List of integrals of irrational functions

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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[edit]

Integrals involving s = x2a2[edit]

Assume x2 > a2 (for x2 < a2, see next section):

  • Here where the positive value of is to be taken.

Integrals involving u = a2x2[edit]

Integrals involving R = ax2 + bx + c[edit]

Assume (ax2 + bx + c) cannot be reduced to the following expression (px + q)2 for some p and q.

Integrals involving S = ax + b[edit]

References[edit]

  • 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.