Q$5$:

Recalling the Fourier transform pair

$f(t)=\{\begin{array}{cc}{e}^{-2t},& t>0\\ e^{2t},& t<mn>0</mn>\\ F()=\frac{4}{4+{}^2}\\ ?\end{array}$

obtain the Fourier transforms of

$($a$)g(t)=\frac{1}{4+t^2}$

$($b$)h(t)=\frac{1}{4+t^2}cos2t.$