\[ \int \frac {e^{\frac {1}{12} e^{-5+2 x}} \left (-2-\frac {1}{3} e^{-5+2 x} x \log (x)\right )}{25 x-10 e^{\frac {1}{12} e^{-5+2 x}} x \log (x)+e^{\frac {1}{6} e^{-5+2 x}} x \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {2}{\ln \! \left (x \right ) {\mathrm e}^{{\mathrm e}^{-\ln \left (12\right )+2 x -5}}-5} \]
command
integrate((-4*x*exp(-log(12)+2*x-5)*log(x)-2)*exp(exp(-log(12)+2*x-5))/(x*log(x)^2*exp(exp(-log(12)+2*x-5))^2-10*x*log(x)*exp(exp(-log(12)+2*x-5))+25*x),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
\[ \frac {2 \, {\left (x e^{\left (2 \, x\right )} \log \left (x\right ) + 6 \, e^{5}\right )}}{x e^{\left (2 \, x + \frac {1}{12} \, e^{\left (2 \, x - 5\right )}\right )} \log \left (x\right )^{2} - 5 \, x e^{\left (2 \, x\right )} \log \left (x\right ) + 6 \, e^{\left (\frac {1}{12} \, e^{\left (2 \, x - 5\right )} + 5\right )} \log \left (x\right ) - 30 \, e^{5}} \]