From Wikipedia, the free encyclopedia
The following is a list of
integrals (
antiderivative functions) of
irrational functions. For a complete list of integral functions, see
lists of integrals. Throughout this article the
constant of integration is omitted for brevity.
Integrals involving r = √a2 + x2
Integrals involving s = √x2 − a2
Assume x2 > a2 (for x2 < a2, see next section):
- Here where the positive value of is to be taken.
Integrals involving u = √a2 − x2
Integrals involving R = √ax2 + bx + c
Assume (ax2 + bx + c) cannot be reduced to the following expression (px + q)2 for some p and q.
Integrals involving S = √ax + b
References
- Abramowitz, Milton; Stegun, Irene A., eds. (1972).
"Chapter 3".
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover.
-
Gradshteyn, Izrail Solomonovich;
Ryzhik, Iosif Moiseevich;
Geronimus, Yuri Veniaminovich;
Tseytlin, Michail Yulyevich; Jeffrey, Alan (2015) [October 2014]. Zwillinger, Daniel;
Moll, Victor Hugo (eds.).
Table of Integrals, Series, and Products. Translated by Scripta Technica, Inc. (8 ed.).
Academic Press, Inc.
ISBN
978-0-12-384933-5.
LCCN
2014010276. (Several previous editions as well.)
- Peirce, Benjamin Osgood (1929) [1899]. "Chapter 3". A Short Table of Integrals (3rd revised ed.). Boston: Ginn and Co. pp. 16–30.