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In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field operations).[1] A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist.[2] This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives.
- ^ Weisstein, Eric W. "Elementary Function." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ElementaryFunction.html From MathWorld Accessed 24 Apr 2017.
- ^ Dunham, William (2005). The Calculus Gallery. Princeton. p. 119. ISBN 978-0-691-13626-4.