solve-this-complex-integral-e-it-1-t-2-dt-

Question Number 75721 by Gazella thomsonii last updated on 15/Dec/19

solve this complex integral \int_{- \infty}^{+ \infty} \frac{e^{i t}}{\sqrt{1 + t^{2}}} d t

Commented by MJS last updated on 15/Dec/19

\underset{- \infty}{\int^{\infty}} \frac{e^{i t}}{\sqrt{t^{2} + 1}} d t = 2 \underset{0}{\int^{\infty}} \frac{\cos t}{\sqrt{t^{2} + 1}} d t + i \underset{- \infty}{\int^{\infty}} \frac{\sin t}{\sqrt{t^{2} + 1}} d t =

= 2 \underset{0}{\int^{\infty}} \frac{\cos t}{\sqrt{t^{2} + 1}} d t

but I cannot solve this \dots

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