risch algorithm

Input interpretation

Risch algorithm

Definition

The Risch algorithm is a decision procedure for indefinite integration that determines whether a given integral is elementary, and if so, returns a closed-form result for the integral. It builds a tower of logarithmic, exponential, and algebraic extensions. The case of algebraic extensions is quite complicated and is therefore not completely implemented in any computer algebra system. Liouville's principle, which dates back to the 19th century, is an important part of the Risch algorithm. There are extensions to the Risch algorithm, notably by Cherry, to be able to handle some special functions.
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Related terms

elementary function | Horowitz reduction | indefinite integral | Liouville's principle

Subject classifications

MathWorld

indefinite integrals
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