I have seen that one can use the euler's formula to complexify the integration, and integrate functions like $\displaystyle e^{nx} \cos mx dx$ easily.(The method has a wikipedia page:

Integration using Euler's formula - Wikipedia, the free encyclopedia)

How can i do $\displaystyle \int \frac{dx}{13+3\cos x+4\sin x}$ using complex exponentials.

PS:I know this can be easily done with standard trig substitutions and might turn out to be longer using complex exponentials, but I want to know if and how can it be done with this method ...