\[ \int \frac {e^{\frac {3 x^2}{4 e^x x-x \log (4)}} \left (-64 e^{2 x} x^2-12 x^3 \log (4)-4 x^2 \log ^2(4)+e^x x \left (48 x^2-48 x^3+32 x \log (4)\right )\right )}{16 e^{2 x} x^4-8 e^x x^4 \log (4)+x^4 \log ^2(4)} \, dx \]
Optimal antiderivative \[ \frac {4 \,{\mathrm e}^{-\frac {3 x^{2}}{2 x \ln \left (2\right )-4 \,{\mathrm e}^{x} x}}}{x} \]
command
Int[(E^((3*x^2)/(4*E^x*x - x*Log[4]))*(-64*E^(2*x)*x^2 - 12*x^3*Log[4] - 4*x^2*Log[4]^2 + E^x*x*(48*x^2 - 48*x^3 + 32*x*Log[4])))/(16*E^(2*x)*x^4 - 8*E^x*x^4*Log[4] + x^4*Log[4]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ -\frac {4 e^{\frac {3 x^2}{4 e^x x-x \log (4)}} \left (-4 e^x x^2+4 e^x x-x \log (4)\right )}{x^2 \left (4 e^x-\log (4)\right )^2 \left (\frac {x^2 \left (4 e^x x+4 e^x-\log (4)\right )}{\left (4 e^x x-x \log (4)\right )^2}-\frac {2 x}{4 e^x x-x \log (4)}\right )} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {e^{\frac {3 x^2}{4 e^x x-x \log (4)}} \left (-64 e^{2 x} x^2-12 x^3 \log (4)-4 x^2 \log ^2(4)+e^x x \left (48 x^2-48 x^3+32 x \log (4)\right )\right )}{16 e^{2 x} x^4-8 e^x x^4 \log (4)+x^4 \log ^2(4)} \, dx \]________________________________________________________________________________________