\[ \int \frac {e^{4 e^{e^{3/x}}} \left (10 e^{2/x}-5 x^2+e^{e^{3/x}+\frac {3}{x}} \left (-60+60 e^{2/x}+60 x\right )\right )}{36 x^2+e^{4 e^{e^{3/x}}} \left (-12 x^2+12 e^{2/x} x^2+12 x^3\right )+e^{8 e^{e^{3/x}}} \left (x^2+e^{4/x} x^2-2 x^3+x^4+e^{2/x} \left (-2 x^2+2 x^3\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {5}{{\mathrm e}^{4 \,{\mathrm e}^{{\mathrm e}^{\frac {3}{x}}}} \left (x +{\mathrm e}^{\frac {2}{x}}-1\right )+6} \]
command
Int[(E^(4*E^E^(3/x))*(10*E^(2/x) - 5*x^2 + E^(E^(3/x) + 3/x)*(-60 + 60*E^(2/x) + 60*x)))/(36*x^2 + E^(4*E^E^(3/x))*(-12*x^2 + 12*E^(2/x)*x^2 + 12*x^3) + E^(8*E^E^(3/x))*(x^2 + E^(4/x)*x^2 - 2*x^3 + x^4 + E^(2/x)*(-2*x^2 + 2*x^3))),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \frac {5}{e^{4 e^{e^{3/x}}} x-e^{4 e^{e^{3/x}}}+e^{4 e^{e^{3/x}}+\frac {2}{x}}+6} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {e^{4 e^{e^{3/x}}} \left (10 e^{2/x}-5 x^2+e^{e^{3/x}+\frac {3}{x}} \left (-60+60 e^{2/x}+60 x\right )\right )}{36 x^2+e^{4 e^{e^{3/x}}} \left (-12 x^2+12 e^{2/x} x^2+12 x^3\right )+e^{8 e^{e^{3/x}}} \left (x^2+e^{4/x} x^2-2 x^3+x^4+e^{2/x} \left (-2 x^2+2 x^3\right )\right )} \, dx \]________________________________________________________________________________________