  Integrability of the quantum Boussinesq equation for c=-2 is demonstrated by
giving a recursive algorithm for generating explicit expressions for the
infinite number of commuting charges based on a reduction of the W(infinity)
algebra. These charges exist for all spins $s \geq 2$. Likewise, reductions of
the W(infinity/2) and W((1+infinity)/2) algebras yield the commuting quantum
charges for the quantum KdV equation at c=-2 and c=1/2, respectively.
