Let $k\geq 2$ be a fixed natural number and $d_k(n)$ denote the number of ways $n$ can be written as a product of $k$ positive integers. Let $\Delta_k(x)$ denote the error term in the asymptotic formula of the summatory function of $d_k(n)$. In this paper we study some integrals involving $\Delta_2(x)$ and $\Delta_3(x)$.