Integration Problem

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

Then the integration problem for (E,E^*) is the problem of deciding, given A in E, whether there is a function f(x) in E^* so that f^'(x)=A(x) (Richardson 1968).

See also

Constant Problem, Richardson's Theorem

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

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Integration Problem

Cite this as:

Weisstein, Eric W. "Integration Problem." From MathWorld--A Wolfram Web Resource.

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