I've been reading Gut's book for probability theory class. I got stuck on the problem 12 from Chapter 10. (p.198)
I don't know how can I proof via Parseval's relation that:
$$\int_{-\infty}^{\infty} \frac{1-\cos(t)}{\pi t^2}\exp{-|t|}dt=\frac{1}{2}-\frac{\ln(2)}{\pi}$$
Any hints would be really appreciated.