Optimal. Leaf size=72 \[ \frac{x^{10}}{10}+\frac{11 x^9}{9}+\frac{55 x^8}{8}+\frac{165 x^7}{7}+55 x^6+\frac{462 x^5}{5}+\frac{231 x^4}{2}+110 x^3+\frac{165 x^2}{2}+55 x-\frac{1}{x}+11 \log (x) \]
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Rubi [A] time = 0.0206652, antiderivative size = 72, 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} \[ \frac{x^{10}}{10}+\frac{11 x^9}{9}+\frac{55 x^8}{8}+\frac{165 x^7}{7}+55 x^6+\frac{462 x^5}{5}+\frac{231 x^4}{2}+110 x^3+\frac{165 x^2}{2}+55 x-\frac{1}{x}+11 \log (x) \]
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^2} \, dx &=\int \frac{(1+x)^{11}}{x^2} \, dx\\ &=\int \left (55+\frac{1}{x^2}+\frac{11}{x}+165 x+330 x^2+462 x^3+462 x^4+330 x^5+165 x^6+55 x^7+11 x^8+x^9\right ) \, dx\\ &=-\frac{1}{x}+55 x+\frac{165 x^2}{2}+110 x^3+\frac{231 x^4}{2}+\frac{462 x^5}{5}+55 x^6+\frac{165 x^7}{7}+\frac{55 x^8}{8}+\frac{11 x^9}{9}+\frac{x^{10}}{10}+11 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0028161, size = 72, normalized size = 1. \[ \frac{x^{10}}{10}+\frac{11 x^9}{9}+\frac{55 x^8}{8}+\frac{165 x^7}{7}+55 x^6+\frac{462 x^5}{5}+\frac{231 x^4}{2}+110 x^3+\frac{165 x^2}{2}+55 x-\frac{1}{x}+11 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 59, normalized size = 0.8 \begin{align*} -{x}^{-1}+55\,x+{\frac{165\,{x}^{2}}{2}}+110\,{x}^{3}+{\frac{231\,{x}^{4}}{2}}+{\frac{462\,{x}^{5}}{5}}+55\,{x}^{6}+{\frac{165\,{x}^{7}}{7}}+{\frac{55\,{x}^{8}}{8}}+{\frac{11\,{x}^{9}}{9}}+{\frac{{x}^{10}}{10}}+11\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.997647, size = 78, normalized size = 1.08 \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 - \frac{1}{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 = 1.22838, size = 215, normalized size = 2.99 \begin{align*} \frac{252 \, x^{11} + 3080 \, x^{10} + 17325 \, x^{9} + 59400 \, x^{8} + 138600 \, x^{7} + 232848 \, x^{6} + 291060 \, x^{5} + 277200 \, x^{4} + 207900 \, x^{3} + 138600 \, x^{2} + 27720 \, x \log \left (x\right ) - 2520}{2520 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.108815, size = 66, normalized size = 0.92 \begin{align*} \frac{x^{10}}{10} + \frac{11 x^{9}}{9} + \frac{55 x^{8}}{8} + \frac{165 x^{7}}{7} + 55 x^{6} + \frac{462 x^{5}}{5} + \frac{231 x^{4}}{2} + 110 x^{3} + \frac{165 x^{2}}{2} + 55 x + 11 \log{\left (x \right )} - \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12655, size = 80, normalized size = 1.11 \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 - \frac{1}{x} + 11 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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