\[ \int \frac {e^{\frac {2 \left (-198 x-558 x^2-18 x^3+288 x^4-72 x^5+e^{2 x} \left (-50 x^2-10 x^3+32 x^4-8 x^5\right )+e^x \left (60 x+336 x^2+36 x^3-192 x^4+48 x^5\right )\right )}{9+90 x+189 x^2-180 x^3+36 x^4+e^x \left (-30 x-138 x^2+120 x^3-24 x^4\right )+e^{2 x} \left (25 x^2-20 x^3+4 x^4\right )}} \left (-1188-756 x-7452 x^2-7020 x^3+14904 x^4-6480 x^5+864 x^6+e^x \left (360+612 x+5040 x^2+9180 x^3-15336 x^4+6480 x^5-864 x^6\right )+e^{3 x} \left (500 x^3-600 x^4+240 x^5-32 x^6\right )+e^{2 x} \left (-900 x^2-3780 x^3+5256 x^4-2160 x^5+288 x^6\right )\right )}{27+405 x+1863 x^2+1755 x^3-3726 x^4+1620 x^5-216 x^6+e^{2 x} \left (225 x^2+945 x^3-1314 x^4+540 x^5-72 x^6\right )+e^{3 x} \left (-125 x^3+150 x^4-60 x^5+8 x^6\right )+e^x \left (-135 x-1296 x^2-2295 x^3+3834 x^4-1620 x^5+216 x^6\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {36}{\left (x \left (-{\mathrm e}^{x}+3\right ) \left (-5+2 x \right )-3\right )^{2}}-4 x -4} \]
command
integrate(((-32*x^6+240*x^5-600*x^4+500*x^3)*exp(x)^3+(288*x^6-2160*x^5+5256*x^4-3780*x^3-900*x^2)*exp(x)^2+(-864*x^6+6480*x^5-15336*x^4+9180*x^3+5040*x^2+612*x+360)*exp(x)+864*x^6-6480*x^5+14904*x^4-7020*x^3-7452*x^2-756*x-1188)*exp(((-8*x^5+32*x^4-10*x^3-50*x^2)*exp(x)^2+(48*x^5-192*x^4+36*x^3+336*x^2+60*x)*exp(x)-72*x^5+288*x^4-18*x^3-558*x^2-198*x)/((4*x^4-20*x^3+25*x^2)*exp(x)^2+(-24*x^4+120*x^3-138*x^2-30*x)*exp(x)+36*x^4-180*x^3+189*x^2+90*x+9))^2/((8*x^6-60*x^5+150*x^4-125*x^3)*exp(x)^3+(-72*x^6+540*x^5-1314*x^4+945*x^3+225*x^2)*exp(x)^2+(216*x^6-1620*x^5+3834*x^4-2295*x^3-1296*x^2-135*x)*exp(x)-216*x^6+1620*x^5-3726*x^4+1755*x^3+1863*x^2+405*x+27),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ e^{\left (-3 \, x - \frac {4 \, x^{5} e^{\left (2 \, x\right )} - 24 \, x^{5} e^{x} + 36 \, x^{5} - 4 \, x^{4} e^{\left (2 \, x\right )} + 24 \, x^{4} e^{x} - 36 \, x^{4} - 55 \, x^{3} e^{\left (2 \, x\right )} + 342 \, x^{3} e^{x} - 531 \, x^{3} + 100 \, x^{2} e^{\left (2 \, x\right )} - 582 \, x^{2} e^{x} + 846 \, x^{2} - 120 \, x e^{x} + 369 \, x}{4 \, x^{4} e^{\left (2 \, x\right )} - 24 \, x^{4} e^{x} + 36 \, x^{4} - 20 \, x^{3} e^{\left (2 \, x\right )} + 120 \, x^{3} e^{x} - 180 \, x^{3} + 25 \, x^{2} e^{\left (2 \, x\right )} - 138 \, x^{2} e^{x} + 189 \, x^{2} - 30 \, x e^{x} + 90 \, x + 9}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________