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:
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.
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.