I would like to calculate the following definite integral 

$$\int\_{-\pi}^{\pi}e^{-x\,u\,i}e^{R\,e^{\,u\,i}}du$$

where $x,R>0$ in terms of elemental or special functions.

A first attempt

$$\int\_{-\pi}^{\pi}e^{-x\,u\,i}e^{R\,e^{\,u\,i}}du=-i\,\int\_Cz^{-x-1}\,e^{R\,z}\,dz$$

with $C$ the unit circle.

It's correct? In this case, how continue? 

Any help or any other way to solve it will be welcomed