How would one solve the following inverse Laplace transform?
$$\mathscr{L}_s^{-1}\left\{\frac{2s}{\left(s-1\right)^2+7}\right\}$$
I know from WolframAlpha that the answer is:
$$\frac{2 e^t \left[\sin(\sqrt{7} t)+\sqrt{7} \cos(\sqrt{7} t)\right]}{\sqrt{7}}$$
The transform is equal to $$\frac{2}{(s-1)^2+\sqrt{7}^2}+\frac{2(s-1)}{(s-1)^2+\sqrt{7}^2}$$ which turn into cosine and sine transforms combined with the first shift theorem.