For what value of p integral (x^p-1)/log(x) from 0 to 1 exist?

Answer 1

p-1>=1 so p>=2
Even at p=2
(x-1)/ lnx at x = 0 and x=1 has limit 0 so you ncan make it continuos at those points.
The integral exists and can be be proven to be =ln2

Answer 2

i see that x has to be positive cuz of the denominator

and for wen x is positive, p can be anything

so the range for p is all reals