This thesis presents the complete derivation of closed-form analytical solutions for the Self-Channel Interference (SCI), Cross-Channel Interference (XCI), and Multi-Channel Interference (MCI) kernel integrals. These integrals are fundamental to the Polynomial Closed-Form Model (PCFM) framework, a powerful and innovative approach for modeling nonlinear effects in optical fiber transmission. The predictive accuracy of the PCFM depends directly on the precise evaluation of these integrals. To accomplish this, we used the symbolic computation tool Mathematica, which was essential for handling the complexity of the problem. The derivation process involved a series of initial mathematical transformations designed to simplify the original complex expressions. This methodical approach allowed us to systematically break down the problem into manageable steps.