中文摘要：

单位冲激函数是“信号与系统”课程中十分重要的一个基本数学模型，其物理含义和广义函数的性质难以形象理解，从而使得单位冲激函数及其复合函数的积分计算容易出现理解上的偏差。本文采用常规函数的计算方法，根据狄拉克对单位冲激函数的数学定义以及广义函数的筛选性质，对单位冲激函数及其复合函数的积分问题进行了归纳和探讨，分别对内层函数为常数、一次函数、二次函数、三次及以上函数的情形进行了分析和推导，试图得出一般性的结论，最后运用已知正确结果对结论的正确性进行了验证。

英文摘要：

In the course of Signal and System, unit impulse function is an important and basic mathematic model. Because of its special physics and generalized function meaning, it is difficult to understand the integral of unit impulse function. Based on Dirac＇s definition of unit impulsive function and the select quali- ty of generalized function, deeper discussion on the integral function is made. Three different situations about the inner-layer function are analyzed in this paper： the inner-layer function is constant, linear func- tion, quadratic function and three or above function. A series of general conclusions are drawn from the above analysis. Finally, some known correct results are used to prove the conclusions in this paper.