Can You Solve this Tough Indefinite Integral?

[FedEx]

A long time since i posted at physics forums. Anyways, try helping me solve the following integral

$$\int\frac{1}{x^{2n} + 1}dx$$

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 that's it. Dead end. I don't 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.

 

[Avodyne]

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

 

[FedEx]

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

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 haven't been taught those yet.