Any idea how to solve this integral, I tried the integration by parts, and it made the things even more difficult. The substitution didn't work either. Here is the integral:
$\displaystyle \int \frac{e^{-\frac{x^2 b c^2}{x^2 + b}}}{\left(b+x^2\right)^2}\,dx $
Or in Mathematica:
Integrate[E^(-((x^2 b c^2)/(x^2 + b)))/(x^2 + b)^2,x]