Can this tricky integral be solved in general?

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Discussion Overview

The discussion centers around the solvability of a specific integral involving the square root of a sum and a combination of polynomial and trigonometric functions. Participants explore whether this integral can be solved in a general form, considering various mathematical approaches.

Discussion Character

  • Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the general solvability of the integral presented.
  • Another participant expresses skepticism about the integral being solvable, suggesting that it likely cannot be solved in general.
  • A different participant proposes using Taylor series as an alternative approach to tackle the integral.
  • There is mention of the possibility of transforming the integral into a series of partial fractions, indicating a potential method for analysis.
  • A link to an external computational tool is provided for further exploration of the integral.

Areas of Agreement / Disagreement

Participants generally express doubt regarding the general solvability of the integral, but there are differing suggestions on how to approach the problem, indicating that multiple views remain on the best method to analyze it.

Contextual Notes

Participants do not provide specific assumptions or limitations regarding the integral's properties or the methods suggested, leaving some aspects of the discussion unresolved.

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[itex]\pi[\int \right[ \frac{\sqrt{x^2+1}}{x^4+sin(x)^2}\left]\;dx[/itex]

Is this soluble generally?
 
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Probably not.
 
hamster143 said:
Probably not.

Taylor series it is then.

It's easy to make into a series of partial fractions.
 
http://www.wolframalpha.com/input/?i=\int+sqrt(x^2%2B1)%2F(x^4%2Bsin(x)^2)+dx+
 

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