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In this communication, original analytical expressions for the quadruple static potential singular integrals on rectangular domains are presented. These integrals can appear when the method of moments is used to solve the mixed potential integral equation but also the electric and the magnetic static integral equations. The analytical expressions have been obtained for both source and test cells integrals when using 3-D rectangular meshes. The reported expressions can be used to solve an extensive range of electrostatic, magnetostatic and full-wave problems.