ON THE INTEGRATION OF ELEMENTARY FUNCTIONS WHICH ARE BUILT UP USING ALGEBRAIC OPERATIONS,

This paper advances the study of the problem of integration of elementary functions in finite terms to within one step of a complete solution. A previous paper gave an algorithm for integrating those elementary functions which are built up using rational operations, exponentials and logarithms, under the condition that the exponentials and logarithms could not be replaced by adjoining constants and performing algebraic operations. Now it is shown that with algebraic operations allowed, the problem reduces to a problem in the theory of algebraic functions which is believed to be decidable. Author