Integral of dx/Sqrt[exp(-x)+x+c]

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Discussion Overview

The discussion revolves around the possibility of finding the anti-derivative of the function 1/Sqrt[exp(-x)+x+c] with respect to x. Participants explore various mathematical techniques, including residue theory and conformal mapping, in the context of this integral.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant questions the feasibility of finding the anti-derivative of 1/Sqrt[exp(-x)+x+c] and notes that Mathematica was unable to compute it.
  • Another participant suggests that residue theory is typically used for infinite integrals or specific ranges, indicating uncertainty about its applicability for general anti-derivatives.
  • A different participant proposes the idea of transforming the problem into a definite integral from xa to xb.
  • Another suggestion involves applying conformal mapping to convert the integral into a form suitable for infinite integration.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the methods for addressing the integral, with multiple competing views and approaches presented.

Contextual Notes

The discussion highlights limitations regarding the applicability of residue theory and the potential need for transformations to evaluate the integral, but these aspects remain unresolved.

nassboy
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Does anybody know if it is possible to find the anti-derivative of 1/Sqrt[exp(-x)+x+c] with respect to x. Mathematica was unable to compute it. Would it be possible to convert it into a form where residue theory is applicable?
 
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Residue theory is usually only good for computing infinite integrals, or integrals from 0 to 2pi. I'm not aware of any way to compute a general anti-derivative using it
 
What if I made it a definite integral...and integrated from xa to xb.
 
and then apply some sort of conformal mapping to change it to an infinite integral
 

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