List of integrals of irrational functions
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 , for , 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
- Peirce, Benjamin Osgood (1929) . "Chap. 3". A Short Table of Integrals (3rd revised ed.). Boston: Ginn and Co. pp. 16–30.
- Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1972, Dover: New York. (See chapter 3.)
- 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.)