  We explicitly exhibit n-1 constants of motion for geodesics in the general
D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from
contractions of even powers of the 2-form obtained by contracting the geodesic
velocity with the dual of the contraction of the velocity with the
(D-2)-dimensional Killing-Yano tensor. These constants of motion are
functionally independent of each other and of the D-n+1 constants of motion
that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a
total of D independent constants of motion in all dimensions D. The Poisson
brackets of all pairs of these D constants are zero, so geodesic motion in
these spacetimes is completely integrable.
