\[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx \]
Optimal antiderivative \[ \left (\ln \left (x^{2}-\frac {1}{x}\right )+\left (5-\ln \left (-2+x \right )\right )^{4} {\mathrm e}^{-5}-{\mathrm e}^{3}\right )^{2} \]
command
integrate((((8*x**4-8*x)*exp(5)*ln(-2+x)**3+(-120*x**4+120*x)*exp(5)*ln(-2+x)**2+(600*x**4-600*x)*exp(5)*ln(-2+x)+(4*x**4-8*x**3+2*x-4)*exp(5)**2+(-1000*x**4+1000*x)*exp(5))*ln((x**3-1)/x)+(8*x**4-8*x)*ln(-2+x)**7+(-280*x**4+280*x)*ln(-2+x)**6+(4200*x**4-4200*x)*ln(-2+x)**5+((4*x**4-8*x**3+2*x-4)*exp(5)-35000*x**4+35000*x)*ln(-2+x)**4+(((-8*x**4+8*x)*exp(3)-80*x**4+160*x**3-40*x+80)*exp(5)+175000*x**4-175000*x)*ln(-2+x)**3+(((120*x**4-120*x)*exp(3)+600*x**4-1200*x**3+300*x-600)*exp(5)-525000*x**4+525000*x)*ln(-2+x)**2+(((-600*x**4+600*x)*exp(3)-2000*x**4+4000*x**3-1000*x+2000)*exp(5)+875000*x**4-875000*x)*ln(-2+x)+(-4*x**4+8*x**3-2*x+4)*exp(3)*exp(5)**2+((1000*x**4-1000*x)*exp(3)+2500*x**4-5000*x**3+1250*x-2500)*exp(5)-625000*x**4+625000*x)/(x**5-2*x**4-x**2+2*x)/exp(5)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {\left (2 \log {\left (x - 2 \right )}^{4} - 40 \log {\left (x - 2 \right )}^{3} + 300 \log {\left (x - 2 \right )}^{2} - 1000 \log {\left (x - 2 \right )}\right ) \log {\left (\frac {x^{3} - 1}{x} \right )}}{e^{5}} + \log {\left (\frac {x^{3} - 1}{x} \right )}^{2} + \frac {\log {\left (x - 2 \right )}^{8}}{e^{10}} - \frac {40 \log {\left (x - 2 \right )}^{7}}{e^{10}} + \frac {700 \log {\left (x - 2 \right )}^{6}}{e^{10}} - \frac {7000 \log {\left (x - 2 \right )}^{5}}{e^{10}} + \frac {\left (43750 - 2 e^{8}\right ) \log {\left (x - 2 \right )}^{4}}{e^{10}} + \frac {\left (-175000 + 40 e^{8}\right ) \log {\left (x - 2 \right )}^{3}}{e^{10}} + \frac {\left (437500 - 300 e^{8}\right ) \log {\left (x - 2 \right )}^{2}}{e^{10}} + \frac {\left (-1250 + 2 e^{8}\right ) \log {\left (x + \frac {- 2 e^{13} + 1250 e^{5} + \left (-1250 + 2 e^{8}\right ) e^{5}}{- 500 e^{8} - 625 e^{5} + 312500 + e^{13}} \right )}}{e^{5}} + \frac {\left (-625000 + 1000 e^{8}\right ) \log {\left (x + \frac {- 2 e^{13} - 625000 + 1250 e^{5} + 1000 e^{8}}{- 500 e^{8} - 625 e^{5} + 312500 + e^{13}} \right )}}{e^{10}} - \frac {2 \left (-5 + e^{2}\right ) \left (5 + e^{2}\right ) \left (25 + e^{4}\right ) \log {\left (x^{3} - 1 \right )}}{e^{5}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________