\[ \int \frac {-12+6 x-2 x^6+e^2 \left (-20 x^4-40 x^5-20 x^6\right )+e^4 \left (-10 x^2-40 x^3-60 x^4-40 x^5-10 x^6\right )+e^5 \left (2 x+10 x^2+20 x^3+20 x^4+10 x^5+2 x^6\right )+e \left (14-6 x+10 x^5+10 x^6\right )+e^3 \left (20 x^3+60 x^4+60 x^5+20 x^6\right )}{-x^5+e^2 \left (-10 x^3-20 x^4-10 x^5\right )+e^4 \left (-5 x-20 x^2-30 x^3-20 x^4-5 x^5\right )+e^5 \left (1+5 x+10 x^2+10 x^3+5 x^4+x^5\right )+e \left (5 x^4+5 x^5\right )+e^3 \left (10 x^2+30 x^3+30 x^4+10 x^5\right )} \, dx \]
Optimal antiderivative \[ 11+x^{2}-\frac {3-2 x}{\left (x -\left (1+x \right ) {\mathrm e}\right )^{4}} \]
command
integrate(((2*x^6+10*x^5+20*x^4+20*x^3+10*x^2+2*x)*exp(1)^5+(-10*x^6-40*x^5-60*x^4-40*x^3-10*x^2)*exp(1)^4+(20*x^6+60*x^5+60*x^4+20*x^3)*exp(1)^3+(-20*x^6-40*x^5-20*x^4)*exp(1)^2+(10*x^6+10*x^5-6*x+14)*exp(1)-2*x^6+6*x-12)/((x^5+5*x^4+10*x^3+10*x^2+5*x+1)*exp(1)^5+(-5*x^5-20*x^4-30*x^3-20*x^2-5*x)*exp(1)^4+(10*x^5+30*x^4+30*x^3+10*x^2)*exp(1)^3+(-10*x^5-20*x^4-10*x^3)*exp(1)^2+(5*x^5+5*x^4)*exp(1)-x^5),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x^{2} e^{10} - 10 \, x^{2} e^{9} + 45 \, x^{2} e^{8} - 120 \, x^{2} e^{7} + 210 \, x^{2} e^{6} - 252 \, x^{2} e^{5} + 210 \, x^{2} e^{4} - 120 \, x^{2} e^{3} + 45 \, x^{2} e^{2} - 10 \, x^{2} e + x^{2}}{e^{10} - 10 \, e^{9} + 45 \, e^{8} - 120 \, e^{7} + 210 \, e^{6} - 252 \, e^{5} + 210 \, e^{4} - 120 \, e^{3} + 45 \, e^{2} - 10 \, e + 1} + \frac {2 \, x - 3}{{\left (x e - x + e\right )}^{4}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________