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An efficient integral-equation method is presented for the analysis of electromagnetic scattering from arbitrarily shaped 3-D dielectric objects embedded in a single layer of a uniaxial planar-layered medium. The proposed method employs a mixed-potential volume electric-field integral equation (VEFIE) that permits the object of interest to be dispersive, anisotropic, inhomogeneous, and of arbitrary shape. The VEFIE is solved by an iterative frequency-domain method-of-moments procedure. The object is discretized by tetrahedral elements, and the procedure is accelerated by the adaptive integral method, which reduces the computational costs by enclosing the tetrahedral mesh with an auxiliary regular grid and performing anterpolation (mesh to grid), propagation (grid to grid), interpolation (grid to mesh), and near-zone correction (mesh to mesh) steps. The computationally dominant propagation step of the method is accelerated by decomposing the Green's functions into convolution and correlation terms in the stratification direction and using 3-D fast Fourier transforms to multiply the resulting propagation matrices with the necessary vectors. If the object of interest is meshed using N tetrahedra that are of a single length scale, then the setup time, memory requirement, and the iterative matrix-solution time (per iteration) of the proposed method scale as O(N), O(N), and O(NlogN), respectively. Numerical results validate the method's accuracy and efficiency for various problems relevant to geophysical exploration.