\[ \int \frac {e^{2 x} \left (120-480 x+400 x^2-40 x^4+e^{2/3} \left (-8+24 x-24 x^2+8 x^3\right )\right )}{64000-72000 x+3000 x^2+14625 x^3-375 x^4-1125 x^5-125 x^6+e^2 \left (-1+3 x-3 x^2+x^3\right )+e^{4/3} \left (120-285 x+195 x^2-15 x^3-15 x^4\right )+e^{2/3} \left (-4800+8400 x-3075 x^2-975 x^3+375 x^4+75 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {4 \,{\mathrm e}^{2 x}}{\left ({\mathrm e}^{\frac {2}{3}}-15+\frac {-5 x +25}{-1+x}-5 x \right )^{2}} \]
command
integrate(((8*x^3-24*x^2+24*x-8)*exp(2/3)-40*x^4+400*x^2-480*x+120)*exp(x)^2/((x^3-3*x^2+3*x-1)*exp(2/3)^3+(-15*x^4-15*x^3+195*x^2-285*x+120)*exp(2/3)^2+(75*x^5+375*x^4-975*x^3-3075*x^2+8400*x-4800)*exp(2/3)-125*x^6-1125*x^5-375*x^4+14625*x^3+3000*x^2-72000*x+64000),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {8 \, {\left (x^{2} e^{\left (2 \, x\right )} - 2 \, x e^{\left (2 \, x\right )} + e^{\left (2 \, x\right )}\right )}}{25 \, x^{4} - 10 \, x^{3} e^{\frac {2}{3}} + 150 \, x^{3} + x^{2} e^{\frac {4}{3}} - 20 \, x^{2} e^{\frac {2}{3}} - 175 \, x^{2} - 2 \, x e^{\frac {4}{3}} + 110 \, x e^{\frac {2}{3}} - 1200 \, x + e^{\frac {4}{3}} - 80 \, e^{\frac {2}{3}} + 1600} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________