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Tough Indefinite Integral

  1. Dec 21, 2008 #1
    A long time since i posted at physics forums. Anyways, try helping me solve the following integral

    [tex]\int\frac{1}{x^{2n} + 1}dx[/tex]

    I tried many ways but all futile. The best way with which i could come up was factorising the denominator by de moivre's theorem. By finding the 2nth roots of unity. Hence i was able to express the denominator in a better way. But thats it. Dead end. I dont why but i get a feeling that we may able to do the sum by that way.

    I am sorry that i am not able to presnt much work to you.

    Hoping that you may be able to do the problem.
     
  2. jcsd
  3. Dec 21, 2008 #2

    Avodyne

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    Science Advisor

    Well, according to the Mathematica online integrator, the result is a hypergeometric function. I believe you get this result by Taylor expanding in powers of x, doing the integral term by term, and then noticing that the result is a hypergeometric series.

    http://integrals.wolfram.com
     
  4. Dec 21, 2008 #3
    Mathematica sometimes even gives answers in complex numbers to a simple problem. And the answer which i have in the book is not a hypertrigo function. There should be a way to bring the answer without Taylor or Maclauren cause we havent been taught those yet.
     
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