研究了积分区间内含有被积函数本性奇点的若干无穷积分,其被积函数是一般有理分式f(x)、x的三角函数和1/x的三角函数三者的乘积.用围线积分方法导出了用留数表示的一般计算公式,并计算了实例.
Several types of infinite integrals involving essential singularities of the integrand in the interval of integration are studied. The integrands are products of a general rational function, a trigonometric function of x and one of 1/x. General formulae are derived by using the approach of contour integration and the results are expressed in terms of residues. Several examples are given.