Calculation of hadronization, decay or scattering processes at nonzero temperatures and densities within the Nambu-Jona-Lasinio-like models requires some techniques for computation of Feynmann diagrams. Decomposition of Feynmann diagrams at the one-loop level leads to the appearance of elementary integrals with one, two, three, and four fermion lines. For example, evaluation of the ππ scattering amplitude requires calculating of a box diagram with four fermion lines. In this work, the real and imaginary parts of the box integral at the one-loop level are provided in the form suitable for numerical evaluation. The obtained expressions are applicable to any value of temperature, particle mass, and chemical potential. We pay special attention to the conditions for the existence of the appearing improper integrals. As a result, we have obtained constraints on possible values of particle momenta. Among the expressions for the box integral, the general formulas for the integral with an arbitrary number of lines are derived for the case with zero or collinear fermion momenta.