\[ \int \frac {20-12 e^{10-8 x}-40 x-8 x^2+24 x^3-12 x^4+e^{5-4 x} \left (-76-8 x+24 x^2\right )}{25-10 x+31 x^2-36 x^3+15 x^4-18 x^5+9 x^6+e^{10-8 x} \left (e^6-6 e^3 x+9 x^2\right )+e^6 \left (x^2-2 x^3+x^4\right )+e^3 \left (-10 x+12 x^2-8 x^3+12 x^4-6 x^5\right )+e^{5-4 x} \left (30 x-6 x^2+18 x^3-18 x^4+e^6 \left (2 x-2 x^2\right )+e^3 \left (-10+2 x-12 x^2+12 x^3\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {4}{3 x -\frac {5-x}{x^{2}-x -{\mathrm e}^{5-4 x}}-{\mathrm e}^{3}} \]
command
integrate((-12*exp(-4*x+5)^2+(24*x^2-8*x-76)*exp(-4*x+5)-12*x^4+24*x^3-8*x^2-40*x+20)/((exp(3)^2-6*x*exp(3)+9*x^2)*exp(-4*x+5)^2+((-2*x^2+2*x)*exp(3)^2+(12*x^3-12*x^2+2*x-10)*exp(3)-18*x^4+18*x^3-6*x^2+30*x)*exp(-4*x+5)+(x^4-2*x^3+x^2)*exp(3)^2+(-6*x^5+12*x^4-8*x^3+12*x^2-10*x)*exp(3)+9*x^6-18*x^5+15*x^4-36*x^3+31*x^2-10*x+25),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {16 \, {\left ({\left (4 \, x - 5\right )}^{2} + 24 \, x - 16 \, e^{\left (-4 \, x + 5\right )} - 25\right )}}{3 \, {\left (4 \, x - 5\right )}^{3} - 4 \, {\left (4 \, x - 5\right )}^{2} e^{3} + 33 \, {\left (4 \, x - 5\right )}^{2} - 24 \, {\left (4 \, x - 5\right )} e^{3} - 48 \, {\left (4 \, x - 5\right )} e^{\left (-4 \, x + 5\right )} + 484 \, x - 20 \, e^{3} + 64 \, e^{\left (-4 \, x + 8\right )} - 240 \, e^{\left (-4 \, x + 5\right )} - 770} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________