I am trying to evaluate the following integral:
$$\int_\mathbb{R} dx \: \frac{1}{\sigma_i} \exp \left( -\frac{(x-\mu_i)^2}{2\sigma_i^2} \right) \log_2\left[1+\frac{\sigma_i}{\sigma_j} \exp\left( -\frac{(x-\mu_j)^2}{2\sigma_j^2} \right) \exp\left( \frac{(x-\mu_i)^2}{2\sigma_i^2} \right) \right] $$
I can't seem to find it in neither the Bronstein nor Gradshteyn. I also tried to solve it symbolically with Maple but it took too long to find a solution.
Every suggestion or idea is welcome, for definite or indefinite solutions of the integral :)