\[ \int \frac {e^{\left .-\frac {3}{2}\right /x} \left (e^{\left .\frac {3}{2}\right /x} \left (480 x^3-320 x^4\right )+e^{e^{\left .-\frac {3}{2}\right /x} \left (-3+e^{\left .\frac {3}{2}\right /x} x\right )} \left (-81+216 x-144 x^2+e^{\left .\frac {3}{2}\right /x} \left (18 x^2-48 x^3+32 x^4\right )\right )\right )}{18 x^2-48 x^3+32 x^4} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x -3 \,{\mathrm e}^{-\frac {3}{2 x}}}-\frac {10 x^{2}}{x -\frac {3}{4}} \]
command
integrate((((32*x^4-48*x^3+18*x^2)*exp(3/2/x)-144*x^2+216*x-81)*exp((x*exp(3/2/x)-3)/exp(3/2/x))+(-320*x^4+480*x^3)*exp(3/2/x))/(32*x^4-48*x^3+18*x^2)/exp(3/2/x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {80 \, x^{2} e^{\left (-\frac {3}{2 \, x}\right )} - 8 \, x e^{\left (\frac {2 \, x^{2} - 6 \, x e^{\left (-\frac {3}{2 \, x}\right )} - 3}{2 \, x}\right )} - 60 \, x e^{\left (-\frac {3}{2 \, x}\right )} + 6 \, e^{\left (\frac {2 \, x^{2} - 6 \, x e^{\left (-\frac {3}{2 \, x}\right )} - 3}{2 \, x}\right )} + 45 \, e^{\left (-\frac {3}{2 \, x}\right )}}{2 \, {\left (4 \, x e^{\left (-\frac {3}{2 \, x}\right )} - 3 \, e^{\left (-\frac {3}{2 \, x}\right )}\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {{\left ({\left (144 \, x^{2} - 2 \, {\left (16 \, x^{4} - 24 \, x^{3} + 9 \, x^{2}\right )} e^{\left (\frac {3}{2 \, x}\right )} - 216 \, x + 81\right )} e^{\left ({\left (x e^{\left (\frac {3}{2 \, x}\right )} - 3\right )} e^{\left (-\frac {3}{2 \, x}\right )}\right )} + 160 \, {\left (2 \, x^{4} - 3 \, x^{3}\right )} e^{\left (\frac {3}{2 \, x}\right )}\right )} e^{\left (-\frac {3}{2 \, x}\right )}}{2 \, {\left (16 \, x^{4} - 24 \, x^{3} + 9 \, x^{2}\right )}}\,{d x} \]________________________________________________________________________________________