关键词: 无穷积分, 留数定理, 多值函数

Abstract:  Inspired by the article［1］，this paper discusses two kinds of infinite integrals solved by residue the-orem again． Firstly，some characteristics of the two kinds of integrals are analyzed concisely． By combing and sim-plifying the method in the article［1］，the two kinds of integrals are processed with the residue theorem，and the re-sults are obtained when they are greater than 1 and are integers． Then，the two kinds of integrals are recalculated by the method of the residue theorem of multivalued function，the results are obtained when they are greater than 1， and the results are briefly explained． Through the treatment of integral by two methods，we can experience the beau-ty of residue theorem，expand students’vision and enhance their enthusiasm for learning，and lay a good founda-tion for their subsequent courses．

Key words:  infinite integral, residue theorem, multivalued function