  This is a translation of an article presented by Leonhard Euler on 18 March
1776 (Opera Omnia I-XVIII, pp. 265-290) and of summaries for it by Sim\'eon
Denis Poisson in 1820 and by Heinrich Burkhardt in 1916. An appendix lists in
modern notation interesting definite integrals and series which Euler, after
using partial fractions to prove his main formula, obtained formally by
allowing the parameters $n, p, zeta and theta$ to take particular, even pure
imaginary, values : the Fourier cosine and two-sided Laplace transforms of the
trigonometric and of the hyperbolic secant (also squared), and their partial
fraction decomposition. The source archive provides, in Plain TeX, LaTeX and
PDF formats, the corrected Latin text and a complete translation into French.
