the Laplace transform of e^4t(cos 2t)??

Question

please i need help. thanks

Answer 1

first, there is s-shifting here since e^4t is multiplied to cos(2t).
from e^4t, we know that a = 4,, and that L{cos 2t} = s/(s^2 + 4) , therefore:
L{e^4t(cos 2t)} = (s-a)/((s-a)^2 + 4) = (s-4)/((s-4)^2 + 4)

so there,, :)

Answer 2

(3m − 2n)(3m + 4n)