Q$1.$ For a signal $x(t),$ its Fourier transform is defined as follows:

$x(){\displaystyle \underset{-}{\overset{+}{}}}x(t)e^{-jt}dt$

$($i$)$ Use the above definition to find $x()$ when:

$x(t)=cos(5t)e^{-2t}u(t)$

$($ii$)$ sketch the magnitude and the phase of $x()$ as a function of $($include both positive and negative frequencies$)$