Integrand size = 277, antiderivative size = 30 \[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=\left (1-\frac {x}{-\frac {\log (3)}{x}+\frac {\log (-e+2 x)}{\log (x)}}\right )^2 \]
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\[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=\int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x \left (\left (x^2+\log (3)\right ) \log (x)-x \log (-e+2 x)\right ) \left (-\left ((-e \log (9)+x \log (81)) \log ^2(x)\right )-(e-2 x) x \log (-e+2 x)-x \log (x) (2 x+(e-2 x) \log (-e+2 x))\right )}{(e-2 x) (\log (3) \log (x)-x \log (-e+2 x))^3} \, dx \\ & = 2 \int \frac {x \left (\left (x^2+\log (3)\right ) \log (x)-x \log (-e+2 x)\right ) \left (-\left ((-e \log (9)+x \log (81)) \log ^2(x)\right )-(e-2 x) x \log (-e+2 x)-x \log (x) (2 x+(e-2 x) \log (-e+2 x))\right )}{(e-2 x) (\log (3) \log (x)-x \log (-e+2 x))^3} \, dx \\ & = 2 \int \left (\frac {x \log (x) \left (-2 \left (1-\frac {e}{2}\right ) x^2-2 x^3-e \log (3)+x \log (9)+e x^2 \log (x)-2 x^3 \log (x)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(e-2 x) (\log (3) \log (x)-x \log (-e+2 x))^2}-\frac {x^3 \log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}-\frac {x (1+\log (x))}{-\log (3) \log (x)+x \log (-e+2 x)}\right ) \, dx \\ & = 2 \int \frac {x \log (x) \left (-2 \left (1-\frac {e}{2}\right ) x^2-2 x^3-e \log (3)+x \log (9)+e x^2 \log (x)-2 x^3 \log (x)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(e-2 x) (\log (3) \log (x)-x \log (-e+2 x))^2} \, dx-2 \int \frac {x^3 \log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3} \, dx-2 \int \frac {x (1+\log (x))}{-\log (3) \log (x)+x \log (-e+2 x)} \, dx \\ & = 2 \int \left (\frac {e \log (x) \left (-2 \left (1-\frac {e}{2}\right ) x^2-2 x^3-e \log (3)+x \log (9)+e x^2 \log (x)-2 x^3 \log (x)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{2 (e-2 x) (\log (3) \log (x)-x \log (-e+2 x))^2}+\frac {\log (x) \left (2 \left (1-\frac {e}{2}\right ) x^2+2 x^3+e \log (3)-x \log (9)-e x^2 \log (x)+2 x^3 \log (x)-e \log (3) \log (x)+x \log (9) \log (x)\right )}{2 (\log (3) \log (x)-x \log (-e+2 x))^2}\right ) \, dx-2 \int \left (\frac {e^2 \log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{8 (\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {e x \log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{4 (\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {x^2 \log ^2(x) \left (2 x^2+e \log (3)-x \log (9)-e \log (3) \log (x)+x \log (9) \log (x)\right )}{2 (\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {e^3 \log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{8 (e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}\right ) \, dx-2 \int \left (\frac {x}{-\log (3) \log (x)+x \log (-e+2 x)}+\frac {x \log (x)}{-\log (3) \log (x)+x \log (-e+2 x)}\right ) \, dx \\ & = -\left (2 \int \frac {x}{-\log (3) \log (x)+x \log (-e+2 x)} \, dx\right )-2 \int \frac {x \log (x)}{-\log (3) \log (x)+x \log (-e+2 x)} \, dx-\frac {1}{2} e \int \frac {x \log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(\log (3) \log (x)-x \log (-e+2 x))^3} \, dx+e \int \frac {\log (x) \left (-2 \left (1-\frac {e}{2}\right ) x^2-2 x^3-e \log (3)+x \log (9)+e x^2 \log (x)-2 x^3 \log (x)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(e-2 x) (\log (3) \log (x)-x \log (-e+2 x))^2} \, dx-\frac {1}{4} e^2 \int \frac {\log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(\log (3) \log (x)-x \log (-e+2 x))^3} \, dx-\frac {1}{4} e^3 \int \frac {\log ^2(x) \left (-2 x^2-e \log (3)+x \log (9)+e \log (3) \log (x)-x \log (9) \log (x)\right )}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3} \, dx+\int \frac {x^2 \log ^2(x) \left (2 x^2+e \log (3)-x \log (9)-e \log (3) \log (x)+x \log (9) \log (x)\right )}{(\log (3) \log (x)-x \log (-e+2 x))^3} \, dx+\int \frac {\log (x) \left (2 \left (1-\frac {e}{2}\right ) x^2+2 x^3+e \log (3)-x \log (9)-e x^2 \log (x)+2 x^3 \log (x)-e \log (3) \log (x)+x \log (9) \log (x)\right )}{(\log (3) \log (x)-x \log (-e+2 x))^2} \, dx \\ & = -\left (2 \int \frac {x}{-\log (3) \log (x)+x \log (-e+2 x)} \, dx\right )-2 \int \frac {x \log (x)}{-\log (3) \log (x)+x \log (-e+2 x)} \, dx-\frac {1}{2} e \int \left (-\frac {2 x^3 \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {e x \log (3) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {x^2 \log (9) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {e x \log (3) \log ^3(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {x^2 \log (9) \log ^3(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}\right ) \, dx+e \int \left (\frac {(-2+e) x^2 \log (x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}-\frac {2 x^3 \log (x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}-\frac {e \log (3) \log (x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}+\frac {x \log (9) \log (x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}+\frac {e x^2 \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}-\frac {2 x^3 \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}+\frac {e \log (3) \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}-\frac {x \log (9) \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^2}\right ) \, dx-\frac {1}{4} e^2 \int \left (-\frac {2 x^2 \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {e \log (3) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {x \log (9) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {e \log (3) \log ^3(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {x \log (9) \log ^3(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}\right ) \, dx-\frac {1}{4} e^3 \int \left (-\frac {2 x^2 \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}-\frac {e \log (3) \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}+\frac {x \log (9) \log ^2(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}+\frac {e \log (3) \log ^3(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}-\frac {x \log (9) \log ^3(x)}{(e-2 x) (-\log (3) \log (x)+x \log (-e+2 x))^3}\right ) \, dx+\int \left (\frac {2 x^4 \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {e x^2 \log (3) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {x^3 \log (9) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}-\frac {e x^2 \log (3) \log ^3(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}+\frac {x^3 \log (9) \log ^3(x)}{(\log (3) \log (x)-x \log (-e+2 x))^3}\right ) \, dx+\int \left (-\frac {(-2+e) x^2 \log (x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}+\frac {2 x^3 \log (x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}+\frac {e \log (3) \log (x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}-\frac {x \log (9) \log (x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}-\frac {e x^2 \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}+\frac {2 x^3 \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}-\frac {e \log (3) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}+\frac {x \log (9) \log ^2(x)}{(\log (3) \log (x)-x \log (-e+2 x))^2}\right ) \, dx \\ & = \text {Too large to display} \\ \end{align*}
\[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=\int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx \]
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Time = 3.41 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.73
method | result | size |
default | \(\frac {\left (x^{2} \ln \left (x \right )+2 \ln \left (3\right ) \ln \left (x \right )-2 \ln \left (-{\mathrm e}+2 x \right ) x \right ) x^{2} \ln \left (x \right )}{\left (\ln \left (3\right ) \ln \left (x \right )-\ln \left (-{\mathrm e}+2 x \right ) x \right )^{2}}\) | \(52\) |
risch | \(\frac {\left (x^{2} \ln \left (x \right )+2 \ln \left (3\right ) \ln \left (x \right )-2 \ln \left (-{\mathrm e}+2 x \right ) x \right ) x^{2} \ln \left (x \right )}{\left (\ln \left (3\right ) \ln \left (x \right )-\ln \left (-{\mathrm e}+2 x \right ) x \right )^{2}}\) | \(52\) |
parallelrisch | \(-\frac {\left (-4 x^{4} \ln \left (x \right )^{2} {\mathrm e}-8 x^{2} \ln \left (x \right )^{2} \ln \left (3\right ) {\mathrm e}+8 \ln \left (x \right ) {\mathrm e} \ln \left (-{\mathrm e}+2 x \right ) x^{3}\right ) {\mathrm e}^{-1}}{4 \left (\ln \left (3\right )^{2} \ln \left (x \right )^{2}-2 \ln \left (3\right ) x \ln \left (x \right ) \ln \left (-{\mathrm e}+2 x \right )+\ln \left (-{\mathrm e}+2 x \right )^{2} x^{2}\right )}\) | \(93\) |
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (30) = 60\).
Time = 0.28 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.63 \[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=-\frac {2 \, x^{3} \log \left (2 \, x - e\right ) \log \left (x\right ) - {\left (x^{4} + 2 \, x^{2} \log \left (3\right )\right )} \log \left (x\right )^{2}}{x^{2} \log \left (2 \, x - e\right )^{2} - 2 \, x \log \left (3\right ) \log \left (2 \, x - e\right ) \log \left (x\right ) + \log \left (3\right )^{2} \log \left (x\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (20) = 40\).
Time = 0.18 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.67 \[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=\frac {x^{4} \log {\left (x \right )}^{2} - 2 x^{3} \log {\left (x \right )} \log {\left (2 x - e \right )} + 2 x^{2} \log {\left (3 \right )} \log {\left (x \right )}^{2}}{x^{2} \log {\left (2 x - e \right )}^{2} - 2 x \log {\left (3 \right )} \log {\left (x \right )} \log {\left (2 x - e \right )} + \log {\left (3 \right )}^{2} \log {\left (x \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (30) = 60\).
Time = 0.56 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.63 \[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=-\frac {2 \, x^{3} \log \left (2 \, x - e\right ) \log \left (x\right ) - {\left (x^{4} + 2 \, x^{2} \log \left (3\right )\right )} \log \left (x\right )^{2}}{x^{2} \log \left (2 \, x - e\right )^{2} - 2 \, x \log \left (3\right ) \log \left (2 \, x - e\right ) \log \left (x\right ) + \log \left (3\right )^{2} \log \left (x\right )^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (30) = 60\).
Time = 0.57 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.67 \[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=\frac {x^{4} \log \left (x\right )^{2} - 2 \, x^{3} \log \left (2 \, x - e\right ) \log \left (x\right ) + 2 \, x^{2} \log \left (3\right ) \log \left (x\right )^{2}}{x^{2} \log \left (2 \, x - e\right )^{2} - 2 \, x \log \left (3\right ) \log \left (2 \, x - e\right ) \log \left (x\right ) + \log \left (3\right )^{2} \log \left (x\right )^{2}} \]
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Timed out. \[ \int \frac {\left (\left (4 e x^3-8 x^4\right ) \log (3)+\left (4 e x-8 x^2\right ) \log ^2(3)\right ) \log ^3(x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)+\log ^2(x) \left (-4 x^5-4 x^3 \log (3)+\left (-2 e x^4+4 x^5+\left (-6 e x^2+12 x^3\right ) \log (3)\right ) \log (-e+2 x)\right )+\log (x) \left (\left (4 x^4-2 e x^4+4 x^5+\left (-2 e x^2+4 x^3\right ) \log (3)\right ) \log (-e+2 x)+\left (2 e x^3-4 x^4\right ) \log ^2(-e+2 x)\right )}{(e-2 x) \log ^3(3) \log ^3(x)+\left (-3 e x+6 x^2\right ) \log ^2(3) \log ^2(x) \log (-e+2 x)+\left (3 e x^2-6 x^3\right ) \log (3) \log (x) \log ^2(-e+2 x)+\left (-e x^3+2 x^4\right ) \log ^3(-e+2 x)} \, dx=\int \frac {\ln \left (x\right )\,\left (\ln \left (2\,x-\mathrm {e}\right )\,\left (2\,x^4\,\mathrm {e}-4\,x^4-4\,x^5+\ln \left (3\right )\,\left (2\,x^2\,\mathrm {e}-4\,x^3\right )\right )-{\ln \left (2\,x-\mathrm {e}\right )}^2\,\left (2\,x^3\,\mathrm {e}-4\,x^4\right )\right )-{\ln \left (2\,x-\mathrm {e}\right )}^2\,\left (2\,x^3\,\mathrm {e}-4\,x^4\right )+{\ln \left (x\right )}^2\,\left (4\,x^3\,\ln \left (3\right )+4\,x^5+\ln \left (2\,x-\mathrm {e}\right )\,\left (2\,x^4\,\mathrm {e}-4\,x^5+\ln \left (3\right )\,\left (6\,x^2\,\mathrm {e}-12\,x^3\right )\right )\right )-{\ln \left (x\right )}^3\,\left ({\ln \left (3\right )}^2\,\left (4\,x\,\mathrm {e}-8\,x^2\right )+\ln \left (3\right )\,\left (4\,x^3\,\mathrm {e}-8\,x^4\right )\right )}{\left (x^3\,\mathrm {e}-2\,x^4\right )\,{\ln \left (2\,x-\mathrm {e}\right )}^3-\ln \left (3\right )\,\left (3\,x^2\,\mathrm {e}-6\,x^3\right )\,{\ln \left (2\,x-\mathrm {e}\right )}^2\,\ln \left (x\right )+{\ln \left (3\right )}^2\,\left (3\,x\,\mathrm {e}-6\,x^2\right )\,\ln \left (2\,x-\mathrm {e}\right )\,{\ln \left (x\right )}^2+{\ln \left (3\right )}^3\,\left (2\,x-\mathrm {e}\right )\,{\ln \left (x\right )}^3} \,d x \]
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