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 = 0.02, antiderivative size = 72, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 72, normalized size = 1.00 \[ \frac {x^{10}}{10}+\frac {11 x^9}{9}+\frac {55 x^8}{8}+\frac {165 x^7}{7}+55 x^6+\frac {462 x^5}{5}+\frac {231 x^4}{2}+110 x^3+\frac {165 x^2}{2}+55 x-\frac {1}{x}+11 \log (x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 62, normalized size = 0.86 \[ \frac {252 \, x^{11} + 3080 \, x^{10} + 17325 \, x^{9} + 59400 \, x^{8} + 138600 \, x^{7} + 232848 \, x^{6} + 291060 \, x^{5} + 277200 \, x^{4} + 207900 \, x^{3} + 138600 \, x^{2} + 27720 \, x \log \relax (x) - 2520}{2520 \, x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 59, normalized size = 0.82 \[ \frac {1}{10} \, x^{10} + \frac {11}{9} \, x^{9} + \frac {55}{8} \, x^{8} + \frac {165}{7} \, x^{7} + 55 \, x^{6} + \frac {462}{5} \, x^{5} + \frac {231}{2} \, x^{4} + 110 \, x^{3} + \frac {165}{2} \, x^{2} + 55 \, x - \frac {1}{x} + 11 \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 59, normalized size = 0.82 \[ \frac {x^{10}}{10}+\frac {11 x^{9}}{9}+\frac {55 x^{8}}{8}+\frac {165 x^{7}}{7}+55 x^{6}+\frac {462 x^{5}}{5}+\frac {231 x^{4}}{2}+110 x^{3}+\frac {165 x^{2}}{2}+55 x +11 \ln \relax (x )-\frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 58, normalized size = 0.81 \[ \frac {1}{10} \, x^{10} + \frac {11}{9} \, x^{9} + \frac {55}{8} \, x^{8} + \frac {165}{7} \, x^{7} + 55 \, x^{6} + \frac {462}{5} \, x^{5} + \frac {231}{2} \, x^{4} + 110 \, x^{3} + \frac {165}{2} \, x^{2} + 55 \, x - \frac {1}{x} + 11 \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 58, normalized size = 0.81 \[ 55\,x+11\,\ln \relax (x)-\frac {1}{x}+\frac {165\,x^2}{2}+110\,x^3+\frac {231\,x^4}{2}+\frac {462\,x^5}{5}+55\,x^6+\frac {165\,x^7}{7}+\frac {55\,x^8}{8}+\frac {11\,x^9}{9}+\frac {x^{10}}{10} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 66, normalized size = 0.92 \[ \frac {x^{10}}{10} + \frac {11 x^{9}}{9} + \frac {55 x^{8}}{8} + \frac {165 x^{7}}{7} + 55 x^{6} + \frac {462 x^{5}}{5} + \frac {231 x^{4}}{2} + 110 x^{3} + \frac {165 x^{2}}{2} + 55 x + 11 \log {\relax (x )} - \frac {1}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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