\[ \int \frac {-1-2 x-4 x^2+(-1-4 x) \log (x)}{2 e^{4 x} x^4+4 e^{4 x} x^3 \log (x)+2 e^{4 x} x^2 \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{-4 x}}{x \left (2 x +2 \ln \! \left (x \right )\right )}-9 \]
command
Int[(-1 - 2*x - 4*x^2 + (-1 - 4*x)*Log[x])/(2*E^(4*x)*x^4 + 4*E^(4*x)*x^3*Log[x] + 2*E^(4*x)*x^2*Log[x]^2),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-1-2 x-4 x^2+(-1-4 x) \log (x)}{2 e^{4 x} x^4+4 e^{4 x} x^3 \log (x)+2 e^{4 x} x^2 \log ^2(x)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {e^{-4 x} \left (x^2+x \log (x)\right )}{2 x^2 (x+\log (x))^2} \]