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

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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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