Optimal. Leaf size=26 \[ \frac {4 x^7 (2-\log (x))}{-(2-x)^2+x^2} \]
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Rubi [B] time = 0.21, antiderivative size = 89, normalized size of antiderivative = 3.42, number of steps used = 15, number of rules used = 8, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {27, 6742, 77, 2357, 2295, 2314, 31, 2304} \begin {gather*} 2 x^6+x^6 (-\log (x))+2 x^5-x^5 \log (x)+2 x^4-x^4 \log (x)+2 x^3-x^3 \log (x)+2 x^2-x^2 \log (x)+2 x-\frac {2}{1-x}+\frac {x \log (x)}{1-x}-x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 31
Rule 77
Rule 2295
Rule 2304
Rule 2314
Rule 2357
Rule 6742
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-13 x^6+11 x^7+\left (7 x^6-6 x^7\right ) \log (x)}{(-1+x)^2} \, dx\\ &=\int \left (\frac {x^6 (-13+11 x)}{(-1+x)^2}-\frac {x^6 (-7+6 x) \log (x)}{(-1+x)^2}\right ) \, dx\\ &=\int \frac {x^6 (-13+11 x)}{(-1+x)^2} \, dx-\int \frac {x^6 (-7+6 x) \log (x)}{(-1+x)^2} \, dx\\ &=\int \left (1+\frac {1}{1-x}-\frac {2}{(-1+x)^2}+3 x+5 x^2+7 x^3+9 x^4+11 x^5\right ) \, dx-\int \left (\log (x)-\frac {\log (x)}{(-1+x)^2}+2 x \log (x)+3 x^2 \log (x)+4 x^3 \log (x)+5 x^4 \log (x)+6 x^5 \log (x)\right ) \, dx\\ &=-\frac {2}{1-x}+x+\frac {3 x^2}{2}+\frac {5 x^3}{3}+\frac {7 x^4}{4}+\frac {9 x^5}{5}+\frac {11 x^6}{6}-\log (1-x)-2 \int x \log (x) \, dx-3 \int x^2 \log (x) \, dx-4 \int x^3 \log (x) \, dx-5 \int x^4 \log (x) \, dx-6 \int x^5 \log (x) \, dx-\int \log (x) \, dx+\int \frac {\log (x)}{(-1+x)^2} \, dx\\ &=-\frac {2}{1-x}+2 x+2 x^2+2 x^3+2 x^4+2 x^5+2 x^6-\log (1-x)-x \log (x)+\frac {x \log (x)}{1-x}-x^2 \log (x)-x^3 \log (x)-x^4 \log (x)-x^5 \log (x)-x^6 \log (x)+\int \frac {1}{-1+x} \, dx\\ &=-\frac {2}{1-x}+2 x+2 x^2+2 x^3+2 x^4+2 x^5+2 x^6-x \log (x)+\frac {x \log (x)}{1-x}-x^2 \log (x)-x^3 \log (x)-x^4 \log (x)-x^5 \log (x)-x^6 \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 23, normalized size = 0.88 \begin {gather*} \frac {2-2 x+2 x^7-x^7 \log (x)}{-1+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 23, normalized size = 0.88 \begin {gather*} -\frac {x^{7} \log \relax (x) - 2 \, x^{7} + 2 \, x - 2}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.22, size = 66, normalized size = 2.54 \begin {gather*} 2 \, x^{6} + 2 \, x^{5} + 2 \, x^{4} + 2 \, x^{3} + 2 \, x^{2} - {\left (x^{6} + x^{5} + x^{4} + x^{3} + x^{2} + x + \frac {1}{x - 1}\right )} \log \relax (x) + 2 \, x + \frac {2}{x - 1} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.64, size = 20, normalized size = 0.77
method | result | size |
norman | \(\frac {2 x^{7}-x^{7} \ln \relax (x )}{x -1}\) | \(20\) |
risch | \(-\frac {\left (x^{7}-x +1\right ) \ln \relax (x )}{x -1}-\frac {-2 x^{7}+x \ln \relax (x )-\ln \relax (x )+2 x -2}{x -1}\) | \(44\) |
default | \(2 x^{6}+2 x^{5}+2 x^{4}+2 x^{3}+2 x^{2}+2 x +\frac {2}{x -1}-x^{6} \ln \relax (x )-x^{5} \ln \relax (x )-x^{4} \ln \relax (x )-x^{3} \ln \relax (x )-x^{2} \ln \relax (x )-x \ln \relax (x )-\frac {\ln \relax (x ) x}{x -1}\) | \(87\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.76, size = 91, normalized size = 3.50 \begin {gather*} \frac {11}{6} \, x^{6} + \frac {9}{5} \, x^{5} + \frac {7}{4} \, x^{4} + \frac {5}{3} \, x^{3} + \frac {3}{2} \, x^{2} + x + \frac {10 \, x^{7} + 2 \, x^{6} + 3 \, x^{5} + 5 \, x^{4} + 10 \, x^{3} + 30 \, x^{2} - 60 \, {\left (x^{7} - x + 1\right )} \log \relax (x) - 60 \, x}{60 \, {\left (x - 1\right )}} + \frac {2}{x - 1} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.98, size = 14, normalized size = 0.54 \begin {gather*} -\frac {x^7\,\left (\ln \relax (x)-2\right )}{x-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 49, normalized size = 1.88 \begin {gather*} 2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x - \log {\relax (x )} + \frac {\left (- x^{7} + x - 1\right ) \log {\relax (x )}}{x - 1} + \frac {2}{x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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