Optimal. Leaf size=70 \[ -\frac {1}{4 x^4}-\frac {11}{3 x^3}-\frac {55}{2 x^2}-\frac {165}{x}+462 x+231 x^2+110 x^3+\frac {165 x^4}{4}+11 x^5+\frac {11 x^6}{6}+\frac {x^7}{7}+330 \log (x) \]
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Rubi [A]
time = 0.01, 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, 45}
\begin {gather*} \frac {x^7}{7}+\frac {11 x^6}{6}+11 x^5+\frac {165 x^4}{4}-\frac {1}{4 x^4}+110 x^3-\frac {11}{3 x^3}+231 x^2-\frac {55}{2 x^2}+462 x-\frac {165}{x}+330 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 45
Rubi steps
\begin {align*} \int \frac {(1+x) \left (1+2 x+x^2\right )^5}{x^5} \, dx &=\int \frac {(1+x)^{11}}{x^5} \, dx\\ &=\int \left (462+\frac {1}{x^5}+\frac {11}{x^4}+\frac {55}{x^3}+\frac {165}{x^2}+\frac {330}{x}+462 x+330 x^2+165 x^3+55 x^4+11 x^5+x^6\right ) \, dx\\ &=-\frac {1}{4 x^4}-\frac {11}{3 x^3}-\frac {55}{2 x^2}-\frac {165}{x}+462 x+231 x^2+110 x^3+\frac {165 x^4}{4}+11 x^5+\frac {11 x^6}{6}+\frac {x^7}{7}+330 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 70, normalized size = 1.00 \begin {gather*} -\frac {1}{4 x^4}-\frac {11}{3 x^3}-\frac {55}{2 x^2}-\frac {165}{x}+462 x+231 x^2+110 x^3+\frac {165 x^4}{4}+11 x^5+\frac {11 x^6}{6}+\frac {x^7}{7}+330 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.62, size = 59, normalized size = 0.84
method | result | size |
risch | \(\frac {x^{7}}{7}+\frac {11 x^{6}}{6}+11 x^{5}+\frac {165 x^{4}}{4}+110 x^{3}+231 x^{2}+462 x +\frac {-165 x^{3}-\frac {55}{2} x^{2}-\frac {11}{3} x -\frac {1}{4}}{x^{4}}+330 \ln \left (x \right )\) | \(58\) |
default | \(-\frac {1}{4 x^{4}}-\frac {11}{3 x^{3}}-\frac {55}{2 x^{2}}-\frac {165}{x}+462 x +231 x^{2}+110 x^{3}+\frac {165 x^{4}}{4}+11 x^{5}+\frac {11 x^{6}}{6}+\frac {x^{7}}{7}+330 \ln \left (x \right )\) | \(59\) |
norman | \(\frac {-\frac {1}{4}-\frac {11}{3} x -\frac {55}{2} x^{2}-165 x^{3}+462 x^{5}+231 x^{6}+110 x^{7}+\frac {165}{4} x^{8}+11 x^{9}+\frac {11}{6} x^{10}+\frac {1}{7} x^{11}}{x^{4}}+330 \ln \left (x \right )\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 58, normalized size = 0.83 \begin {gather*} \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 - \frac {1980 \, x^{3} + 330 \, x^{2} + 44 \, x + 3}{12 \, x^{4}} + 330 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.23, size = 62, normalized size = 0.89 \begin {gather*} \frac {12 \, x^{11} + 154 \, x^{10} + 924 \, x^{9} + 3465 \, x^{8} + 9240 \, x^{7} + 19404 \, x^{6} + 38808 \, x^{5} + 27720 \, x^{4} \log \left (x\right ) - 13860 \, x^{3} - 2310 \, x^{2} - 308 \, x - 21}{84 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 63, normalized size = 0.90 \begin {gather*} \frac {x^{7}}{7} + \frac {11 x^{6}}{6} + 11 x^{5} + \frac {165 x^{4}}{4} + 110 x^{3} + 231 x^{2} + 462 x + 330 \log {\left (x \right )} + \frac {- 1980 x^{3} - 330 x^{2} - 44 x - 3}{12 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.53, size = 59, normalized size = 0.84 \begin {gather*} \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 - \frac {1980 \, x^{3} + 330 \, x^{2} + 44 \, x + 3}{12 \, x^{4}} + 330 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 58, normalized size = 0.83 \begin {gather*} 462\,x+330\,\ln \left (x\right )+231\,x^2+110\,x^3+\frac {165\,x^4}{4}+11\,x^5+\frac {11\,x^6}{6}+\frac {x^7}{7}-\frac {165\,x^3+\frac {55\,x^2}{2}+\frac {11\,x}{3}+\frac {1}{4}}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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