Simple integral formulations for a general potential depending on an arbitrary radial function in three-dimensional spherical and hyperbolic spaces of constant curvature are presented. The propagators are calculated in the usual 3D polar coordinates by using the Weyl-ordering prescription. By analyzing the radial function, the obtained expressions are compared with the path integrals for the Smorodinsky-Winternitz (SW) and generalized Kepler-Coulomb (GKC) systems. The results can be applied to obtain solvable path integral forms for interesting potentials.
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