160 x^{7} + 77616 x^{6} + 58212 x^{5} + 33264 x^{4} + 13860 x^{3} + 3960 x^{2} + 693 x + 56}{504 x^{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12616, size = 80, normalized size = 1.14 \begin{align*} \frac{1}{2} \, x^{2} + 11 \, x - \frac{83160 \, x^{8} + 83160 \, x^{7} + 77616 \, x^{6} + 58212 \, x^{5} + 33264 \, x^{4} + 13860 \, x^{3} + 3960 \, x^{2} + 693 \, x + 56}{504 \, x^{9}} + 55 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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