To your question: How to calculate this integral?
My preliminary answer is: Don't use Maples sophisticated algorithms.
Zoomed in it looks like this
This could explain why Maples sophisticated integration methods have difficulties. They will try to follow all the oscillations.
Annother reason could be: The function you want to integrate is not always real valued also (see the attachment).
Could you tell a bit more about your integrand?
PS:: I have just seen Roubens answer. Zoomed it looks also jagged.
Integral_reply.mw