\[ \int \frac {e^4 \left (44-28 x+111 x^2-90 x^3+e^6 \left (4-12 x+9 x^2\right )\right )}{484 x^2-308 x^3+709 x^4-210 x^5+225 x^6+e^{12} \left (4 x^2-12 x^3+9 x^4\right )+e^6 \left (88 x^2-160 x^3+102 x^4-90 x^5\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{4}}{\left (5 x -{\mathrm e}^{6}+\frac {16}{2 x -\frac {4}{3}}+1\right ) x} \]
command
integrate(((9*x^2-12*x+4)*exp(3)^2-90*x^3+111*x^2-28*x+44)*exp(4)/((9*x^4-12*x^3+4*x^2)*exp(3)^4+(-90*x^5+102*x^4-160*x^3+88*x^2)*exp(3)^2+225*x^6-210*x^5+709*x^4-308*x^3+484*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {{\left (3 \, x - 2\right )} e^{4}}{15 \, x^{3} - 3 \, x^{2} e^{6} - 7 \, x^{2} + 2 \, x e^{6} + 22 \, x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________