Lists of integrals
Published July 9th, 2008 in UncategorizedSee the following pages for lists of integrals:
- List of integrals of rational functions
- List of integrals of irrational functions
- List of integrals of trigonometric functions
- List of integrals of inverse trigonometric functions
- List of integrals of hyperbolic functions
- List of integrals of arc hyperbolic functions
- List of integrals of exponential functions
- List of integrals of logarithmic functions
- List of integrals of arc functions
Also see table of integrals for the most common integral functions.
Historical developments
A compilation of a list of integrals (Integraltafeln) and techniques of integral calculus
was published by the German mathematician Meyer Hirsch in 1810. These tables were republished in the
United Kingdom in 1823. More extensive tables were compiled in 1858 by the Dutch mathematician David de Bierens de Haan. A new edition was published in 1862. These tables, which contain mainly integrals of elementary functions, remained in use until the middle of
the 20th century. They were then replaced by the much more extensive tables of Gradshteyn and Rhyzik.
In Gradshteyn and Rhyzik, integrals originating from the book by de Bierens are denoted by BI.
Other lists of integrals
Gradshteyn and Ryzhik contains a large collection of results. Other useful resources include the CRC Standard Mathematical Tables and Formulae and Abramowitz and Stegun. A&S contains many identities concerning specific integrals, which are organized with the most relevant topic instead of being collected into a separate table.
There are several web sites which have tables of integrals and integrals on demand.
References
- Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables.
- I.S. Gradshteyn (И.С. Градштейн), I.M. Ryzhik (И.М. Рыжик); Alan Jeffrey, Daniel Zwillinger, editors. Table of Integrals, Series, and Products, seventh edition. Academic Press, 2007. ISBN 978-0-12-373637-6. Errata. (Several previous editions as well.)
- Daniel Zwillinger. CRC Standard Mathematical Tables and Formulae, 31st edition. Chapman & Hall/CRC Press, 2002. ISBN 1-58488-291-3. (Many earlier editions as well.)
External links
Integrals on demand
- The Integrator (at Wolfram Research)
- TILU Table of Integrals Look Up (maintained by Richard Fateman)
Tables of integrals
- S.O.S. Mathematics: Tables and Formulas
- Indefinite and Definite Integrals (at EqWorld)
Historical
- Meyer Hirsch, Integraltafeln, oder, Sammlung von Integralformeln (Duncker un Humblot, Berlin, 1810)
- Meyer Hirsch, Integral Tables, Or, A Collection of Integral Formulae (Baynes and son, London, 1823)
- David de Bierens de Haan, Nouvelles Tables d’Intégrales définies (Engels, Leiden, 1862)
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