Integration Help Needed: How to Solve This Messy Fraction?

In summary, the conversation is discussing a complicated integral and how to solve it. The integral is shown and one person asks for a hint or clarification on how to solve it. Another person suggests using the Wolfram tool but acknowledges that the answer may not be easy to obtain. Another person offers a comment on how to simplify the problem using algebra.
  • #1
basty
95
0
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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  • #2
Where did this show up? It doesn't appear to have an elementary antiderivative.
 
  • #3
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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  • #4
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).
 
  • #5
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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