A set of approximative methods is proposed to radically accelerate the calculation of the contribution of Coulomb integrals in the calculations of DFT giant biomolecules - the limiting stage of such relevant but extremely resource-intensive calculations, including calculations of thousands of docking complexes of thousands of atoms. The proposed complex includes, through a quick and accurate approximation of the contribution of a huge number of 4-center Coulomb integrals through a linear combination of 3-center integrals, and then through a combination of 2-center integrals. The non-multi-complete short-range components of these 2-center integrals are very quickly considered pre-prepared splines from the center-to-center distances. The remaining long-range multipole contributions are quickly calculated for giant molecules in the FMM style (splitting a huge space into regions and subdomains, was originally developed for the dynamics of galaxies). Calculations are saved as much as possible everywhere due to pre-selected combinations of integrals. All two-center components (including the approximation of two-center overlaps of basic functions through linear combinations of single-center auxiliary density functions) are quickly calculated due to splines from internuclear distances from a specially prepared database. For new bases, the database is easily and quickly replenished by decomposing the new basis into a set of universal ex-ponents and a database with them.