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Math Help - Looks Simple Integral But it is fake

  1. #1
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    Looks Simple Integral But it is fake

    HI , can anyone give me a way to solve :

    <br />
  \int \frac{x^2}{1+x^4}dx<br />
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  2. #2
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    Thought

    I'm considering multiply both top and bottom by x^{-2}, then let x = e^u which I believe converts to a familiar function (but you may also have to integrate by parts).
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by parkhid View Post
    HI , can anyone give me a way to solve :

    <br />
  \int \frac{x^2}{1+x^4}dx<br />
    Another way is to expand the integrand using partial fractions.

     \frac{x^2}{1+x^4}=\frac{1}{2\sqrt{2}}\cdot\frac{x}  {x^2-\sqrt{2}x+1}-\frac{1}{2\sqrt{2}}\cdot\frac{x}{x^2+\sqrt{2}x+1}
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  4. #4
    A Plied Mathematician
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    You can also use complex line integration. See here for a very similar sort of integral.
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  5. #5
    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by Ackbeet View Post
    You can also use complex line integration. See here for a very similar sort of integral.
    There is only a minor detail: the integral proposed by parkhid is indefinite and its solution is a family of functions... the integral of Your example is definite and its solution [if it exists...] is a real [or complex] number...

    Kind regards

    \chi \sigma
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  6. #6
    A Plied Mathematician
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    Very true. My bad.
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