The analysis of propagation in multiple coupled microstrip lines, by using Galerkin's method performed in the spectral domain with analytically Fourier transformable expansion functions factorising the correct edge behaviour of the fields, leads to the evaluation of improper single integrals of oscillating functions with a slow asymptotic decaying. In this work an appropriate contribution is extracted by the kernel of the integrals so that the numerical computation of the integrals of the accelerate contributions is very fast, being the integrands exponentially decaying functions, and the remaining integrals are expressed as combination of fast converging integrals by means of an integration procedure in the complex plane.