Optimal. Leaf size=81 \[ -\frac{1}{9 x^9}-\frac{11}{10 x^{10}}-\frac{5}{x^{11}}-\frac{55}{4 x^{12}}-\frac{330}{13 x^{13}}-\frac{33}{x^{14}}-\frac{154}{5 x^{15}}-\frac{165}{8 x^{16}}-\frac{165}{17 x^{17}}-\frac{55}{18 x^{18}}-\frac{11}{19 x^{19}}-\frac{1}{20 x^{20}} \]
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Rubi [A] time = 0.021086, antiderivative size = 81, 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} \[ -\frac{1}{9 x^9}-\frac{11}{10 x^{10}}-\frac{5}{x^{11}}-\frac{55}{4 x^{12}}-\frac{330}{13 x^{13}}-\frac{33}{x^{14}}-\frac{154}{5 x^{15}}-\frac{165}{8 x^{16}}-\frac{165}{17 x^{17}}-\frac{55}{18 x^{18}}-\frac{11}{19 x^{19}}-\frac{1}{20 x^{20}} \]
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^{21}} \, dx &=\int \frac{(1+x)^{11}}{x^{21}} \, dx\\ &=\int \left (\frac{1}{x^{21}}+\frac{11}{x^{20}}+\frac{55}{x^{19}}+\frac{165}{x^{18}}+\frac{330}{x^{17}}+\frac{462}{x^{16}}+\frac{462}{x^{15}}+\frac{330}{x^{14}}+\frac{165}{x^{13}}+\frac{55}{x^{12}}+\frac{11}{x^{11}}+\frac{1}{x^{10}}\right ) \, dx\\ &=-\frac{1}{20 x^{20}}-\frac{11}{19 x^{19}}-\frac{55}{18 x^{18}}-\frac{165}{17 x^{17}}-\frac{165}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{33}{x^{14}}-\frac{330}{13 x^{13}}-\frac{55}{4 x^{12}}-\frac{5}{x^{11}}-\frac{11}{10 x^{10}}-\frac{1}{9 x^9}\\ \end{align*}
Mathematica [A] time = 0.0022271, size = 81, normalized size = 1. \[ -\frac{1}{9 x^9}-\frac{11}{10 x^{10}}-\frac{5}{x^{11}}-\frac{55}{4 x^{12}}-\frac{330}{13 x^{13}}-\frac{33}{x^{14}}-\frac{154}{5 x^{15}}-\frac{165}{8 x^{16}}-\frac{165}{17 x^{17}}-\frac{55}{18 x^{18}}-\frac{11}{19 x^{19}}-\frac{1}{20 x^{20}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 62, normalized size = 0.8 \begin{align*} -{\frac{1}{20\,{x}^{20}}}-{\frac{11}{19\,{x}^{19}}}-{\frac{55}{18\,{x}^{18}}}-{\frac{165}{17\,{x}^{17}}}-{\frac{165}{8\,{x}^{16}}}-{\frac{154}{5\,{x}^{15}}}-33\,{x}^{-14}-{\frac{330}{13\,{x}^{13}}}-{\frac{55}{4\,{x}^{12}}}-5\,{x}^{-11}-{\frac{11}{10\,{x}^{10}}}-{\frac{1}{9\,{x}^{9}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0051, size = 81, normalized size = 1. \begin{align*} -\frac{167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24241, size = 247, normalized size = 3.05 \begin{align*} -\frac{167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.227974, size = 61, normalized size = 0.75 \begin{align*} - \frac{167960 x^{11} + 1662804 x^{10} + 7558200 x^{9} + 20785050 x^{8} + 38372400 x^{7} + 49884120 x^{6} + 46558512 x^{5} + 31177575 x^{4} + 14671800 x^{3} + 4618900 x^{2} + 875160 x + 75582}{1511640 x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13124, size = 81, normalized size = 1. \begin{align*} -\frac{167960 \, x^{11} + 1662804 \, x^{10} + 7558200 \, x^{9} + 20785050 \, x^{8} + 38372400 \, x^{7} + 49884120 \, x^{6} + 46558512 \, x^{5} + 31177575 \, x^{4} + 14671800 \, x^{3} + 4618900 \, x^{2} + 875160 \, x + 75582}{1511640 \, x^{20}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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