In [here](http://journals.aps.org/pre/abstract/10.1103/PhysRevE.69.066138), there is an identity in equation 17
$$
k {N-1\choose{k}}\int\_0^1 p^{k-1}(1-p)^{N-k-1}\log p\,dp
=\psi(k)-\psi(N),
$$
where $N$, $k(<N)$ are integers and $p$ can be regarded as the integration variable. I attempted to derive the above identity from
$$
\int\_0^1\dfrac{x^{p-1}-x^{q-1}}{1-x}dx=\psi(q)-\psi(p)
$$
without success.

How can I derive the above identity?