I'm struggling to work out how to integrate the following

$\displaystyle \int_0^t(\gamma^{1/\kappa}-2i\zeta{w}(1-t/s)_+^{H-1/2})^{\kappa}ds$

here (.)_+ denotes the positive part

if I did not have the ^(H-1/2) I can do it, alas it does have it! and so it stumps me on how to evaluate this integral.

any advice much appreciated