\[ \int \frac {e^{\frac {41958+104976 x+122472 x^2+81648 x^3+34020 x^4+9072 x^5+1512 x^6+144 x^7+6 x^8}{19683 x+52488 x^2+61236 x^3+40824 x^4+17010 x^5+4536 x^6+756 x^7+72 x^8+3 x^9+e^{2 x} \left (6561 x+17496 x^2+20412 x^3+13608 x^4+5670 x^5+1512 x^6+252 x^7+24 x^8+x^9\right )}} \left (-377622-1132866 x-1417176 x^2-1102248 x^3-551124 x^4-183708 x^5-40824 x^6-5832 x^7-486 x^8-18 x^9+e^{2 x} \left (-125874-629370 x-1186164 x^2-1312200 x^3-918540 x^4-428652 x^5-136080 x^6-29160 x^7-4050 x^8-330 x^9-12 x^{10}\right )\right )}{177147 x^2+531441 x^3+708588 x^4+551124 x^5+275562 x^6+91854 x^7+20412 x^8+2916 x^9+243 x^{10}+9 x^{11}+e^{4 x} \left (19683 x^2+59049 x^3+78732 x^4+61236 x^5+30618 x^6+10206 x^7+2268 x^8+324 x^9+27 x^{10}+x^{11}\right )+e^{2 x} \left (118098 x^2+354294 x^3+472392 x^4+367416 x^5+183708 x^6+61236 x^7+13608 x^8+1944 x^9+162 x^{10}+6 x^{11}\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\frac {2592}{\left (3+x \right )^{8}}+6}{x \left (3+{\mathrm e}^{2 x}\right )}} \]
command
integrate(((-12*x^10-330*x^9-4050*x^8-29160*x^7-136080*x^6-428652*x^5-918540*x^4-1312200*x^3-1186164*x^2-629370*x-125874)*exp(x)^2-18*x^9-486*x^8-5832*x^7-40824*x^6-183708*x^5-551124*x^4-1102248*x^3-1417176*x^2-1132866*x-377622)*exp((6*x^8+144*x^7+1512*x^6+9072*x^5+34020*x^4+81648*x^3+122472*x^2+104976*x+41958)/((x^9+24*x^8+252*x^7+1512*x^6+5670*x^5+13608*x^4+20412*x^3+17496*x^2+6561*x)*exp(x)^2+3*x^9+72*x^8+756*x^7+4536*x^6+17010*x^5+40824*x^4+61236*x^3+52488*x^2+19683*x))/((x^11+27*x^10+324*x^9+2268*x^8+10206*x^7+30618*x^6+61236*x^5+78732*x^4+59049*x^3+19683*x^2)*exp(x)^4+(6*x^11+162*x^10+1944*x^9+13608*x^8+61236*x^7+183708*x^6+367416*x^5+472392*x^4+354294*x^3+118098*x^2)*exp(x)^2+9*x^11+243*x^10+2916*x^9+20412*x^8+91854*x^7+275562*x^6+551124*x^5+708588*x^4+531441*x^3+177147*x^2),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ e^{\left (-\frac {864}{3 \, x^{8} + 72 \, x^{7} + 756 \, x^{6} + 4536 \, x^{5} + 17010 \, x^{4} + 40824 \, x^{3} + 61236 \, x^{2} + {\left (x^{8} + 24 \, x^{7} + 252 \, x^{6} + 1512 \, x^{5} + 5670 \, x^{4} + 13608 \, x^{3} + 20412 \, x^{2} + 17496 \, x + 6561\right )} e^{\left (2 \, x\right )} + 52488 \, x + 19683} - \frac {288}{3 \, x^{7} + 63 \, x^{6} + 567 \, x^{5} + 2835 \, x^{4} + 8505 \, x^{3} + 15309 \, x^{2} + {\left (x^{7} + 21 \, x^{6} + 189 \, x^{5} + 945 \, x^{4} + 2835 \, x^{3} + 5103 \, x^{2} + 5103 \, x + 2187\right )} e^{\left (2 \, x\right )} + 15309 \, x + 6561} - \frac {96}{3 \, x^{6} + 54 \, x^{5} + 405 \, x^{4} + 1620 \, x^{3} + 3645 \, x^{2} + {\left (x^{6} + 18 \, x^{5} + 135 \, x^{4} + 540 \, x^{3} + 1215 \, x^{2} + 1458 \, x + 729\right )} e^{\left (2 \, x\right )} + 4374 \, x + 2187} - \frac {32}{3 \, x^{5} + 45 \, x^{4} + 270 \, x^{3} + 810 \, x^{2} + {\left (x^{5} + 15 \, x^{4} + 90 \, x^{3} + 270 \, x^{2} + 405 \, x + 243\right )} e^{\left (2 \, x\right )} + 1215 \, x + 729} - \frac {32}{3 \, {\left (3 \, x^{4} + 36 \, x^{3} + 162 \, x^{2} + {\left (x^{4} + 12 \, x^{3} + 54 \, x^{2} + 108 \, x + 81\right )} e^{\left (2 \, x\right )} + 324 \, x + 243\right )}} - \frac {32}{9 \, {\left (3 \, x^{3} + 27 \, x^{2} + {\left (x^{3} + 9 \, x^{2} + 27 \, x + 27\right )} e^{\left (2 \, x\right )} + 81 \, x + 81\right )}} - \frac {32}{27 \, {\left (3 \, x^{2} + {\left (x^{2} + 6 \, x + 9\right )} e^{\left (2 \, x\right )} + 18 \, x + 27\right )}} - \frac {32}{81 \, {\left ({\left (x + 3\right )} e^{\left (2 \, x\right )} + 3 \, x + 9\right )}} + \frac {518}{81 \, {\left (x e^{\left (2 \, x\right )} + 3 \, x\right )}}\right )} \]
Maxima 5.44 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________