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Math Help - How to integrate this

  1. #1
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    How to integrate this

    1/(x^5+1)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CrazyAsian View Post
    1/(x^5+1)
    This simple looking integral turned out to be a monster. See what people came up with here
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  3. #3
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    Quote Originally Posted by CrazyAsian View Post
    1/(x^5+1)
    The major step is as follows:

    You need to factorize the polynomial into irreducible polynomials in \mathbb{R}[x].

    The best way to do this is to factorize this in \mathbb{C}[x] in linear factors.

    We need to find all solutions to,
    x^5 = -1 = \cos (\pi+2\pi n) + i \sin (\pi+2\pi n)
    De Moiver's theorem,
    x = \cos \left( \frac{\pi}{5} + \frac{2\pi n}{5} \right) + i \sin \left( \frac{\pi}{5} + \frac{2\pi n}{5} \right) \mbox{ for }n=0,1,2,3,4

    But why you want to do that I have no idea. I guess that is why you are a CrazyAsian.
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