Finding the Spectrum of a Function with Exponential and Trig Terms

[frenzal_dude]

Homework Statement

Hi, I need to find the spectrum of the following function:
$$i=I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]$$

Homework Equations

the Fourier Transform would be:
$$\int_{-\infty }^{\infty }I_0[e^{\frac{-0.01(cos(2\pi 1000t)+cos(2\pi 100000t))}{0.026}}-1]e^{-j2\pi ft}dt$$

The Attempt at a Solution

I'm not sure where to start because I'm not sure how to take the integral of an exponential when there is a trig term in there. Is this integral even possible or would it diverge to infinity?

Hope you guys can help,
frenzal

 

[frenzal_dude]

I think I worked it out! I need to express the exp(x) function as a taylor series, and as n gets larger (greater than say 3) the number approaches 0! So you can approximate it up to n=3 and then integration should be ok.