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The Problem of Integration in Finite Terms

The Problem of Integration in Finite Terms PDF Author: Robert H. Risch
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Languages : en
Pages : 114

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Book Description
An elementary function is (roughly speaking) a function of a real or complex variable which can be built up using such operations as sine, exponentiation, log, 1/tan and algebraic operations. The problem of integration in finite terms asks whether we can tell, for a given elementary function, f, whether or not the integral of f is again an elementary function. If it is elementary, then one should be able to find it in a systematic manner. In this paper, the problem is formulated precisely, the underlying theory is discussed and finally the problem is solved for those elementary functions in the subclass built up without using irrational algebraic operations. (Author).