An approximate, linearized equation for the pair correlation function, containing a Debye potential instead of the Coulomb potential, is used to derive by direct integration a solution for the pair correlation function for the case of long‐wavelength plasma oscillations in a fully ionized gas without a magnetic field. The correlation function is then applied to describe the effect of collisions in a linearized Boltzmann equation for the single‐particle distribution function, which again is integrated directly. By substituting the integral of the single‐particle function over the velocity space (so as to obtain the number density of the particles) into Poisson's equation for the electric field, a dispersion equation is constructed for the oscillations. From this dispersion equation the damping of the oscillations can be found. The result combines the Landau damping with the collisional damping. The purpose of the paper is to show what can be done with direct integration in coordinate space, without introducing Fourier and Laplace transforms and without integrations in a complex plane. Only the most interesting terms have been considered. The results obtained are not essentially different from those derived by means of other methods.