  We present a method to calculate integrals over monomials of matrix elements
with invariant measures in terms of Wick contractions. The method gives exact
results for monomials of low order. For higher--order monomials, it leads to an
error of order 1/N^alpha where N is the dimension of the matrix and where alpha
is independent of the degree of the monomial. We give a lower bound on the
integer alpha and show how alpha can be increased systematically. The method is
particularly suited for symbolic computer calculation. Explicit results are
given for O(N), U(N) and for the circular orthogonal ensemble.
