狄利克雷积分的分析学计算方法

Calculation Methods of Dirichlet Integral

本文探讨了狄利克雷积分的计算方法,综合整理了前人运用分析学知识计算此积分的方法。由于此积分的被积函数不能直接求出其原函数,所以不能直接利用牛顿莱布尼茨公式计算其结果。本文整理的五种方法利用数学分析中反常积分、分部积分的相关定理,对被积函数进行变形、展开、还原逐步得到积分结果。

The calculation of the Dirichlet integral is discussed,and five calculating methods using analysis knowledge are summarized.Because the integral function of this integral can not be directly calculated,the original function can not be obtained directly.The five methods presented in this paper use the theorems of abnormal integral,partial integral in mathematical analysis to deform and expand the integral function,and to restore the integral result step by step.