探究留数定理在求解不同类型积分上的应用

留数定理作为复变函数中留数理论的重要定理之一,其定理在实际生活中得到广泛的应用.尤其是当某些定积分被积函数的原函数不容易给出时,利用留数定理来计算这些比较困难的定积分是解决定积分的求解问题上的一个有效方法,文章就怎样利用留数定理求某几种特殊情形的定积分的值做以下阐述。

As one of the important theorems of residue theory in complex function,residue theorem has been widely used in real life.Especially when the original functions of some integral functions are not easy to be given,using the residue theorem to calculate these difficult definite integrals is an effective method to solve the problem of definite integrals.This paper expounds how to use the residue theorem to calculate the value of definite integral in some special cases.