Design equations for non-isothermal Laminar Flow Tubular Reactors (LFTRs) with homogeneous and heterogeneous at the reactor wall reactions with arbitrary kinetic equations have been satisfactorily treated transforming the original P.D.E. problem into a system of integral equations. The kernels of the integral operators are related to an eigenvalue problem which does not depend on the kinetic equations; this avoids repetitive computational effort in the treating of different reaction kinetics. To render a more efficient numerical treatment and according to the governing reaction rate regime, modified expressions of the general solution were obtained was follows: (i) a solution with kernels depending only on the diffusion and convective times was obtained for a low reaction regime; (ii) another solution with kernels including the reaction rime, besides the diffusion and convective ones, was necessary for a fast reaction regime and (iii) the local quasi-steady-state approximation was obtained as limiting case of solution (ii) for a instantaneous reaction regime.