\[ \int \frac {e^{\frac {92416-184832 x^2-92416 x^3+138624 x^4+138624 x^5-11552 x^6-69312 x^7-28880 x^8+5776 x^9+8664 x^{10}+2888 x^{11}+361 x^{12}+e \left (-9728+19456 x^2+9728 x^3-14592 x^4-14592 x^5+1216 x^6+7296 x^7+3040 x^8-608 x^9-912 x^{10}-304 x^{11}-38 x^{12}\right )+e^2 \left (256-512 x^2-256 x^3+384 x^4+384 x^5-32 x^6-192 x^7-80 x^8+16 x^9+24 x^{10}+8 x^{11}+x^{12}\right )}{x^4}} \left (-369664+369664 x^2+92416 x^3+138624 x^5-23104 x^6-207936 x^7-115520 x^8+28880 x^9+51984 x^{10}+20216 x^{11}+2888 x^{12}+e \left (38912-38912 x^2-9728 x^3-14592 x^5+2432 x^6+21888 x^7+12160 x^8-3040 x^9-5472 x^{10}-2128 x^{11}-304 x^{12}\right )+e^2 \left (-1024+1024 x^2+256 x^3+384 x^5-64 x^6-576 x^7-320 x^8+80 x^9+144 x^{10}+56 x^{11}+8 x^{12}\right )\right )}{x^5} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x^{4} \left (2+x -\frac {4}{x^{2}}\right )^{4} \left ({\mathrm e}-19\right )^{2}} \]
command
Int[(E^((92416 - 184832*x^2 - 92416*x^3 + 138624*x^4 + 138624*x^5 - 11552*x^6 - 69312*x^7 - 28880*x^8 + 5776*x^9 + 8664*x^10 + 2888*x^11 + 361*x^12 + E*(-9728 + 19456*x^2 + 9728*x^3 - 14592*x^4 - 14592*x^5 + 1216*x^6 + 7296*x^7 + 3040*x^8 - 608*x^9 - 912*x^10 - 304*x^11 - 38*x^12) + E^2*(256 - 512*x^2 - 256*x^3 + 384*x^4 + 384*x^5 - 32*x^6 - 192*x^7 - 80*x^8 + 16*x^9 + 24*x^10 + 8*x^11 + x^12))/x^4)*(-369664 + 369664*x^2 + 92416*x^3 + 138624*x^5 - 23104*x^6 - 207936*x^7 - 115520*x^8 + 28880*x^9 + 51984*x^10 + 20216*x^11 + 2888*x^12 + E*(38912 - 38912*x^2 - 9728*x^3 - 14592*x^5 + 2432*x^6 + 21888*x^7 + 12160*x^8 - 3040*x^9 - 5472*x^10 - 2128*x^11 - 304*x^12) + E^2*(-1024 + 1024*x^2 + 256*x^3 + 384*x^5 - 64*x^6 - 576*x^7 - 320*x^8 + 80*x^9 + 144*x^10 + 56*x^11 + 8*x^12)))/x^5,x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {\exp \left (\frac {92416-184832 x^2-92416 x^3+138624 x^4+138624 x^5-11552 x^6-69312 x^7-28880 x^8+5776 x^9+8664 x^{10}+2888 x^{11}+361 x^{12}+e \left (-9728+19456 x^2+9728 x^3-14592 x^4-14592 x^5+1216 x^6+7296 x^7+3040 x^8-608 x^9-912 x^{10}-304 x^{11}-38 x^{12}\right )+e^2 \left (256-512 x^2-256 x^3+384 x^4+384 x^5-32 x^6-192 x^7-80 x^8+16 x^9+24 x^{10}+8 x^{11}+x^{12}\right )}{x^4}\right ) \left (-369664+369664 x^2+92416 x^3+138624 x^5-23104 x^6-207936 x^7-115520 x^8+28880 x^9+51984 x^{10}+20216 x^{11}+2888 x^{12}+e \left (38912-38912 x^2-9728 x^3-14592 x^5+2432 x^6+21888 x^7+12160 x^8-3040 x^9-5472 x^{10}-2128 x^{11}-304 x^{12}\right )+e^2 \left (-1024+1024 x^2+256 x^3+384 x^5-64 x^6-576 x^7-320 x^8+80 x^9+144 x^{10}+56 x^{11}+8 x^{12}\right )\right )}{x^5} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {(19-e)^2 \left (-x^3-2 x^2+4\right )^4}{x^4}} \]