Respuesta :

Answer:

Step-by-step explanation:

To find Laplace transform of [tex]t^2e^4^t[/tex]

We know that Laplace transform for

[tex]t^n e^{at}[/tex] is

[tex]\frac{n!}{(s-a)^{n+1} }[/tex], for all n = 1,2,3.... and real values a..

Here n =2 and a=4

Hence substituting we get

Laplace transform of given term is

[tex]\frac{2!}{(s-4)^{2+1} } \\=\frac{2}{(s-4)^3}[/tex]