The general treatment of linear mammillary models employing input and disposition functions and Laplace transforms is expanded to solve concentration-time equations AUC and AUMC in any compartment without restricting sites of input or output. In this integrated approach to noncompartmental pharmacokinetic analysis, the values of AUC and AUMC can be calculated from Laplace transforms with some very simplified treatments. Tables of input functions, disposition functions, Laplace transforms, and derivatives of the Laplace transforms are presented. The relationships between the integrated parameters and various mammillary model parameters are presented using several examples.