积分上极限为$x=1$或$x=\infty$时公式$\int (x^{n+p} - 2 x^n\cosζ+ x^{n-p})/(x^{2n} - 2 x^n\cosθ+ 1) dx/x$积分的简便求法
An easy method for finding the integral of the formula $\int (x^{n+p} - 2 x^n\cosζ+ x^{n-p})/(x^{2n} - 2 x^n\cosθ+ 1) dx/x$ when the upper limit of integration is $x=1$ or $x=\infty$
摘要：
这是一篇由莱昂哈德·欧拉于1776年3月18日发表的文章的翻译（Opera Omnia I-XVIII，第118页）。265-290）和总结，它由西蒙丹尼斯泊松在1820年和海因里希Burkhardt在1916年。附录中列出了有趣的现代符号定积分和级数，欧拉，后使用部分分数证明他的主要公式，正式获得允许参数$n, p, zeta and theta$采取特别的，甚至纯虚数，价值观：傅里叶余弦和双边拉普拉斯变换的三角和双曲正割（也平方），和他们的部分分式分解。源档案提供了Plain TeX、LaTeX和PDF格式的更正的拉丁文文本和完整的法文翻译。
英文摘要：
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 Siméon 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.
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