GATE EC 2022: Fourier Transform of t/(1+t^2)^2

EC > GATE 2022 > Fourier Transform

The Fourier transform X(jω) of the signal
x(t) = t/(1 + t²)²
is _______

π/(2j) ωe^−|ω|

π/2 ωe^−|ω|

π/(2j) e^−|ω|

π/2 e^−|ω|

Correct : π/(2j) ωe^−|ω|

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