No. 295 in my list of difficult integrals ...
Integral of the general power of : the object here is to establish the following reduction formula:
What I've tried: Integration by Parts, which gets me to:
... I waded further into this morass but I lost my boots.
I have also tried substitutions etc. but nothing useful happens, and trying to split it into a form with a is also unfruitful.
The usual: hints for a substitution or a splitting?