The Risch Integration Algorithm

K. O. Geddes, S. R. Czapor and G. Labahn
Additional contact information
K. O. Geddes: University of Waterloo
S. R. Czapor: Laurentian University
G. Labahn: University of Waterloo

Chapter Chapter 12 in Algorithms for Computer Algebra, 1992, pp 511-573 from Springer

Abstract: Abstract When solving for an indefinite integral, it is not enough simply to ask to find an antiderivative of a given function f(x). After all, the fundamental theorem of integral calculus gives the area function A(x)=∭ x a f(t) dt as an antiderivative of f (x). One really wishes to have some sort of closed expression for the antiderivative in terms of well-known functions (e.g. sin(x), e x, log(x)) allowing for common function operations (e.g. addition, multiplication, composition). This is known as the problem of integration in closed form or integration in finite terms. Thus, one is given an elementary function f(x), and asks to find if there exists an elementary function g(x) which is the antiderivative of f(x) and, if so, to determine g(x)

Keywords: Computer Algebra; Rational Part; Integration Algorithm; Constant Field; Integral Basis (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-0-585-33247-5_12

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