Optimal. Leaf size=70 \[ \frac{x^7}{7}+\frac{11 x^6}{6}+11 x^5+\frac{165 x^4}{4}+110 x^3+231 x^2-\frac{55}{2 x^2}-\frac{11}{3 x^3}-\frac{1}{4 x^4}+462 x-\frac{165}{x}+330 \log (x) \]
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Rubi [A] time = 0.0217264, 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} \[ \frac{x^7}{7}+\frac{11 x^6}{6}+11 x^5+\frac{165 x^4}{4}+110 x^3+231 x^2-\frac{55}{2 x^2}-\frac{11}{3 x^3}-\frac{1}{4 x^4}+462 x-\frac{165}{x}+330 \log (x) \]
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^5} \, dx &=\int \frac{(1+x)^{11}}{x^5} \, dx\\ &=\int \left (462+\frac{1}{x^5}+\frac{11}{x^4}+\frac{55}{x^3}+\frac{165}{x^2}+\frac{330}{x}+462 x+330 x^2+165 x^3+55 x^4+11 x^5+x^6\right ) \, dx\\ &=-\frac{1}{4 x^4}-\frac{11}{3 x^3}-\frac{55}{2 x^2}-\frac{165}{x}+462 x+231 x^2+110 x^3+\frac{165 x^4}{4}+11 x^5+\frac{11 x^6}{6}+\frac{x^7}{7}+330 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0025982, size = 70, normalized size = 1. \[ \frac{x^7}{7}+\frac{11 x^6}{6}+11 x^5+\frac{165 x^4}{4}+110 x^3+231 x^2-\frac{55}{2 x^2}-\frac{11}{3 x^3}-\frac{1}{4 x^4}+462 x-\frac{165}{x}+330 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 59, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,{x}^{4}}}-{\frac{11}{3\,{x}^{3}}}-{\frac{55}{2\,{x}^{2}}}-165\,{x}^{-1}+462\,x+231\,{x}^{2}+110\,{x}^{3}+{\frac{165\,{x}^{4}}{4}}+11\,{x}^{5}+{\frac{11\,{x}^{6}}{6}}+{\frac{{x}^{7}}{7}}+330\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01605, size = 78, normalized size = 1.11 \begin{align*} \frac{1}{7} \, x^{7} + \frac{11}{6} \, x^{6} + 11 \, x^{5} + \frac{165}{4} \, x^{4} + 110 \, x^{3} + 231 \, x^{2} + 462 \, x - \frac{1980 \, x^{3} + 330 \, x^{2} + 44 \, x + 3}{12 \, x^{4}} + 330 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24607, size = 192, normalized size = 2.74 \begin{align*} \frac{12 \, x^{11} + 154 \, x^{10} + 924 \, x^{9} + 3465 \, x^{8} + 9240 \, x^{7} + 19404 \, x^{6} + 38808 \, x^{5} + 27720 \, x^{4} \log \left (x\right ) - 13860 \, x^{3} - 2310 \, x^{2} - 308 \, x - 21}{84 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.122352, size = 61, normalized size = 0.87 \begin{align*} \frac{x^{7}}{7} + \frac{11 x^{6}}{6} + 11 x^{5} + \frac{165 x^{4}}{4} + 110 x^{3} + 231 x^{2} + 462 x + 330 \log{\left (x \right )} - \frac{1980 x^{3} + 330 x^{2} + 44 x + 3}{12 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.137, size = 80, normalized size = 1.14 \begin{align*} \frac{1}{7} \, x^{7} + \frac{11}{6} \, x^{6} + 11 \, x^{5} + \frac{165}{4} \, x^{4} + 110 \, x^{3} + 231 \, x^{2} + 462 \, x - \frac{1980 \, x^{3} + 330 \, x^{2} + 44 \, x + 3}{12 \, x^{4}} + 330 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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