Integral calculus | Integrals

Nonelementary integral

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). A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives. (Wikipedia).

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Related pages

Numerical integration | Elliptic integral | Elementary function | Fresnel integral | Antiderivative | Dirichlet integral | Exponential integral | Radius of convergence | Gaussian integral | Polynomial | Special functions | Exponential function | Error function | Improper integral | Liouvillian function | Mathematics | Function (mathematics) | Field (mathematics) | Risch algorithm | Algebraic function | Incomplete gamma function | Logarithmic integral function | Constant function | Taylor series | Analytic function | Liouville's theorem (differential algebra)