Does any one know how to solve this integration? $$\int_0^{\infty } r e^{-a r^2} \ln \left[1+b (c+r)^{-\alpha }\right] \, dr$$
I tried with integration by parts, but it did not help so far since the function in $\ln[.]$ is complicated.
One approximation I could get is by neglecting 1 in $\ln[.]$ but it is not valid in my case.