\[ \int -\frac {5}{50 x+20 e^{25} x \log (x)+2 e^{50} x \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \left (x \right )}{-10-2 \,{\mathrm e}^{25} \ln \left (x \right )} \]
command
integrate(-5/(2*x*exp(25)^2*log(x)^2+20*x*exp(25)*log(x)+50*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {5 \, e^{\left (-25\right )}}{2 \, {\left (e^{25} \log \left (x\right ) + 5\right )}} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________