Question

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

Answer 1

Recall that

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

Then

$F(s)=\dfrac2{(s-5)^3}+\dfrac4{(s-5)^2}+\dfrac7{s-5}$