The fluid density distribution within microscopic pores is determined by solving integral equations relating the local chemical potential to the van der Waals attractions and hard sphere repulsions of surrounding material. To avoid resolving the density distribution on submolecular scales, the governing equations are averaged over zones of molecular size using analytic functions to represent local density variations within each zone, These local density profiles range from singularities to uniform distributions depending on the local variation of the potential field. Sample calculations indicate that this integral approach yields results in very good agreement with those based on traditional density functional theory, while reducing computing times by three or four orders of magnitude for one-dimensional geometries.