Optimal. Leaf size=70 \[ \frac{x^4}{4}+\frac{11 x^3}{3}+\frac{55 x^2}{2}-\frac{231}{x^2}-\frac{110}{x^3}-\frac{165}{4 x^4}-\frac{11}{x^5}-\frac{11}{6 x^6}-\frac{1}{7 x^7}+165 x-\frac{462}{x}+330 \log (x) \]
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Rubi [A] time = 0.0212897, 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} \[ \frac{x^4}{4}+\frac{11 x^3}{3}+\frac{55 x^2}{2}-\frac{231}{x^2}-\frac{110}{x^3}-\frac{165}{4 x^4}-\frac{11}{x^5}-\frac{11}{6 x^6}-\frac{1}{7 x^7}+165 x-\frac{462}{x}+330 \log (x) \]
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^8} \, dx &=\int \frac{(1+x)^{11}}{x^8} \, dx\\ &=\int \left (165+\frac{1}{x^8}+\frac{11}{x^7}+\frac{55}{x^6}+\frac{165}{x^5}+\frac{330}{x^4}+\frac{462}{x^3}+\frac{462}{x^2}+\frac{330}{x}+55 x+11 x^2+x^3\right ) \, dx\\ &=-\frac{1}{7 x^7}-\frac{11}{6 x^6}-\frac{11}{x^5}-\frac{165}{4 x^4}-\frac{110}{x^3}-\frac{231}{x^2}-\frac{462}{x}+165 x+\frac{55 x^2}{2}+\frac{11 x^3}{3}+\frac{x^4}{4}+330 \log (x)\\ \end{align*}
Mathematica [A] time = 0.0025562, size = 70, normalized size = 1. \[ \frac{x^4}{4}+\frac{11 x^3}{3}+\frac{55 x^2}{2}-\frac{231}{x^2}-\frac{110}{x^3}-\frac{165}{4 x^4}-\frac{11}{x^5}-\frac{11}{6 x^6}-\frac{1}{7 x^7}+165 x-\frac{462}{x}+330 \log (x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 59, normalized size = 0.8 \begin{align*} -{\frac{1}{7\,{x}^{7}}}-{\frac{11}{6\,{x}^{6}}}-11\,{x}^{-5}-{\frac{165}{4\,{x}^{4}}}-110\,{x}^{-3}-231\,{x}^{-2}-462\,{x}^{-1}+165\,x+{\frac{55\,{x}^{2}}{2}}+{\frac{11\,{x}^{3}}{3}}+{\frac{{x}^{4}}{4}}+330\,\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00113, size = 78, normalized size = 1.11 \begin{align*} \frac{1}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{55}{2} \, x^{2} + 165 \, x - \frac{38808 \, x^{6} + 19404 \, x^{5} + 9240 \, x^{4} + 3465 \, x^{3} + 924 \, x^{2} + 154 \, x + 12}{84 \, x^{7}} + 330 \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.52973, size = 192, normalized size = 2.74 \begin{align*} \frac{21 \, x^{11} + 308 \, x^{10} + 2310 \, x^{9} + 13860 \, x^{8} + 27720 \, x^{7} \log \left (x\right ) - 38808 \, x^{6} - 19404 \, x^{5} - 9240 \, x^{4} - 3465 \, x^{3} - 924 \, x^{2} - 154 \, x - 12}{84 \, x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.141676, size = 61, normalized size = 0.87 \begin{align*} \frac{x^{4}}{4} + \frac{11 x^{3}}{3} + \frac{55 x^{2}}{2} + 165 x + 330 \log{\left (x \right )} - \frac{38808 x^{6} + 19404 x^{5} + 9240 x^{4} + 3465 x^{3} + 924 x^{2} + 154 x + 12}{84 x^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13724, size = 80, normalized size = 1.14 \begin{align*} \frac{1}{4} \, x^{4} + \frac{11}{3} \, x^{3} + \frac{55}{2} \, x^{2} + 165 \, x - \frac{38808 \, x^{6} + 19404 \, x^{5} + 9240 \, x^{4} + 3465 \, x^{3} + 924 \, x^{2} + 154 \, x + 12}{84 \, x^{7}} + 330 \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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