🔗 Risch Algorithm for Symbolic Integration

🔗 Mathematics

In symbolic computation (or computer algebra), at the intersection of mathematics and computer science, the Risch algorithm is an algorithm for indefinite integration. It is used in some computer algebra systems to find antiderivatives. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.

The algorithm transforms the problem of integration into a problem in algebra. It is based on the form of the function being integrated and on methods for integrating rational functions, radicals, logarithms, and exponential functions. Risch called it a decision procedure, because it is a method for deciding whether a function has an elementary function as an indefinite integral, and if it does, for determining that indefinite integral.

The complete description of the Risch algorithm takes over 100 pages. The Risch–Norman algorithm is a simpler, faster, but less powerful variant that was developed in 1976 by Arthur Norman.