Question

Compute F(s), the Laplace transform of f(t) = e^(5t) (t^2 +4t +7)

Answer 1

Recall that

`\mathcal L_s\{t^ne^(ct)\}=(n!)/((s-c)^(n+1))`

Then

`F(s)=\frac2{(s-5)^3}+\frac4{(s-5)^2}+\frac7{s-5}`