\[ \int \frac {-1476225+25 e^{15}+4920714 x-6561024 x^2+4374000 x^3-1458000 x^4+194400 x^5+e^{12} (-1125+750 x)+e^9 \left (20250-27000 x+9000 x^2\right )+e^6 \left (-182250+364500 x-243000 x^2+54000 x^3\right )+e^3 \left (820125-2186996 x+2187000 x^2-972000 x^3+162000 x^4\right )}{-1476225+25 e^{15}+4920750 x-6561000 x^2+4374000 x^3-1458000 x^4+194400 x^5+e^{12} (-1125+750 x)+e^9 \left (20250-27000 x+9000 x^2\right )+e^6 \left (-182250+364500 x-243000 x^2+54000 x^3\right )+e^3 \left (820125-2187000 x+2187000 x^2-972000 x^3+162000 x^4\right )} \, dx \]
Optimal antiderivative \[ x +\frac {2 x^{2}}{25 \left ({\mathrm e}^{3}+6 x -9\right )^{4}} \]
command
integrate((25*exp(3)^5+(750*x-1125)*exp(3)^4+(9000*x^2-27000*x+20250)*exp(3)^3+(54000*x^3-243000*x^2+364500*x-182250)*exp(3)^2+(162000*x^4-972000*x^3+2187000*x^2-2186996*x+820125)*exp(3)+194400*x^5-1458000*x^4+4374000*x^3-6561024*x^2+4920714*x-1476225)/(25*exp(3)^5+(750*x-1125)*exp(3)^4+(9000*x^2-27000*x+20250)*exp(3)^3+(54000*x^3-243000*x^2+364500*x-182250)*exp(3)^2+(162000*x^4-972000*x^3+2187000*x^2-2187000*x+820125)*exp(3)+194400*x^5-1458000*x^4+4374000*x^3-6561000*x^2+4920750*x-1476225),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x + \frac {2 \, x^{2}}{25 \, {\left (6 \, x + e^{3} - 9\right )}^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________