[20 pts] Derive the Laplace transforms F(s) of the following signals. You may use anyvalid method. v(t) = 2(t-1)u(t-1) + 4(2 t)u(t− 2) +2(t-3)u(t - 3) v(t) = 5u(t) - 2e-3tu(t) + 5e¹tu(t-3)4t v(t)=\cos \left(\omega_{0} t\right) u(t-T) \quad(T>0)