Optimal. Leaf size=70 \[ -\frac {1}{9 x^9}-\frac {11}{8 x^8}-\frac {55}{7 x^7}-\frac {55}{2 x^6}-\frac {66}{x^5}-\frac {231}{2 x^4}-\frac {154}{x^3}+\frac {x^2}{2}-\frac {165}{x^2}+11 x-\frac {165}{x}+55 \log (x) \]
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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^2}{2}-\frac {165}{x^2}-\frac {154}{x^3}-\frac {231}{2 x^4}-\frac {66}{x^5}-\frac {55}{2 x^6}-\frac {55}{7 x^7}-\frac {11}{8 x^8}-\frac {1}{9 x^9}+11 x-\frac {165}{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^{10}} \, dx &=\int \frac {(1+x)^{11}}{x^{10}} \, dx\\ &=\int \left (11+\frac {1}{x^{10}}+\frac {11}{x^9}+\frac {55}{x^8}+\frac {165}{x^7}+\frac {330}{x^6}+\frac {462}{x^5}+\frac {462}{x^4}+\frac {330}{x^3}+\frac {165}{x^2}+\frac {55}{x}+x\right ) \, dx\\ &=-\frac {1}{9 x^9}-\frac {11}{8 x^8}-\frac {55}{7 x^7}-\frac {55}{2 x^6}-\frac {66}{x^5}-\frac {231}{2 x^4}-\frac {154}{x^3}-\frac {165}{x^2}-\frac {165}{x}+11 x+\frac {x^2}{2}+55 \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 70, normalized size = 1.00 \begin {gather*} -\frac {1}{9 x^9}-\frac {11}{8 x^8}-\frac {55}{7 x^7}-\frac {55}{2 x^6}-\frac {66}{x^5}-\frac {231}{2 x^4}-\frac {154}{x^3}+\frac {x^2}{2}-\frac {165}{x^2}+11 x-\frac {165}{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^{10}} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.41, size = 62, normalized size = 0.89 \begin {gather*} \frac {252 \, x^{11} + 5544 \, x^{10} + 27720 \, x^{9} \log \relax (x) - 83160 \, x^{8} - 83160 \, x^{7} - 77616 \, x^{6} - 58212 \, x^{5} - 33264 \, x^{4} - 13860 \, x^{3} - 3960 \, x^{2} - 693 \, x - 56}{504 \, x^{9}} \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}{2} \, x^{2} + 11 \, x - \frac {83160 \, x^{8} + 83160 \, x^{7} + 77616 \, x^{6} + 58212 \, x^{5} + 33264 \, x^{4} + 13860 \, x^{3} + 3960 \, x^{2} + 693 \, x + 56}{504 \, x^{9}} + 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^{2}}{2}+11 x +55 \ln \relax (x )-\frac {165}{x}-\frac {165}{x^{2}}-\frac {154}{x^{3}}-\frac {231}{2 x^{4}}-\frac {66}{x^{5}}-\frac {55}{2 x^{6}}-\frac {55}{7 x^{7}}-\frac {11}{8 x^{8}}-\frac {1}{9 x^{9}} \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}{2} \, x^{2} + 11 \, x - \frac {83160 \, x^{8} + 83160 \, x^{7} + 77616 \, x^{6} + 58212 \, x^{5} + 33264 \, x^{4} + 13860 \, x^{3} + 3960 \, x^{2} + 693 \, x + 56}{504 \, x^{9}} + 55 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 58, normalized size = 0.83 \begin {gather*} 11\,x+55\,\ln \relax (x)+\frac {x^2}{2}-\frac {165\,x^8+165\,x^7+154\,x^6+\frac {231\,x^5}{2}+66\,x^4+\frac {55\,x^3}{2}+\frac {55\,x^2}{7}+\frac {11\,x}{8}+\frac {1}{9}}{x^9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 60, normalized size = 0.86 \begin {gather*} \frac {x^{2}}{2} + 11 x + 55 \log {\relax (x )} + \frac {- 83160 x^{8} - 83160 x^{7} - 77616 x^{6} - 58212 x^{5} - 33264 x^{4} - 13860 x^{3} - 3960 x^{2} - 693 x - 56}{504 x^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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