\[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx \]
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
Int[(625000*x - 625000*x^4 + E^13*(4 - 2*x + 8*x^3 - 4*x^4) + E^5*(-2500 + 1250*x - 5000*x^3 + 2500*x^4 + E^3*(-1000*x + 1000*x^4)) + (-875000*x + 875000*x^4 + E^5*(2000 - 1000*x + 4000*x^3 - 2000*x^4 + E^3*(600*x - 600*x^4)))*Log[-2 + x] + (525000*x - 525000*x^4 + E^5*(-600 + 300*x - 1200*x^3 + 600*x^4 + E^3*(-120*x + 120*x^4)))*Log[-2 + x]^2 + (-175000*x + 175000*x^4 + E^5*(80 - 40*x + 160*x^3 - 80*x^4 + E^3*(8*x - 8*x^4)))*Log[-2 + x]^3 + (35000*x - 35000*x^4 + E^5*(-4 + 2*x - 8*x^3 + 4*x^4))*Log[-2 + x]^4 + (-4200*x + 4200*x^4)*Log[-2 + x]^5 + (280*x - 280*x^4)*Log[-2 + x]^6 + (-8*x + 8*x^4)*Log[-2 + x]^7 + (E^5*(1000*x - 1000*x^4) + E^10*(-4 + 2*x - 8*x^3 + 4*x^4) + E^5*(-600*x + 600*x^4)*Log[-2 + x] + E^5*(120*x - 120*x^4)*Log[-2 + x]^2 + E^5*(-8*x + 8*x^4)*Log[-2 + x]^3)*Log[(-1 + x^3)/x])/(E^10*(2*x - x^2 - 2*x^4 + x^5)),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \text {\$Aborted} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {\left (e^5 \log \left (-\frac {1-x^3}{x}\right )+\log ^4(x-2)-20 \log ^3(x-2)+150 \log ^2(x-2)-500 \log (x-2)-e^8+625\right )^2}{e^{10}} \]