\[ \int \frac {16384 x^5+e^{\frac {256+e^{16}+768 x+864 x^2+176 x^3-495 x^4-432 x^5-12 x^6+144 x^7+54 x^8-16 x^9-12 x^{10}+x^{12}+e^{12} \left (16+12 x-4 x^3\right )+e^8 \left (96+144 x+54 x^2-48 x^3-36 x^4+6 x^6\right )+e^4 \left (256+576 x+432 x^2-84 x^3-288 x^4-108 x^5+48 x^6+36 x^7-4 x^9\right )}{65536 x^4}} \left (-256-e^{16}-576 x-432 x^2-44 x^3-108 x^5-6 x^6+108 x^7+54 x^8-20 x^9-18 x^{10}+2 x^{12}+e^{12} \left (-16-9 x+x^3\right )+e^8 \left (-96-108 x-27 x^2+12 x^3+3 x^6\right )+e^4 \left (-256-432 x-216 x^2+21 x^3-27 x^5+24 x^6+27 x^7-5 x^9\right )\right )}{16384 x^5} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {\left (4-x^{2}+\frac {{\mathrm e}^{4}}{x}+\frac {-x +4}{x}\right )^{2} \left (\frac {1}{4}-\frac {x^{2}}{16}+\frac {{\mathrm e}^{4}}{16 x}+\frac {-x +4}{16 x}\right )^{2}}{256}}+x \]
command
Int[(16384*x^5 + E^((256 + E^16 + 768*x + 864*x^2 + 176*x^3 - 495*x^4 - 432*x^5 - 12*x^6 + 144*x^7 + 54*x^8 - 16*x^9 - 12*x^10 + x^12 + E^12*(16 + 12*x - 4*x^3) + E^8*(96 + 144*x + 54*x^2 - 48*x^3 - 36*x^4 + 6*x^6) + E^4*(256 + 576*x + 432*x^2 - 84*x^3 - 288*x^4 - 108*x^5 + 48*x^6 + 36*x^7 - 4*x^9))/(65536*x^4))*(-256 - E^16 - 576*x - 432*x^2 - 44*x^3 - 108*x^5 - 6*x^6 + 108*x^7 + 54*x^8 - 20*x^9 - 18*x^10 + 2*x^12 + E^12*(-16 - 9*x + x^3) + E^8*(-96 - 108*x - 27*x^2 + 12*x^3 + 3*x^6) + E^4*(-256 - 432*x - 216*x^2 + 21*x^3 - 27*x^5 + 24*x^6 + 27*x^7 - 5*x^9)))/(16384*x^5),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {16384 x^5+\exp \left (\frac {256+e^{16}+768 x+864 x^2+176 x^3-495 x^4-432 x^5-12 x^6+144 x^7+54 x^8-16 x^9-12 x^{10}+x^{12}+e^{12} \left (16+12 x-4 x^3\right )+e^8 \left (96+144 x+54 x^2-48 x^3-36 x^4+6 x^6\right )+e^4 \left (256+576 x+432 x^2-84 x^3-288 x^4-108 x^5+48 x^6+36 x^7-4 x^9\right )}{65536 x^4}\right ) \left (-256-e^{16}-576 x-432 x^2-44 x^3-108 x^5-6 x^6+108 x^7+54 x^8-20 x^9-18 x^{10}+2 x^{12}+e^{12} \left (-16-9 x+x^3\right )+e^8 \left (-96-108 x-27 x^2+12 x^3+3 x^6\right )+e^4 \left (-256-432 x-216 x^2+21 x^3-27 x^5+24 x^6+27 x^7-5 x^9\right )\right )}{16384 x^5} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ e^{\frac {\left (-x^3+3 x+e^4+4\right )^4}{65536 x^4}}+x \]