MHB Confused about Laplace and Inverse Laplace Transform of Various Functions?

[kJS]

Hi.
I`m new here and I need some help with Inverse Laplace Transform: f(t)=5+3t+e^3t g(t)=(t+1)u(t-2) g(t)=(t^2-9t+20)u(t-5) and Laplace Transform: F(s)=1/(s+2)^5 F(s)= 2s^2+10/s(s^2+2s+10) G(S)=2s/s^2+4e^-sso if anywone can please help me:)

 

[Ackbach]

It's a little unclear what you're asking. Usually, $t$ is the time-domain variable, and you'd usually take the Laplace Transform to get to the $s$ domain. Conversely, you usually take the Inverse Laplace Transform to get from the $s$ domain to the $t$ domain. Your formatting is also difficult to read. Are you trying to take the Laplace Transform of the following functions?
\begin{align*}
f(t)&=5+3t+e^{3t}, \\
g(t)&=(t+1) \, u(t-2), \; \text{and} \\
g(t)&=(t^2-9t+20) \, u(t-5)?
\end{align*}

And are you trying to compute the Inverse Laplace Transform of
\begin{align*}
F(s)&=\frac{1}{(s+2)^5}, \\
F(s)&= \frac{2s^2+10}{s(s^2+2s+10)}, \; \text{and} \\
G(s)&=\frac{2s}{s^2+4e^{-s}}?
\end{align*}