Can anyone simplify the following expression? I guess something from Fourier transform can help:

$f(\omega) = \lim_\limits{R \to \infty} \frac{a}{R^2}\left( 1 - (1+bR)e^{-cR}\right) \int_{r=0}^{R}{re^{i \omega r^{-\gamma}}} \mathrm{d}r$, where all parameters are constant except $i$ which is the imaginary unit, and $\gamma > 2$.