用Laplace变换求一类无穷限积分

Solution of one type of infinite integral by Laplace transform

无穷限积分是微积分学中广义积分的一种类型,是积分知识的一个难点内容。积分学中介绍的初等方法只能解决少数类型的无穷限积分的求值。本文介绍的求值方法是利用Laplace变换本身的特点及其具有的积分性质,来求一些特殊类型的无穷限积分的值,例如,∫0+∞f(xx)dx∫,0+∞f(x)e-axdx型。这些方法克服了初等方法的局限性,适用范围得到了扩大,是初等方法的一个很好的补充,具有很大的实用价值。

Infinite integral is a type of improper integral in calculi, and it is also a difficult point in integral. The primary method in calculi can only solve a thimbleful type of evaluations of infinite integral, This article introduces some new methods, which utilize the own specialties and integral characters in Laplace transform to solve some soecial types of infinite integral. For example,∫0^＋∞f（x）/xdx,∫0^＋∞f（x）c^-axdx The new methods overcome the disadvantage in the primary method and expand the application range. This is a good complement of the primary method and has a great applicable value,