\[ \int \frac {e^{4+2 e^{-\frac {1}{-4+x}}+16 \log ^2(x)} \left (-32+16 x+2 e^{-\frac {1}{-4+x}} x-2 x^2+\left (512-256 x+32 x^2\right ) \log (x)\right )}{16 x^3-8 x^4+x^5} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{16 \ln \left (x \right )^{2}} {\mathrm e}^{2 \,{\mathrm e}^{\frac {1}{4-x}}+4}}{x^{2}}-5 \]
command
integrate(((32*x^2-256*x+512)*log(x)+2*x*exp(-1/(x-4))-2*x^2+16*x-32)*exp(exp(-1/(x-4))+2)^2*exp(4*log(x)^2)^4/(x^5-8*x^4+16*x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {e^{\left (\frac {64 \, x \log \left (x\right )^{2} + 8 \, x e^{\left (-\frac {1}{x - 4}\right )} - 256 \, \log \left (x\right )^{2} - x - 32 \, e^{\left (-\frac {1}{x - 4}\right )}}{4 \, {\left (x - 4\right )}} + \frac {1}{x - 4} + \frac {17}{4}\right )}}{x^{2}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {2 \, {\left (x^{2} - x e^{\left (-\frac {1}{x - 4}\right )} - 16 \, {\left (x^{2} - 8 \, x + 16\right )} \log \left (x\right ) - 8 \, x + 16\right )} e^{\left (16 \, \log \left (x\right )^{2} + 2 \, e^{\left (-\frac {1}{x - 4}\right )} + 4\right )}}{x^{5} - 8 \, x^{4} + 16 \, x^{3}}\,{d x} \]________________________________________________________________________________________