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Hard Integration

  1. May 4, 2015 #1
    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.
  2. jcsd
  3. May 4, 2015 #2
    Where did this show up? It doesn't appear to have an elementary antiderivative.
  4. May 4, 2015 #3
    http://www4f.wolframalpha.com/Calculate/MSP/MSP38391c8f64e86fd2d40600005d2f4cd39i0aef9c?MSPStoreType=image/gif&s=8&w=489.&h=88. [Broken]
    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?
    Last edited by a moderator: May 7, 2017
  5. May 6, 2015 #4


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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).
  6. May 6, 2015 #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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