  In this short paper, we derive an integral representation for Euler sums of
hyperharmonic numbers. We use results established by other authors to then show
that the integral has a closed-form in terms of zeta values and Stirling
numbers of the first kind. Specifically, the integral has the form of
$$\int_0^\infty \frac{t^{m-1}\ln(1-e^{-t})}{(1-e^{-t})^r} \ dt$$ where $m, r
\in \mathbb{N}$, $m > r$ and $r\ge1$.
