Optimal. Leaf size=74 \[ -\frac{55}{2 x^2}-\frac{55}{x^3}-\frac{165}{2 x^4}-\frac{462}{5 x^5}-\frac{77}{x^6}-\frac{330}{7 x^7}-\frac{165}{8 x^8}-\frac{55}{9 x^9}-\frac{11}{10 x^{10}}-\frac{1}{11 x^{11}}-\frac{11}{x}+\log (x) \]
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Rubi [A] time = 0.0211485, antiderivative size = 74, 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} \[ -\frac{55}{2 x^2}-\frac{55}{x^3}-\frac{165}{2 x^4}-\frac{462}{5 x^5}-\frac{77}{x^6}-\frac{330}{7 x^7}-\frac{165}{8 x^8}-\frac{55}{9 x^9}-\frac{11}{10 x^{10}}-\frac{1}{11 x^{11}}-\frac{11}{x}+\log (x) \]
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*}
Mathematica [A] time = 0.0025088, size = 74, normalized size = 1. \[ -\frac{55}{2 x^2}-\frac{55}{x^3}-\frac{165}{2 x^4}-\frac{462}{5 x^5}-\frac{77}{x^6}-\frac{330}{7 x^7}-\frac{165}{8 x^8}-\frac{55}{9 x^9}-\frac{11}{10 x^{10}}-\frac{1}{11 x^{11}}-\frac{11}{x}+\log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 59, normalized size = 0.8 \begin{align*} -{\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}}}-77\,{x}^{-6}-{\frac{462}{5\,{x}^{5}}}-{\frac{165}{2\,{x}^{4}}}-55\,{x}^{-3}-{\frac{55}{2\,{x}^{2}}}-11\,{x}^{-1}+\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.999884, size = 78, normalized size = 1.05 \begin{align*} -\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 (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24185, size = 235, normalized size = 3.18 \begin{align*} \frac{27720 \, x^{11} \log \left (x\right ) - 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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.176887, size = 58, normalized size = 0.78 \begin{align*} \log{\left (x \right )} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.158, size = 80, normalized size = 1.08 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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