Analytical results of the energy density functionals are obtained by using a finite-range density-dependent Brink-Boeker effective interaction to calculate the energy dependent heavy-ion optical potential in the energy density model (EDM) and folding model (FM) with similar computational benefit as achieved by short-range interaction. The resulting potentials and elastic scattering cross sections for the system ⁴⁰Ca+⁴⁰Ca (E_CM=120 MeV) are compared with those obtained previously from the short-range Skyrme interaction.