Integration
Integration may refer to:
Biology
* Multisensory integration
* Path integration
* Pre-integration complex, viral genetic material used to insert a viral genome into a host genome
*DNA integration, by means of site-specific recombinase technolo ...
is the basic operation in
integral calculus
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with di ...
. While
differentiation has straightforward
rules
Rule or ruling may refer to:
Education
* Royal University of Law and Economics (RULE), a university in Cambodia
Human activity
* The exercise of political or personal control by someone with authority or power
* Business rule, a rule pert ...
by which the derivative of a complicated
function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. This page lists some of the most common
antiderivative
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function . This can be stated symbolically ...
s.
Historical development of integrals
A compilation of a list of integrals (Integraltafeln) and techniques of integral calculus was published by the German mathematician (aka ) in 1810. These tables were republished in the United Kingdom in 1823. More extensive tables were compiled in 1858 by the Dutch mathematician
David Bierens de Haan for his ''
Tables d'intégrales définies
David Bierens de Haan (3 May 1822, in Amsterdam – 12 August 1895, in Leiden) was a Dutch mathematician and historian of science.
Biography
Bierens de Haan was a son of the rich merchant Abraham Pieterszoon de Haan (1795–1880) and Catharina J ...
'', supplemented by ''
Supplément aux tables d'intégrales définies
David Bierens de Haan (3 May 1822, in Amsterdam – 12 August 1895, in Leiden) was a Dutch mathematician and historian of science.
Biography
Bierens de Haan was a son of the rich merchant Abraham Pieterszoon de Haan (1795–1880) and Catharina J ...
'' in ca. 1864