\[ \int \frac {-225-30 x-4 x^2-6 x^3-x^4+e^{12} \left (-625-250 x-25 x^2\right )+e^9 \left (-2000-525 x+50 x^2+15 x^3\right )+e^3 \left (-1200-215 x+40 x^2+4 x^3-2 x^4\right )+e^6 \left (-2350-500 x+115 x^2+25 x^3-x^4\right )}{225 x+240 x^2+94 x^3+16 x^4+x^5+e^{12} \left (625 x+250 x^2+25 x^3\right )+e^9 \left (2000 x+1150 x^2+200 x^3+10 x^4\right )+e^6 \left (2350 x+1750 x^2+435 x^3+40 x^4+x^5\right )+e^3 \left (1200 x+1090 x^2+350 x^3+46 x^4+2 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {\frac {x}{3+x +{\mathrm e}^{3} \left (5+x \right )}+2+x}{{\mathrm e}^{3}+1+\frac {x}{5}}-\ln \left (x \right ) \]
command
integrate(((-25*x^2-250*x-625)*exp(3)^4+(15*x^3+50*x^2-525*x-2000)*exp(3)^3+(-x^4+25*x^3+115*x^2-500*x-2350)*exp(3)^2+(-2*x^4+4*x^3+40*x^2-215*x-1200)*exp(3)-x^4-6*x^3-4*x^2-30*x-225)/((25*x^3+250*x^2+625*x)*exp(3)^4+(10*x^4+200*x^3+1150*x^2+2000*x)*exp(3)^3+(x^5+40*x^4+435*x^3+1750*x^2+2350*x)*exp(3)^2+(2*x^5+46*x^4+350*x^3+1090*x^2+1200*x)*exp(3)+x^5+16*x^4+94*x^3+240*x^2+225*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {5 \, {\left (5 \, x e^{6} + 8 \, x e^{3} + 2 \, x + 25 \, e^{6} + 30 \, e^{3} + 9\right )}}{x^{2} e^{3} + x^{2} + 5 \, x e^{6} + 15 \, x e^{3} + 8 \, x + 25 \, e^{6} + 40 \, e^{3} + 15} - \log \left ({\left | x \right |}\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________