  In this paper we show examples of computations achieved using the formulas of
our previous paper, which express the push-forwards in equivariant cohomology
as iterated residues at infinity. We consider the equivariant cohomology of the
complex Lagrangian Grassmannian $LG(n)$ and the orthogonal Grassmannian with
the action of the maximal torus. In particular, we show how to obtain some
well-known results due to P. Pragacz and J. Ratajski on integrals of Schur
polynomials over the Lagrangian Grassmannian $LG(n)$ and the orthogonal
Grassmannian $OG(n)$.
