Hi. I'm not sure how you're supposed to solve it but, using Fourier transform (I assumed that this could be the way since you had a function against ) I arrived to the result:

First, let's call your function so the integral you want to solve is

Then, from Parseval's identity:

(1)

We can assume that (2)

Since we have , we might want to find to solve it easily. First, I'll rewrite the function so we can use a transform I've got from my table.

The trasform is: . Where P stands for square pulse and a total width.

Antitransforming:

(3)

Once we have everything, we can assume from (1), (2) and (3) that:

Now we solve the first part (which is easier):

I hope this is what you needed.