This problem arises in a paper on population genetics (Kimura 1962). 1. The problem statement Let [itex]f(p) = \int_0^p ((1 - x)/x)^k dx[/itex]. For a small value of p, we have approximately f(p) = (p ^ (1-k)) / (1-k) How is this obtained? 2. My attempt at a solution I tried to expand the f(p) around p = 0. However, f'(p) = ((1 - p)/p)^k is undefined at p=0. Furthermore, it does not seem that this approach can yield the form p^(1-k) / (1-k). I must be missing something. I would appreciate any insights. Thanks.