  We study integrals of completely integrable quantum systems associated with
classical root systems. We review integrals of the systems invariant under the
corresponding Weyl group and as their limits we construct enough integrals of
the non-invariant systems, which include systems whose complete integrability
will be first established in this paper. We also present a conjecture claiming
that the quantum systems with enough integrals given in this note coincide with
the systems that have the integrals with constant principal symbols
corresponding to the homogeneous generators of the $B_n$-invariants. We review
conditions supporting the conjecture and give a new condition assuring it.
