Let then

the integral becomes:

now

and the integral becomes

This looks like a dead end . But I include it because it might give you an idea?

Perhaps there is no closed form solution? In my last line I am trying to integrate sinc(X) raised to the power of 1-b. But if you google 'integral of sinc' it seems like this is far from trivial. See here Sine Integral -- from Wolfram MathWorld for the integral of sinc.