How can I proceed to resolve this integral?

$$ c_1\int_{-\infty}^{\infty}{\frac{\cos\left(x\tau\right)}{\left(1 + c_{2}\,x\right)^{\alpha}}}\, \,{\rm d}x $$ where $c_1, c_2$ are positive constants, and $\alpha \in \Bbb R$. and what is the asymptotic expansion of the integral for large $\tau$. Thank you.

  • $\begingroup$ Have a look to the accepted answer of: math.stackexchange.com/questions/895436/… (second addendum) $\endgroup$ – Dmoreno Aug 14 '14 at 23:24
  • $\begingroup$ @Dmoreno It is the same OP that accepted it. I am not sure if you (OP) was not sure about the answer? :/ $\endgroup$ – Chinny84 Aug 14 '14 at 23:30
  • $\begingroup$ Oh, I see it now. Maybe he's looking for a more detailed explanation. He should show us, by the way, what his efforts on the resolution of the problem are. $\endgroup$ – Dmoreno Aug 14 '14 at 23:37
  • $\begingroup$ I am searching an explanation or a way to resolve the problem :) and not a result. $\endgroup$ – Ahmed Abrous Aug 14 '14 at 23:44
  • $\begingroup$ Is it ok like that :) ? $\endgroup$ – Ahmed Abrous Aug 14 '14 at 23:48

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