Integration Help Needed: How to Solve This Messy Fraction?

[basty]

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.

 

[axmls]

Where did this show up? It doesn't appear to have an elementary antiderivative.

 

[leafjerky]

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?

 

[Svein]

Just a quick comment: $\sqrt[4]{-1}=e^{\frac{i\pi}{4}}=\frac{\sqrt{2}}{2}(1+i)$ (and, of course, the three others).

 

[Obliv]

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