Integration Problem

Let  be a set of expressions representing real, single-valued partially defined functions of one real variable. Let  be the set of functions represented by expressions in , where  contains the identity function and the rational numbers as constant functions and that  is closed under addition, multiplication, and composition. If  is an expression in , then let  be the function denoted by .

Then the integration problem for  is the problem of deciding, given  in , whether there is a function  in  so that  (Richardson 1968).

REFERENCES:

Richardson, D. "Some Unsolvable Problems Involving Elementary Functions of a Real Variable." J. Symbolic Logic 33, 514-520, 1968.