Optimal. Leaf size=26 \[ \frac {x (2+x) \left (1-x^4\right )}{2 (-2+x) (1+\log (x))} \]
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Rubi [F] time = 0.37, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-4 x+16 x^4+4 x^5-4 x^6+\left (-4-4 x+x^2+20 x^4+4 x^5-5 x^6\right ) \log (x)}{8-8 x+2 x^2+\left (16-16 x+4 x^2\right ) \log (x)+\left (8-8 x+2 x^2\right ) \log ^2(x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4 \left (x-4 x^4-x^5+x^6\right )+\left (-4-4 x+x^2+20 x^4+4 x^5-5 x^6\right ) \log (x)}{2 (2-x)^2 (1+\log (x))^2} \, dx\\ &=\frac {1}{2} \int \frac {-4 \left (x-4 x^4-x^5+x^6\right )+\left (-4-4 x+x^2+20 x^4+4 x^5-5 x^6\right ) \log (x)}{(2-x)^2 (1+\log (x))^2} \, dx\\ &=\frac {1}{2} \int \left (\frac {-2-x+2 x^4+x^5}{(-2+x) (1+\log (x))^2}+\frac {-4-4 x+x^2+20 x^4+4 x^5-5 x^6}{(-2+x)^2 (1+\log (x))}\right ) \, dx\\ &=\frac {1}{2} \int \frac {-2-x+2 x^4+x^5}{(-2+x) (1+\log (x))^2} \, dx+\frac {1}{2} \int \frac {-4-4 x+x^2+20 x^4+4 x^5-5 x^6}{(-2+x)^2 (1+\log (x))} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.22, size = 29, normalized size = 1.12 \begin {gather*} -\frac {x \left (-2-x+2 x^4+x^5\right )}{2 (-2+x) (1+\log (x))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 30, normalized size = 1.15 \begin {gather*} -\frac {x^{6} + 2 \, x^{5} - x^{2} - 2 \, x}{2 \, {\left ({\left (x - 2\right )} \log \relax (x) + x - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.40, size = 32, normalized size = 1.23 \begin {gather*} -\frac {x^{6} + 2 \, x^{5} - x^{2} - 2 \, x}{2 \, {\left (x \log \relax (x) + x - 2 \, \log \relax (x) - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 1.08
method | result | size |
risch | \(-\frac {x \left (x^{5}+2 x^{4}-x -2\right )}{2 \left (x -2\right ) \left (\ln \relax (x )+1\right )}\) | \(28\) |
norman | \(\frac {x +\frac {1}{2} x^{2}-x^{5}-\frac {1}{2} x^{6}}{\left (\ln \relax (x )+1\right ) \left (x -2\right )}\) | \(30\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 30, normalized size = 1.15 \begin {gather*} -\frac {x^{6} + 2 \, x^{5} - x^{2} - 2 \, x}{2 \, {\left ({\left (x - 2\right )} \log \relax (x) + x - 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.77, size = 106, normalized size = 4.08 \begin {gather*} \frac {60\,x}{x^2-4\,x+4}-\frac {31\,x}{2}-\frac {\frac {2\,x^2\,\left (-x^5+x^4+4\,x^3-1\right )}{{\left (x-2\right )}^2}-\frac {x\,\ln \relax (x)\,\left (5\,x^6-4\,x^5-20\,x^4-x^2+4\,x+4\right )}{2\,{\left (x-2\right )}^2}}{\ln \relax (x)+1}-16\,x^2-12\,x^3-8\,x^4-\frac {5\,x^5}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 27, normalized size = 1.04 \begin {gather*} \frac {- x^{6} - 2 x^{5} + x^{2} + 2 x}{2 x + \left (2 x - 4\right ) \log {\relax (x )} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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