I was calculating a characteristic function and I couldn't compute this integral: $$\int_{0}^{\infty} \frac{e^{itx}}{(1+x^{c})^{k+1}} \, \mathrm{d}x $$ Where $k,c>0$, any hint would be of great help.
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1$\int_0^\infty \frac{\cos(x)}{(1+x^2)^2} = \frac{\pi}{2 e} \approx $ Euler--Mascheroni constant – user66081 Aug 20 '16 at 22:36
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1Isn't the caracteristic function supposed to be a function of $t$? – Toney Shields Aug 20 '16 at 22:40
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1Have you tried contour integration? – Alex R. Aug 21 '16 at 00:43