Fourier transform

[salvomic]

there is a way to solve an integral like that in the attached image and to avoid the errors that Terminal shows?

the integral is a tentative to get Fourier transform of \( \frac{1}{1+t^{2}} \), that's \( \sqrt{\frac{\pi}{2}}e^{-|\omega|} \) ...

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Also, there is a way to solve laplace(\( \frac{1}{1+t^{2}} \), t, s) without getting "Limit: Max order reached or unable to make series expansion Error: Bad argument" error?