Optimal. Leaf size=72 \[ \frac{x^{11}}{11}+\frac{11 x^{10}}{10}+\frac{55 x^9}{9}+\frac{165 x^8}{8}+\frac{330 x^7}{7}+77 x^6+\frac{462 x^5}{5}+\frac{165 x^4}{2}+55 x^3+\frac{55 x^2}{2}+11 x+\log (x) \]
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Rubi [A] time = 0.0174979, 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} \[ \frac{x^{11}}{11}+\frac{11 x^{10}}{10}+\frac{55 x^9}{9}+\frac{165 x^8}{8}+\frac{330 x^7}{7}+77 x^6+\frac{462 x^5}{5}+\frac{165 x^4}{2}+55 x^3+\frac{55 x^2}{2}+11 x+\log (x) \]
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} \, dx &=\int \frac{(1+x)^{11}}{x} \, dx\\ &=\int \left (11+\frac{1}{x}+55 x+165 x^2+330 x^3+462 x^4+462 x^5+330 x^6+165 x^7+55 x^8+11 x^9+x^{10}\right ) \, dx\\ &=11 x+\frac{55 x^2}{2}+55 x^3+\frac{165 x^4}{2}+\frac{462 x^5}{5}+77 x^6+\frac{330 x^7}{7}+\frac{165 x^8}{8}+\frac{55 x^9}{9}+\frac{11 x^{10}}{10}+\frac{x^{11}}{11}+\log (x)\\ \end{align*}
Mathematica [A] time = 0.0107727, size = 96, normalized size = 1.33 \[ \frac{1}{11} (x+1)^{11}+\frac{1}{10} (x+1)^{10}+\frac{1}{9} (x+1)^9+\frac{1}{8} (x+1)^8+\frac{1}{7} (x+1)^7+\frac{1}{6} (x+1)^6+\frac{1}{5} (x+1)^5+\frac{1}{4} (x+1)^4+\frac{1}{3} (x+1)^3+\frac{1}{2} (x+1)^2+x+\log (-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 57, normalized size = 0.8 \begin{align*} 11\,x+{\frac{55\,{x}^{2}}{2}}+55\,{x}^{3}+{\frac{165\,{x}^{4}}{2}}+{\frac{462\,{x}^{5}}{5}}+77\,{x}^{6}+{\frac{330\,{x}^{7}}{7}}+{\frac{165\,{x}^{8}}{8}}+{\frac{55\,{x}^{9}}{9}}+{\frac{11\,{x}^{10}}{10}}+{\frac{{x}^{11}}{11}}+\ln \left ( x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.998479, size = 76, normalized size = 1.06 \begin{align*} \frac{1}{11} \, x^{11} + \frac{11}{10} \, x^{10} + \frac{55}{9} \, x^{9} + \frac{165}{8} \, x^{8} + \frac{330}{7} \, x^{7} + 77 \, x^{6} + \frac{462}{5} \, x^{5} + \frac{165}{2} \, x^{4} + 55 \, x^{3} + \frac{55}{2} \, x^{2} + 11 \, x + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.32182, size = 173, normalized size = 2.4 \begin{align*} \frac{1}{11} \, x^{11} + \frac{11}{10} \, x^{10} + \frac{55}{9} \, x^{9} + \frac{165}{8} \, x^{8} + \frac{330}{7} \, x^{7} + 77 \, x^{6} + \frac{462}{5} \, x^{5} + \frac{165}{2} \, x^{4} + 55 \, x^{3} + \frac{55}{2} \, x^{2} + 11 \, x + \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.129152, size = 68, normalized size = 0.94 \begin{align*} \frac{x^{11}}{11} + \frac{11 x^{10}}{10} + \frac{55 x^{9}}{9} + \frac{165 x^{8}}{8} + \frac{330 x^{7}}{7} + 77 x^{6} + \frac{462 x^{5}}{5} + \frac{165 x^{4}}{2} + 55 x^{3} + \frac{55 x^{2}}{2} + 11 x + \log{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13489, size = 77, normalized size = 1.07 \begin{align*} \frac{1}{11} \, x^{11} + \frac{11}{10} \, x^{10} + \frac{55}{9} \, x^{9} + \frac{165}{8} \, x^{8} + \frac{330}{7} \, x^{7} + 77 \, x^{6} + \frac{462}{5} \, x^{5} + \frac{165}{2} \, x^{4} + 55 \, x^{3} + \frac{55}{2} \, x^{2} + 11 \, x + \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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