Laplace transform of $(3e)^t\sin^2 t$

Question

The existence of Laplace Transform of $(3e)^t\sin^2 t$ exists but can you help me in finding the Laplace transform of this function?

Answer 1

HINT

Observe that

1. $3e=e^{\log 3+1}$, and then $(3e)^t=e^{at}$ with $a=\log 3+1$;
2. $\sin^2(t)=\frac{1}{2}\big[1-\cos (2t)\big]$