This paper presents a study of the analytical solutions obtained in the integration of the kernels from the influence matrices A and B. Also are presented integral expressions inside points integral expressions for potential and flow. The analytical solutions obtained in this investigation for potential problems in two dimensions, were collected using quadratic elements sub parametric. The analytical expressions presented were validated using the known standard integration numerical methods. It also considered several cases in which the point of placement was positioned inside and outside the element, thus obtaining using the software Mathematical 7.0 and Maple 11.0 for the development of analytical relationships, good CPU times in the calculation of the integrals.