Risch Algorithm

In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives, named after the American mathematician Robert Henry Risch, who developed it in 1968. It transforms the problem of integration into a problem in algebra, 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 decides whether a function has an elementary antiderivative and, if so, determines it, though the algorithm cannot always resolve the constant problem, which is undecidable when it must determine whether an arbitrary complex number expression equals zero.