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

$$\mathrm{solve}\mathrm{this}\mathrm{complex}\mathrm{integral}{\int }_{-\mathrm{\infty }}^{+\mathrm{\infty }}\frac{e^{\mathit{i}t}}{\sqrt{1+t^2}}\mathrm{d}t$$

Commented by MJS last updated on 15/Dec/19

$$\underset{-\mathrm{\infty }}{\stackrel{\mathrm{\infty }}{\int }}\frac{{\mathrm{e}}^{\mathrm{i}t}}{\sqrt{t^2+1}}dt=2\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{\cos t}{\sqrt{t^2+1}}dt+\mathrm{i}\underset{-\mathrm{\infty }}{\stackrel{\mathrm{\infty }}{\int }}\frac{\sin t}{\sqrt{t^2+1}}dt=$$$$=2\underset{0}{\stackrel{\mathrm{\infty }}{\int }}\frac{\cos t}{\sqrt{t^2+1}}dt$$$$\mathrm{but}\mathrm{I}\mathrm{cannot}\mathrm{solve}\mathrm{this}...$$

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