Revisiting SU(N) integrals

In this note, I revisit integrals over $\text{SU}\left(N\right)$ of the form ${\int }^{}DU{U}_{i_1{j}_1}\cdots U_{i_p{j}_p}{U}_{k_1{l}_1}^{†}\cdots U_{k_n{l}_n}^{†}$. While the case p  =  n is well known, it seems that explicit expressions for p  =  n  +  N had not appeared in the literature. Similarities and differences, in particular in the large N limit, between the two cases are discussed. (paper)