Integration Help Needed: How to Solve This Messy Fraction?

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    Hard Integration
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Discussion Overview

The discussion revolves around the integration of a complex fractional expression involving a square root and polynomial terms. Participants are exploring methods to approach the integral, discussing its potential complexity and the existence of an elementary antiderivative.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant requests assistance with the integral, expressing uncertainty about how to begin.
  • Another participant notes that the integral does not seem to have an elementary antiderivative, suggesting it may be complex.
  • A third participant shares a link to Wolfram Alpha's output for the integral, indicating skepticism about finding a simpler solution or the possibility of an error in the problem statement.
  • One participant introduces a comment about the fourth root of -1, which may relate to complex numbers, but its relevance to the integral is unclear.
  • Another participant suggests that the problem could be approached through partial fraction decomposition, although they acknowledge the integral's complexity.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the integral, with some suggesting it may not have a straightforward solution while others propose methods to tackle it. No consensus is reached regarding the best approach or the correctness of the problem statement.

Contextual Notes

Participants have not fully explored the assumptions or definitions underlying the integral, and there is uncertainty regarding the mathematical steps involved in the proposed methods.

basty
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Anyone know how to integrate this?

##\int{\frac{(1 + x^2)}{(1 - x^2)\sqrt{1 + x^4}}dx}##

Please give me a hint as I even don't know what to do.
 
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Where did this show up? It doesn't appear to have an elementary antiderivative.
 
http://www4f.wolframalpha.com/Calculate/MSP/MSP38391c8f64e86fd2d40600005d2f4cd39i0aef9c?MSPStoreType=image/gif&s=8&w=489.&h=88.
This is what Wolfram gives so I'm not even going to attempt. Surely there's an easier answer or maybe the problem was written down wrong?
 
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Just a quick comment: [itex]\sqrt[4]{-1}=e^{\frac{i\pi}{4}}=\frac{\sqrt{2}}{2}(1+i)[/itex] (and, of course, the three others).
 
i believe this is a partial fraction decomposition problem? It doesn't look nice and clean like other integrals but if you have a good understanding of algebra it is possible :p
 

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