ENGR201 Laplace deck example, partial fractions with a repeated pole (ENGR5001)

ENGR201 Laplace deck example, partial fractions with a repeated poleTutorialOld spec ENGR2012:28 min

Find $\mathcal{L}^{-1}[X(s)]$ for $X(s) = \frac{s^2 + 3s + 4}{(s + 1)^3}$ and evaluate the result at $t = 1$ .

Formulas you may need

Repeated factor $(s + 1)^3$ : terms $\dfrac{A}{s + 1} + \dfrac{B}{(s + 1)^2} + \dfrac{C}{(s + 1)^3}$ (learn this)
$\mathcal{L}^{-1}\left[\dfrac{n!}{(s - a)^{n+1}}\right] = t^ne^{at}$ (learn this)

A =

B =

C =

x(1) =