{"title":"用简单代数方法求非初等积分的可数集","authors":"Stefan Leitner, M. Bertotti","doi":"10.12988/imf.2022.912305","DOIUrl":null,"url":null,"abstract":"Many integrals can be solved in an elementary way. However, the overwhelming majority of functions cannot be integrated via one of the elementary integration techniques. Moreover, their antiderivative is not expressible in terms of elementary functions. In this note an alternative approach for the solution of a countable set of non-elementary integrals is provided. This approach involves the use of algebraic manipulation and an integral form of the Zeta function. Mathematics Subject Classification: 26A42, 11M06","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"144 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solutions of a countable set of non-elementary integrals by means of simple algebra\",\"authors\":\"Stefan Leitner, M. Bertotti\",\"doi\":\"10.12988/imf.2022.912305\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Many integrals can be solved in an elementary way. However, the overwhelming majority of functions cannot be integrated via one of the elementary integration techniques. Moreover, their antiderivative is not expressible in terms of elementary functions. In this note an alternative approach for the solution of a countable set of non-elementary integrals is provided. This approach involves the use of algebraic manipulation and an integral form of the Zeta function. Mathematics Subject Classification: 26A42, 11M06\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"144 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/imf.2022.912305\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/imf.2022.912305","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Solutions of a countable set of non-elementary integrals by means of simple algebra
Many integrals can be solved in an elementary way. However, the overwhelming majority of functions cannot be integrated via one of the elementary integration techniques. Moreover, their antiderivative is not expressible in terms of elementary functions. In this note an alternative approach for the solution of a countable set of non-elementary integrals is provided. This approach involves the use of algebraic manipulation and an integral form of the Zeta function. Mathematics Subject Classification: 26A42, 11M06
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