Since a week I've been having much difficulty solving this integral. Help me please, with some insights at least. I know some techniques of contour integration, this is a probability distribution:

$\displaystyle
f_{Z}(z)=\int^{\infty}_{-\infty} \frac{e^{-i u z}}{(1+i u \beta_{1})^{k_{1}}(1-i u \frac{\beta_{2}}{N})^{N k_{2}}}du
$

$\displaystyle i $ - imaginary unit and $\displaystyle k_{1} , k_{2}, \beta_{1} , \beta_{2} > 0, N - Integer $

Thank you.