  Integral means are important class of bivariate means. In this paper we prove
the very general algorithm for calculation of coefficients in asymptotic
expansion of integral mean. It is based on explicit solving the equation of the
form $B(A(x))=C(x)$, where $B$ and $C$ have known asymptotic expansions. The
results are illustrated by calculation of some important integral means
connected with gamma and digamma functions.
