\[ \int -\frac {e^{25+\frac {1}{5} \left (-1+\log ^{-\frac {e^{25} x}{5+2 x}}(5)\right )} \log ^{-\frac {e^{25} x}{5+2 x}}(5) \log (\log (5))}{25+20 x+4 x^2} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {{\mathrm e}^{\frac {\ln \left (\ln \left (5\right )\right ) x \,{\mathrm e}^{25}}{-2 x -5}}}{5}-\frac {1}{5}} \]
command
integrate(-exp(25)*log(log(5))*exp(-x*exp(25)*log(log(5))/(5+2*x))*exp(1/5*exp(-x*exp(25)*log(log(5))/(5+2*x))-1/5)/(4*x^2+20*x+25),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (\frac {1}{5} \, \log \left (5\right )^{-\frac {x e^{25}}{2 \, x + 5}} - \frac {1}{5}\right )} \]