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词条 List of integrals of irrational functions
释义

  1. Integrals involving r = {{sqrt|a2 + x2}}

  2. Integrals involving s = {{sqrt|x2 − a2}}

  3. Integrals involving u = {{sqrt|a2 − x2}}

  4. Integrals involving R = {{sqrt|ax2 + bx + c}}

  5. Integrals involving S = {{sqrt|ax + b}}

  6. References

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 = {{sqrt|a2 + x2}}

Integrals involving s = {{sqrt|x2 − a2}}

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

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

Integrals involving u = {{sqrt|a2 − x2}}

Integrals involving R = {{sqrt|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 = {{sqrt|ax + b}}

References

  • {{cite book

|last=Peirce
|first=Benjamin Osgood
|title=A Short Table of Integrals
|origyear=1899
|edition=3rd revised
|year=1929
|publisher=Ginn and Co
|location=Boston
|pages=16–30
|chapter=Chap. 3
  • Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 1972, Dover: New York. (See chapter 3.)
  • {{cite book |author-first1=Izrail Solomonovich |author-last1=Gradshteyn |author-link1=Izrail Solomonovich Gradshteyn |author-first2=Iosif Moiseevich |author-last2=Ryzhik |author-link2=Iosif Moiseevich Ryzhik |author-first3=Yuri Veniaminovich |author-last3=Geronimus |author-link3=Yuri Veniaminovich Geronimus |author-first4=Michail Yulyevich |author-last4=Tseytlin |author-link4=Michail Yulyevich Tseytlin |author-first5=Alan |author-last5=Jeffrey |editor-first1=Daniel |editor-last1=Zwillinger |editor-first2=Victor Hugo |editor-last2=Moll |translator=Scripta Technica, Inc. |title=Table of Integrals, Series, and Products |publisher=Academic Press, Inc. |date=2015 |orig-year=October 2014 |edition=8 |language=English |isbn=0-12-384933-0 |id={{ISBN|978-0-12-384933-5}} |lccn=2014010276 |title-link=Gradshteyn and Ryzhik}} (Several previous editions as well.)
{{Lists of integrals}}

2 : Integrals|Mathematics-related lists
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