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
 

FAQ: Integration Help Needed: How to Solve This Messy Fraction?

What is hard integration?

Hard integration is a process in science that involves combining multiple pieces of data or information from different sources into a cohesive whole. It is often used in fields such as genetics, neuroscience, and computer science.

Why is hard integration important?

Hard integration allows scientists to gain a better understanding of complex systems by combining different types of data or information. It can also lead to new insights and discoveries that may not have been possible with just one type of data.

What are some common challenges in hard integration?

Some common challenges in hard integration include dealing with data from different sources that may use different formats or units of measurement, addressing conflicting or incomplete information, and ensuring that the integration process does not introduce bias or errors.

How is hard integration different from other types of data integration?

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What are some tools and methods used in hard integration?

Some common tools and methods used in hard integration include machine learning algorithms, statistical modeling, data fusion techniques, and ontologies. These tools and methods help to automate the integration process and ensure accuracy and consistency in the final results.

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