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We reproduce the rotation curve of the Andromeda galaxy (M31) by taking into account its bulge, disk, and halo components, considering the last one to contain the major part of dark matter mass. Hence, our prescription is to split the galactic bulge into two components, namely, the inner and main bulges, respectively. Both bulges are thus modeled by exponential density profiles since we underline that the widely accepted de Vaucouleurs law fails to reproduce the whole galactic bulge rotation curve. In addition, we adopt various well-known phenomenological dark matter profiles to estimate the dark matter mass in the halo region. Moreover, we apply the least-squares fitting method to determine from the rotation curve the model free parameters, namely, the characteristic (central) density, scale radius, and consequently the total mass. To do so, we perform Markov chain Monte Carlo statistical analyses based on the Metropolis algorithm, maximizing our likelihoods adopting velocity and radii data points of the rotation curves. We do not fit separately the components for bulges, disk and halo, but we perform an overall fit including all the components and employing all the data points. Thus, we critically analyze our corresponding findings and, in particular, we employ the Bayesian Information Criterion to assess the most accredited model to describe M31 dark matter dynamics.