II:$(50$ pts$)$ Find the appropriate transform or inverse:

$n{e}^{-j\frac{}{4}n}(\frac{1}{2}{)}^{n+3}u(n-3)+sin(5n^2)[u(n)-u(n-2)]$

$tcos(2t)rect(\frac{3t-4}{10})(F)$

$\frac{e^{-j6t}cos(2t-7)u(3t-7)}{t}(L)$

$\frac{e^{-j3}(j{)}^6(j+1)}{(2+j)(3+j{)}^2}$

$\frac{z^{-4}(z-1)}{(z-\frac{1}{2}{)}^2(z-\frac{1}{4})}+Ln(z^2-1)$

$-\frac{d}{ds}(\frac{s^5{e}^{-4s}(s+3)}{(s^2+10s+29)(s+2)})$