\[ \int \frac {e^{\frac {1}{-400 x^5+\left (2000 x^4+400 x^5\right ) \log (x)}} (-5+4 x+(-20-5 x) \log (x))}{200 x^7+\left (-2000 x^6-400 x^7\right ) \log (x)+\left (5000 x^5+2000 x^6+200 x^7\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ 2 \,{\mathrm e}^{-\frac {1}{400 x^{4} \left (x +\left (-x -5\right ) \ln \left (x \right )\right )}} \]
command
integrate(((-5*x-20)*log(x)+4*x-5)/((200*x^7+2000*x^6+5000*x^5)*log(x)^2+(-400*x^7-2000*x^6)*log(x)+200*x^7)/exp(-1/((400*x^5+2000*x^4)*log(x)-400*x^5)),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 2 \, e^{\left (\frac {1}{400 \, {\left (x^{5} \log \left (x\right ) - x^{5} + 5 \, x^{4} \log \left (x\right )\right )}}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {{\left (5 \, {\left (x + 4\right )} \log \left (x\right ) - 4 \, x + 5\right )} e^{\left (-\frac {1}{400 \, {\left (x^{5} - {\left (x^{5} + 5 \, x^{4}\right )} \log \left (x\right )\right )}}\right )}}{200 \, {\left (x^{7} + {\left (x^{7} + 10 \, x^{6} + 25 \, x^{5}\right )} \log \left (x\right )^{2} - 2 \, {\left (x^{7} + 5 \, x^{6}\right )} \log \left (x\right )\right )}}\,{d x} \]________________________________________________________________________________________