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).

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

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Weisstein, Eric W. "Integration Problem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IntegrationProblem.html