Inverse Laplace Transform of $\frac{s^2+2s+2}{s+1}$

Question

I want detailed steps of this if anyone can help.

Answer 1

$$\frac{s^2+2s+2}{s+1}=\frac{(s+1)^2+1}{s+1}=s+1+\frac1{s+1}$$

Now, can you set the proper value of $a$ in $$L\{e^{at}\}=\frac1{s-a}$$

Set $c=0$ in $$L\{\delta(t-c)\}=e^{-cs}$$

Finally use Finding the inverse laplace transform of $s$

Answer 2

Hint: $$\frac{s^2 + 2s + 2}{s + 1} = \frac{(s + 1)^2 + 1}{s + 1} = s + 1 + \frac{1}{s + 1}$$