\[ \int \frac {e^{\frac {1}{\log ^2\left (4-40 x+36 x^2+320 x^3+256 x^4\right )}} \left (-20-44 x+64 x^2+\left (-1+5 x+8 x^2\right ) \log ^3\left (4-40 x+36 x^2+320 x^3+256 x^4\right )\right )}{\left (-1+7 x-3 x^2-11 x^3+8 x^4\right ) \log ^3\left (4-40 x+36 x^2+320 x^3+256 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{\frac {1}{{\ln \left (\left (3-2 x -\left (1+4 x \right )^{2}\right )^{2}\right )}^{2}}}}{1-x} \]
command
Int[(E^Log[4 - 40*x + 36*x^2 + 320*x^3 + 256*x^4]^(-2)*(-20 - 44*x + 64*x^2 + (-1 + 5*x + 8*x^2)*Log[4 - 40*x + 36*x^2 + 320*x^3 + 256*x^4]^3))/((-1 + 7*x - 3*x^2 - 11*x^3 + 8*x^4)*Log[4 - 40*x + 36*x^2 + 320*x^3 + 256*x^4]^3),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{\frac {1}{\log ^2\left (4-40 x+36 x^2+320 x^3+256 x^4\right )}} \left (-20-44 x+64 x^2+\left (-1+5 x+8 x^2\right ) \log ^3\left (4-40 x+36 x^2+320 x^3+256 x^4\right )\right )}{\left (-1+7 x-3 x^2-11 x^3+8 x^4\right ) \log ^3\left (4-40 x+36 x^2+320 x^3+256 x^4\right )} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \frac {\left (-16 x^2+11 x+5\right ) \left (64 x^4+80 x^3+9 x^2-10 x+1\right ) e^{\frac {1}{\log ^2\left (256 x^4+320 x^3+36 x^2-40 x+4\right )}}}{\left (-128 x^3-120 x^2-9 x+5\right ) \left (-8 x^4+11 x^3+3 x^2-7 x+1\right )} \]