Been stuck on this for a while now and I have an exam tomorrow at 10am and I fear this might come up and it's only inverse laplace I can't do, this is my attempt at it but I know it's wrong..can anyone point me in the right direction? I'm replacing $s+1$ with $s$
$$L^{-1}\frac{(s+1)^{2}}{s^{3}}$$ $$L^{-1}\frac{s^{2}}{s^{3}}|s=s-1$$ $$L^{-1}\frac{1}{s}|s=s-1$$ $$e^{t}$$
You keep using this sloppy, confusing notation in multiple questions. Here you don't even want the substitution:
$$\frac{(s+1)^2}{s^3}=\frac{s^2+2s+1}{s^3}=\frac{1}{s}+\frac{2}{s^2}+\frac{1}{s^3}.$$
Now deal with the terms separately.