I have to solve a definite integral of the form:

\int_{-\infty}^{+\infity} dt exp(ik t)\prod_j exp(g_j exp(i \omega_j t))

Does anyone have an idea how to solve this or at least bring the exp(exp(i\omega t)) part into a form that makes it look a little nicer.

A form that makes it easy to convert into a code for analytical or numerical solution with variable omega_j is what I need.

Thanks for your help,