= Solution
In the distinction relevant here, an <integral of motion> is a single-valued function $I(\mathbf x,\mathbf v)$ of instantaneous <phase space>, with no explicit time dependence, constant along the <orbit>. In an autonomous <Hamiltonian> system this is \b[$\{I,H\}=0$], where the bracket is the <Poisson bracket>. An integral must be defined consistently on the <phase space> region under discussion; an arbitrary multivalued formula obtained by solving one trajectory does not supply a global integral. Some conventions call explicitly time-dependent conserved functions integrals too; the stationary interpretation is needed for the following counts.
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