\[ \int \frac {-20-160 x-315 x^2-195 x^3-25 x^4+e^4 \left (96+256 x+190 x^2+25 x^3\right )+\left (-20 x-45 x^2-25 x^3+e^4 \left (16+40 x+25 x^2\right )\right ) \log \left (\frac {e^4 (-4-5 x)+5 x+5 x^2}{4+5 x}\right )}{-100 x-245 x^2-170 x^3-25 x^4+e^4 \left (80+216 x+165 x^2+25 x^3\right )+\left (-20 x-45 x^2-25 x^3+e^4 \left (16+40 x+25 x^2\right )\right ) \log \left (\frac {e^4 (-4-5 x)+5 x+5 x^2}{4+5 x}\right )} \, dx \]
Optimal antiderivative \[ x +\ln \! \left (5+\ln \! \left (x +\frac {x}{4+5 x}-{\mathrm e}^{4}\right )+x \right ) \]
command
Int[(-20 - 160*x - 315*x^2 - 195*x^3 - 25*x^4 + E^4*(96 + 256*x + 190*x^2 + 25*x^3) + (-20*x - 45*x^2 - 25*x^3 + E^4*(16 + 40*x + 25*x^2))*Log[(E^4*(-4 - 5*x) + 5*x + 5*x^2)/(4 + 5*x)])/(-100*x - 245*x^2 - 170*x^3 - 25*x^4 + E^4*(80 + 216*x + 165*x^2 + 25*x^3) + (-20*x - 45*x^2 - 25*x^3 + E^4*(16 + 40*x + 25*x^2))*Log[(E^4*(-4 - 5*x) + 5*x + 5*x^2)/(4 + 5*x)]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-20-160 x-315 x^2-195 x^3-25 x^4+e^4 \left (96+256 x+190 x^2+25 x^3\right )+\left (-20 x-45 x^2-25 x^3+e^4 \left (16+40 x+25 x^2\right )\right ) \log \left (\frac {e^4 (-4-5 x)+5 x+5 x^2}{4+5 x}\right )}{-100 x-245 x^2-170 x^3-25 x^4+e^4 \left (80+216 x+165 x^2+25 x^3\right )+\left (-20 x-45 x^2-25 x^3+e^4 \left (16+40 x+25 x^2\right )\right ) \log \left (\frac {e^4 (-4-5 x)+5 x+5 x^2}{4+5 x}\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ x+\log \left (x+\log \left (\frac {5 x (x+1)}{5 x+4}-e^4\right )+5\right ) \]