(Solved): 2. Using partial fraction expansion where required, find \( x(t) \) for a) \( X(s)=\frac{s(s+1)}{( ...

2. Using partial fraction expansion where required, find \( x(t) \) for a) \( X(s)=\frac{s(s+1)}{(s+2)(s+3)(s+4)} \) b) \( X(s)=\frac{s+1}{(s+2)(s+3)\left(s^{2}+4\right)} \) c) \( X(s)=\frac{s+4}{(s+1)^{2}} \) d) \( X(s)=\frac{1}{s^{2}+s+1} \) e) \( X(s)=\frac{s+1}{s(s+2)(s+3)} e^{-0.5 s} \)