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Omniscience Group Title

Integrate (1+x^2)/(1+x^4)dx

  • 2 years ago
  • 2 years ago

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  1. Omniscience Group Title
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    \[\large \int\limits\frac{1+x^{2}}{1+x^{4}} dx\]

    • 2 years ago
  2. lgbasallote Group Title
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    ugh why couldnt it be 1 - x^4 :p lol

    • 2 years ago
  3. Omniscience Group Title
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    If it was it would have defeated the purpose of this integral. (:

    • 2 years ago
  4. lgbasallote Group Title
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    exactly why im complaining :p

    • 2 years ago
  5. Omniscience Group Title
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    No need to complain. Just think of an intuitive method. :)

    • 2 years ago
  6. blockcolder Group Title
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    Completing the square of the denominator then a substitution is what I have in mind, but I'm not completely sure.

    • 2 years ago
  7. Omniscience Group Title
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    Not that easy.

    • 2 years ago
  8. Omniscience Group Title
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    There are two methods.

    • 2 years ago
  9. goxenul Group Title
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    http://www.wolframalpha.com/input/?i=integrate+%5Cfrac%7B1%2Bx%5E%7B2%7D%7D%7B1%2Bx%5E%7B4%7D%7D+dx (look at "Show steps") Well, this looks... difficult. I wonder if there's an easier way to do this, than splitting it into two integrals.

    • 2 years ago
  10. lgbasallote Group Title
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    okay...hmm \[u = \frac{1}{1+x^4} \rightarrow du = \frac{4x^3}{(1+x^4)^2}\] \[dv = 1+ x^2 \rightarrow v = \tan^{-!} x\] LOL really isn't easy :P

    • 2 years ago
  11. blockcolder Group Title
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    Separation, perhaps? \[\frac{1}{1+x^4}+\frac{x^2}{1+x^4}\] Might this work?

    • 2 years ago
  12. Omniscience Group Title
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    Not really. Wolfram Alpha method is tedious.

    • 2 years ago
  13. Omniscience Group Title
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    You can try if it works; but I dont think so.

    • 2 years ago
  14. lgbasallote Group Title
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    the first term would be integrable i think

    • 2 years ago
  15. Ishaan94 Group Title
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    \[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x -\frac{1}x\right)+2} \]This should do it.

    • 2 years ago
  16. blockcolder Group Title
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    Wow. O_O

    • 2 years ago
  17. Ishaan94 Group Title
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    \[\large\frac{1+\frac1{x^2}}{x^2 + \frac{1}{x^2}} = \frac{1 + \frac1{x^2}}{\left(x -\frac{1}x\right)^2+2}\]

    • 2 years ago
  18. Omniscience Group Title
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    Very nice Ishaan94; trig sub would work as well (: But that is easier.

    • 2 years ago
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