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The problem of integration in finite terms

1969
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Transactions of the American Mathematical Society
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This paper deals with the problem of telling whether a given elementary function, in the sense of analysis, has an elementary indefinite integral. In §1 of this work, we give a precise definition of the elementary functions and develop the theory of integration of functions of a single variai ¿. By using functions of a complex, rather than a real variable, we can limit ourselves to exponentiation, taking logs, and algebraic operations in defining the elementary functions, since sin, tan"1,

doi:10.1090/s0002-9947-1969-0237477-8
fatcat:kjjlirqkbvckdc542jrmixftj4