Optimal. Leaf size=83 \[ -\frac{1}{10 x^{10}}-\frac{1}{x^{11}}-\frac{55}{12 x^{12}}-\frac{165}{13 x^{13}}-\frac{165}{7 x^{14}}-\frac{154}{5 x^{15}}-\frac{231}{8 x^{16}}-\frac{330}{17 x^{17}}-\frac{55}{6 x^{18}}-\frac{55}{19 x^{19}}-\frac{11}{20 x^{20}}-\frac{1}{21 x^{21}} \]
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Rubi [A] time = 0.0216553, antiderivative size = 83, 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} \[ -\frac{1}{10 x^{10}}-\frac{1}{x^{11}}-\frac{55}{12 x^{12}}-\frac{165}{13 x^{13}}-\frac{165}{7 x^{14}}-\frac{154}{5 x^{15}}-\frac{231}{8 x^{16}}-\frac{330}{17 x^{17}}-\frac{55}{6 x^{18}}-\frac{55}{19 x^{19}}-\frac{11}{20 x^{20}}-\frac{1}{21 x^{21}} \]
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^{22}} \, dx &=\int \frac{(1+x)^{11}}{x^{22}} \, dx\\ &=\int \left (\frac{1}{x^{22}}+\frac{11}{x^{21}}+\frac{55}{x^{20}}+\frac{165}{x^{19}}+\frac{330}{x^{18}}+\frac{462}{x^{17}}+\frac{462}{x^{16}}+\frac{330}{x^{15}}+\frac{165}{x^{14}}+\frac{55}{x^{13}}+\frac{11}{x^{12}}+\frac{1}{x^{11}}\right ) \, dx\\ &=-\frac{1}{21 x^{21}}-\frac{11}{20 x^{20}}-\frac{55}{19 x^{19}}-\frac{55}{6 x^{18}}-\frac{330}{17 x^{17}}-\frac{231}{8 x^{16}}-\frac{154}{5 x^{15}}-\frac{165}{7 x^{14}}-\frac{165}{13 x^{13}}-\frac{55}{12 x^{12}}-\frac{1}{x^{11}}-\frac{1}{10 x^{10}}\\ \end{align*}
Mathematica [A] time = 0.004206, size = 83, normalized size = 1. \[ -\frac{1}{10 x^{10}}-\frac{1}{x^{11}}-\frac{55}{12 x^{12}}-\frac{165}{13 x^{13}}-\frac{165}{7 x^{14}}-\frac{154}{5 x^{15}}-\frac{231}{8 x^{16}}-\frac{330}{17 x^{17}}-\frac{55}{6 x^{18}}-\frac{55}{19 x^{19}}-\frac{11}{20 x^{20}}-\frac{1}{21 x^{21}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 62, normalized size = 0.8 \begin{align*} -{\frac{1}{21\,{x}^{21}}}-{\frac{11}{20\,{x}^{20}}}-{\frac{55}{19\,{x}^{19}}}-{\frac{55}{6\,{x}^{18}}}-{\frac{330}{17\,{x}^{17}}}-{\frac{231}{8\,{x}^{16}}}-{\frac{154}{5\,{x}^{15}}}-{\frac{165}{7\,{x}^{14}}}-{\frac{165}{13\,{x}^{13}}}-{\frac{55}{12\,{x}^{12}}}-{x}^{-11}-{\frac{1}{10\,{x}^{10}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01334, size = 81, normalized size = 0.98 \begin{align*} -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.19624, size = 255, normalized size = 3.07 \begin{align*} -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.231117, size = 61, normalized size = 0.73 \begin{align*} - \frac{352716 x^{11} + 3527160 x^{10} + 16166150 x^{9} + 44767800 x^{8} + 83140200 x^{7} + 108636528 x^{6} + 101846745 x^{5} + 68468400 x^{4} + 32332300 x^{3} + 10210200 x^{2} + 1939938 x + 167960}{3527160 x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17526, size = 81, normalized size = 0.98 \begin{align*} -\frac{352716 \, x^{11} + 3527160 \, x^{10} + 16166150 \, x^{9} + 44767800 \, x^{8} + 83140200 \, x^{7} + 108636528 \, x^{6} + 101846745 \, x^{5} + 68468400 \, x^{4} + 32332300 \, x^{3} + 10210200 \, x^{2} + 1939938 \, x + 167960}{3527160 \, x^{21}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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