For γ>0,δ>0

, How do I evaluate this integral?

I=∫H0eitxlog(HH−x)1γ−1⎛⎝(kHlog(HH−x))−1/γ+1⎞⎠−γ−δ−1γ(H−x)dx,

with gratitude.

I tried the usual tricks, with no result so far.

Thank you.