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The closed-form integration of arbitrary functions

Published online by Cambridge University Press:  01 August 2016

A.D. Fitt  and
G.T.Q. Hoare
A.D. Fitt
Affiliation:
Faculty of Mathematics, University of Southampton, SO9 5NH, Dr. Challoner’s Grammar School, Amersham, Bucks
G.T.Q. Hoare
Affiliation:
Faculty of Mathematics, University of Southampton, SO9 5NH, Dr. Challoner’s Grammar School, Amersham, Bucks
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Extract

Consider the usual experience of a student who progresses far enough in school mathematics to begin to study the calculus. After motivation of the topic of “rates of change”, simple differentiation of polynomials is learned. More advanced functions are then considered, and eventually the student meets the product, quotient and chain rules. The result: with enough algebraic accuracy and persistence, the student can determine derived functions for virtually any sufficiently wellbehaved combination of standard functions.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 77 , Issue 479 , July 1993 , pp. 227 - 236
Copyright
Copyright © The Mathematical Association 1993

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References

1. Ritt, J.F., Integration in finite terms, Columbia University Press, New York (1948).CrossRefGoogle Scholar
2. Davenport, J.H., Siret, Y. and Tournier, E., Computer algebra. Academic Press (1988).Google Scholar
3. Liouville, J. “Sur la determination des integrales dont la valeur est algebraique”, J. Ecole Polytech. 14 124–193 (1833).Google Scholar
4. Rosenlicht, M. “Integration in finite terms”. Amer. Math. Month. 79 963–972 (1972).CrossRefGoogle Scholar
5. Mead, D.G. “Integration”, Amer. Math. Month. 68 152–156 (1961).CrossRefGoogle Scholar
6. Risch, R.H. “Implicitly elementary integrals”, Proc. Amer. Math. Soc. 57 1–7 (1976).Google Scholar
7. Ostrowski, A. “Sur la integrabilite elementaire de quelques classes d’expressions”. Comm. Math. Helv. 18 283–308 (1946).CrossRefGoogle Scholar
8. Hardy, G.H. The integration of functions of a single variable, Cambridge University Press (1905).Google Scholar
9. Risch, R.H. “The problem of integration in finite terms”. Trans. Amer. Math. Soc. 139 167–189 (1969).CrossRefGoogle Scholar