\[ \int \frac {-7-e^{12}+36 x-111 x^2+66 x^3+12 x^4-24 x^5+53 x^6-42 x^7+20 x^9-15 x^{10}+6 x^{11}-x^{12}+e^8 \left (-9-3 x^2+6 x^3-3 x^4\right )+e^4 \left (-15-6 x^2+3 x^4+12 x^5-18 x^6+12 x^7-3 x^8\right )}{1+e^{12}+3 x^2-6 x^3+6 x^4-12 x^5+19 x^6-18 x^7+18 x^8-20 x^9+15 x^{10}-6 x^{11}+x^{12}+e^8 \left (3+3 x^2-6 x^3+3 x^4\right )+e^4 \left (3+6 x^2-12 x^3+9 x^4-12 x^5+18 x^6-12 x^7+3 x^8\right )} \, dx \]
Optimal antiderivative \[ x^{2}-\left (x +\frac {3}{1+{\mathrm e}^{4}+\left (x^{2}-x \right )^{2}}\right )^{2}-x \]
command
integrate((-exp(4)^3+(-3*x^4+6*x^3-3*x^2-9)*exp(4)^2+(-3*x^8+12*x^7-18*x^6+12*x^5+3*x^4-6*x^2-15)*exp(4)-x^12+6*x^11-15*x^10+20*x^9-42*x^7+53*x^6-24*x^5+12*x^4+66*x^3-111*x^2+36*x-7)/(exp(4)^3+(3*x^4-6*x^3+3*x^2+3)*exp(4)^2+(3*x^8-12*x^7+18*x^6-12*x^5+9*x^4-12*x^3+6*x^2+3)*exp(4)+x^12-6*x^11+15*x^10-20*x^9+18*x^8-18*x^7+19*x^6-12*x^5+6*x^4-6*x^3+3*x^2+1),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -x - \frac {3 \, {\left (2 \, x^{5} - 4 \, x^{4} + 2 \, x^{3} + 2 \, x e^{4} + 2 \, x + 3\right )}}{{\left (x^{4} - 2 \, x^{3} + x^{2} + e^{4} + 1\right )}^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________