\[ \int \frac {39-9 \log \left (4+e^2\right )}{169-78 e^2 x+9 e^4 x^2+\left (-78+18 e^2 x\right ) \log \left (4+e^2\right )+9 \log ^2\left (4+e^2\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{\frac {13}{3}-\ln \left (4+{\mathrm e}^{2}\right )-{\mathrm e}^{2} x} \]
command
integrate((-9*log(4+exp(2))+39)/(9*log(4+exp(2))^2+(18*exp(2)*x-78)*log(4+exp(2))+9*x^2*exp(2)^2-78*exp(2)*x+169),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {{\left (3 \, \log \left (e^{2} + 4\right ) - 13\right )} e^{\left (-2\right )}}{3 \, x e^{2} + 3 \, \log \left (e^{2} + 4\right ) - 13} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: NotImplementedError} \]________________________________________________________________________________________