\[ \int \frac {e^{27} \left (-250 e^3-750 e^5-750 e^7-250 e^9\right )}{-216+e^9 \left (e (-1080+540 x)+e^3 (-1080+540 x)\right )+e^{18} \left (e^4 \left (-3600+3600 x-900 x^2\right )+e^2 \left (-1800+1800 x-450 x^2\right )+e^6 \left (-1800+1800 x-450 x^2\right )\right )+e^{27} \left (e^3 \left (-1000+1500 x-750 x^2+125 x^3\right )+e^9 \left (-1000+1500 x-750 x^2+125 x^3\right )+e^5 \left (-3000+4500 x-2250 x^2+375 x^3\right )+e^7 \left (-3000+4500 x-2250 x^2+375 x^3\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {x^{2}}{\left (x^{2}-2 x -\frac {6 x \,{\mathrm e}^{-9}}{5 \left ({\mathrm e}+{\mathrm e}^{3}\right )}\right )^{2}} \]
command
integrate((-250*exp(3)^3-750*exp(1)*exp(3)^2-750*exp(1)^2*exp(3)-250*exp(1)^3)*exp(9)^3/(((125*x^3-750*x^2+1500*x-1000)*exp(3)^3+(375*x^3-2250*x^2+4500*x-3000)*exp(1)*exp(3)^2+(375*x^3-2250*x^2+4500*x-3000)*exp(1)^2*exp(3)+(125*x^3-750*x^2+1500*x-1000)*exp(1)^3)*exp(9)^3+((-450*x^2+1800*x-1800)*exp(3)^2+(-900*x^2+3600*x-3600)*exp(1)*exp(3)+(-450*x^2+1800*x-1800)*exp(1)^2)*exp(9)^2+((540*x-1080)*exp(3)+(540*x-1080)*exp(1))*exp(9)-216),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {25 \, {\left (e^{9} + 3 \, e^{7} + 3 \, e^{5} + e^{3}\right )} e^{27}}{{\left (5 \, x e^{12} + 5 \, x e^{10} - 10 \, e^{12} - 10 \, e^{10} - 6\right )}^{2} {\left (e^{12} + e^{10}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {250 \, {\left (e^{9} + 3 \, e^{7} + 3 \, e^{5} + e^{3}\right )} e^{27}}{125 \, {\left ({\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )} e^{9} + 3 \, {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )} e^{7} + 3 \, {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )} e^{5} + {\left (x^{3} - 6 \, x^{2} + 12 \, x - 8\right )} e^{3}\right )} e^{27} - 450 \, {\left ({\left (x^{2} - 4 \, x + 4\right )} e^{6} + 2 \, {\left (x^{2} - 4 \, x + 4\right )} e^{4} + {\left (x^{2} - 4 \, x + 4\right )} e^{2}\right )} e^{18} + 540 \, {\left ({\left (x - 2\right )} e^{3} + {\left (x - 2\right )} e\right )} e^{9} - 216}\,{d x} \]________________________________________________________________________________________