Optimal. Leaf size=70 \[ \frac {x^9}{9}+\frac {11 x^8}{8}+\frac {55 x^7}{7}+\frac {55 x^6}{2}+66 x^5+\frac {231 x^4}{2}+154 x^3+165 x^2-\frac {1}{2 x^2}+165 x-\frac {11}{x}+55 \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 70, 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} \begin {gather*} \frac {x^9}{9}+\frac {11 x^8}{8}+\frac {55 x^7}{7}+\frac {55 x^6}{2}+66 x^5+\frac {231 x^4}{2}+154 x^3+165 x^2-\frac {1}{2 x^2}+165 x-\frac {11}{x}+55 \log (x) \end {gather*}
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^3} \, dx &=\int \frac {(1+x)^{11}}{x^3} \, dx\\ &=\int \left (165+\frac {1}{x^3}+\frac {11}{x^2}+\frac {55}{x}+330 x+462 x^2+462 x^3+330 x^4+165 x^5+55 x^6+11 x^7+x^8\right ) \, dx\\ &=-\frac {1}{2 x^2}-\frac {11}{x}+165 x+165 x^2+154 x^3+\frac {231 x^4}{2}+66 x^5+\frac {55 x^6}{2}+\frac {55 x^7}{7}+\frac {11 x^8}{8}+\frac {x^9}{9}+55 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 70, normalized size = 1.00 \begin {gather*} \frac {x^9}{9}+\frac {11 x^8}{8}+\frac {55 x^7}{7}+\frac {55 x^6}{2}+66 x^5+\frac {231 x^4}{2}+154 x^3+165 x^2-\frac {1}{2 x^2}+165 x-\frac {11}{x}+55 \log (x) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.39, size = 62, normalized size = 0.89 \begin {gather*} \frac {56 \, x^{11} + 693 \, x^{10} + 3960 \, x^{9} + 13860 \, x^{8} + 33264 \, x^{7} + 58212 \, x^{6} + 77616 \, x^{5} + 83160 \, x^{4} + 83160 \, x^{3} + 27720 \, x^{2} \log \relax (x) - 5544 \, x - 252}{504 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 59, normalized size = 0.84 \begin {gather*} \frac {1}{9} \, x^{9} + \frac {11}{8} \, x^{8} + \frac {55}{7} \, x^{7} + \frac {55}{2} \, x^{6} + 66 \, x^{5} + \frac {231}{2} \, x^{4} + 154 \, x^{3} + 165 \, x^{2} + 165 \, x - \frac {22 \, x + 1}{2 \, x^{2}} + 55 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 59, normalized size = 0.84 \begin {gather*} \frac {x^{9}}{9}+\frac {11 x^{8}}{8}+\frac {55 x^{7}}{7}+\frac {55 x^{6}}{2}+66 x^{5}+\frac {231 x^{4}}{2}+154 x^{3}+165 x^{2}+165 x +55 \ln \relax (x )-\frac {11}{x}-\frac {1}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 58, normalized size = 0.83 \begin {gather*} \frac {1}{9} \, x^{9} + \frac {11}{8} \, x^{8} + \frac {55}{7} \, x^{7} + \frac {55}{2} \, x^{6} + 66 \, x^{5} + \frac {231}{2} \, x^{4} + 154 \, x^{3} + 165 \, x^{2} + 165 \, x - \frac {22 \, x + 1}{2 \, x^{2}} + 55 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 58, normalized size = 0.83 \begin {gather*} 165\,x+55\,\ln \relax (x)-\frac {11\,x+\frac {1}{2}}{x^2}+165\,x^2+154\,x^3+\frac {231\,x^4}{2}+66\,x^5+\frac {55\,x^6}{2}+\frac {55\,x^7}{7}+\frac {11\,x^8}{8}+\frac {x^9}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 66, normalized size = 0.94 \begin {gather*} \frac {x^{9}}{9} + \frac {11 x^{8}}{8} + \frac {55 x^{7}}{7} + \frac {55 x^{6}}{2} + 66 x^{5} + \frac {231 x^{4}}{2} + 154 x^{3} + 165 x^{2} + 165 x + 55 \log {\relax (x )} + \frac {- 22 x - 1}{2 x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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