Find the Laplace transform for each of the following signals:
(a) x(t)=2u(t)+4δ(t)−6e−³ᵗu(t)
(b) x(t)=te−⁴ᵗcos(t)u(t)
(c) x(t)=(e−⁶ᵗ+e−⁵ᵗsin(4t))u(t)
(d) x(t)=2 for 1≤t≤3;x(t)=0 otherwise
(e) x(t)=t for 0≤1≤1;x(t)=2−t for 1≤1≤2;x(t)=0 otherwise
(f) x(t)=te−⁴ᵗsin(α/2t)δ(t−1)