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The analysis of propagation of bound and leaky modes in single and multiple coupled microstrip lines in planarly layered media by means of Galerkin's method applied to an electric field integral-equation formulation in the spectral domain with Chebyshev polynomials basis functions weighted with the edge behavior of the unknown surface current densities on the metallic strips leads to the evaluation of improper integrals of oscillating functions with a slow asymptotic decay. In this paper, a new analytical technique for drastically speeding up the computation of such integrals is presented. First, suitable half-space contributions are pulled out of the kernels, which makes the integrands exponentially decaying functions. The integrals of the extracted contributions are then expressed as combinations of proper integrals and fast converging improper integrals by means of appropriate integration procedures in the complex plane.