\[ \int \frac {10485760 x+18874368 x^2+14155776 x^3+5914624 x^4+1545728 x^5+267520 x^6+31232 x^7+2384 x^8+106 x^9+2 x^{10}+e^{16} \left (655360 x+1310720 x^2+1146880 x^3+573440 x^4+179200 x^5+35840 x^6+4480 x^7+320 x^8+10 x^9\right )+e^{12} \left (5242880 x+10158080 x^2+8519680 x^3+4034560 x^4+1177600 x^5+216320 x^6+24320 x^7+1520 x^8+40 x^9\right )+e^8 \left (15728640 x+29622272 x^2+23855104 x^3+10735616 x^4+2956288 x^5+512000 x^6+55168 x^7+3536 x^8+124 x^9+2 x^{10}\right )+e^4 \left (20971520 x+38535168 x^2+29884416 x^3+12881920 x^4+3414016 x^5+581120 x^6+64512 x^7+4624 x^8+200 x^9+4 x^{10}\right )}{2097152000+2516582400 x+1515192320 x^2+626524160 x^3+201646080 x^4+52879360 x^5+11408640 x^6+2030720 x^7+297885 x^8+35140 x^9+3110 x^{10}+180 x^{11}+5 x^{12}+e^{32} \left (8192000+16384000 x+14336000 x^2+7168000 x^3+2240000 x^4+448000 x^5+56000 x^6+4000 x^7+125 x^8\right )+e^{28} \left (131072000+245760000 x+200704000 x^2+93184000 x^3+26880000 x^4+4928000 x^5+560000 x^6+36000 x^7+1000 x^8\right )+e^{24} \left (917504000+1612185600 x+1231667200 x^2+534732800 x^3+144614400 x^4+25088000 x^5+2766400 x^6+184800 x^7+6700 x^8+100 x^9\right )+e^{20} \left (3670016000+6042419200 x+4333568000 x^2+1776230400 x^3+459110400 x^4+77952000 x^5+8780800 x^6+644000 x^7+28600 x^8+600 x^9\right )+e^{16} \left (9175040000+14155776000 x+9581035520 x^2+3757015040 x^3+951324160 x^4+164334080 x^5+19918400 x^6+1702880 x^7+100110 x^8+3740 x^9+70 x^{10}\right )+e^{12} \left (14680064000+21233664000 x+13668188160 x^2+5221580800 x^3+1335685120 x^4+244779520 x^5+33366400 x^6+3407840 x^7+251800 x^8+12080 x^9+280 x^{10}\right )+e^8 \left (14680064000+19922944000 x+12332564480 x^2+4699586560 x^3+1257328640 x^4+253757440 x^5+39852480 x^6+4837920 x^7+436140 x^8+27260 x^9+1060 x^{10}+20 x^{11}\right )+e^4 \left (8388608000+10695475200 x+6464471040 x^2+2527723520 x^3+731463680 x^4+166676480 x^5+30293760 x^6+4308960 x^7+462280 x^8+35320 x^9+1720 x^{10}+40 x^{11}\right )} \, dx \]
Optimal antiderivative \[ \frac {1}{4+\frac {\left (x +5 \left ({\mathrm e}^{4}+\frac {\frac {4 x}{4+x}+x}{x}\right )^{2}\right )^{2}}{x^{2}}} \]
command
integrate(((10*x^9+320*x^8+4480*x^7+35840*x^6+179200*x^5+573440*x^4+1146880*x^3+1310720*x^2+655360*x)*exp(4)^4+(40*x^9+1520*x^8+24320*x^7+216320*x^6+1177600*x^5+4034560*x^4+8519680*x^3+10158080*x^2+5242880*x)*exp(4)^3+(2*x^10+124*x^9+3536*x^8+55168*x^7+512000*x^6+2956288*x^5+10735616*x^4+23855104*x^3+29622272*x^2+15728640*x)*exp(4)^2+(4*x^10+200*x^9+4624*x^8+64512*x^7+581120*x^6+3414016*x^5+12881920*x^4+29884416*x^3+38535168*x^2+20971520*x)*exp(4)+2*x^10+106*x^9+2384*x^8+31232*x^7+267520*x^6+1545728*x^5+5914624*x^4+14155776*x^3+18874368*x^2+10485760*x)/((125*x^8+4000*x^7+56000*x^6+448000*x^5+2240000*x^4+7168000*x^3+14336000*x^2+16384000*x+8192000)*exp(4)^8+(1000*x^8+36000*x^7+560000*x^6+4928000*x^5+26880000*x^4+93184000*x^3+200704000*x^2+245760000*x+131072000)*exp(4)^7+(100*x^9+6700*x^8+184800*x^7+2766400*x^6+25088000*x^5+144614400*x^4+534732800*x^3+1231667200*x^2+1612185600*x+917504000)*exp(4)^6+(600*x^9+28600*x^8+644000*x^7+8780800*x^6+77952000*x^5+459110400*x^4+1776230400*x^3+4333568000*x^2+6042419200*x+3670016000)*exp(4)^5+(70*x^10+3740*x^9+100110*x^8+1702880*x^7+19918400*x^6+164334080*x^5+951324160*x^4+3757015040*x^3+9581035520*x^2+14155776000*x+9175040000)*exp(4)^4+(280*x^10+12080*x^9+251800*x^8+3407840*x^7+33366400*x^6+244779520*x^5+1335685120*x^4+5221580800*x^3+13668188160*x^2+21233664000*x+14680064000)*exp(4)^3+(20*x^11+1060*x^10+27260*x^9+436140*x^8+4837920*x^7+39852480*x^6+253757440*x^5+1257328640*x^4+4699586560*x^3+12332564480*x^2+19922944000*x+14680064000)*exp(4)^2+(40*x^11+1720*x^10+35320*x^9+462280*x^8+4308960*x^7+30293760*x^6+166676480*x^5+731463680*x^4+2527723520*x^3+6464471040*x^2+10695475200*x+8388608000)*exp(4)+5*x^12+180*x^11+3110*x^10+35140*x^9+297885*x^8+2030720*x^7+11408640*x^6+52879360*x^5+201646080*x^4+626524160*x^3+1515192320*x^2+2516582400*x+2097152000),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {2 \, x^{5} e^{8} + 4 \, x^{5} e^{4} + 2 \, x^{5} + 5 \, x^{4} e^{16} + 20 \, x^{4} e^{12} + 62 \, x^{4} e^{8} + 100 \, x^{4} e^{4} + 53 \, x^{4} + 80 \, x^{3} e^{16} + 400 \, x^{3} e^{12} + 912 \, x^{3} e^{8} + 1136 \, x^{3} e^{4} + 576 \, x^{3} + 480 \, x^{2} e^{16} + 2880 \, x^{2} e^{12} + 6752 \, x^{2} e^{8} + 7552 \, x^{2} e^{4} + 3456 \, x^{2} + 1280 \, x e^{16} + 8960 \, x e^{12} + 23552 \, x e^{8} + 27648 \, x e^{4} + 12288 \, x + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480}{5 \, {\left (x^{6} + 2 \, x^{5} e^{8} + 4 \, x^{5} e^{4} + 18 \, x^{5} + 5 \, x^{4} e^{16} + 20 \, x^{4} e^{12} + 62 \, x^{4} e^{8} + 100 \, x^{4} e^{4} + 149 \, x^{4} + 80 \, x^{3} e^{16} + 400 \, x^{3} e^{12} + 912 \, x^{3} e^{8} + 1136 \, x^{3} e^{4} + 832 \, x^{3} + 480 \, x^{2} e^{16} + 2880 \, x^{2} e^{12} + 6752 \, x^{2} e^{8} + 7552 \, x^{2} e^{4} + 3712 \, x^{2} + 1280 \, x e^{16} + 8960 \, x e^{12} + 23552 \, x e^{8} + 27648 \, x e^{4} + 12288 \, x + 1280 \, e^{16} + 10240 \, e^{12} + 30720 \, e^{8} + 40960 \, e^{4} + 20480\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________