Please help me find the inverse Laplace transform of
$$F(s) = \dfrac{4}{(s^2+2s+5)^2}.$$
The answer I got is $\frac 1 5 (e^t - e^{-t}) \cos 2t - \frac 1 2 (e^t + e^{-t}) \sin 2t$.
I first applied the convolution theorem, then had to do integration by parts and the solution turned out to be too long is there any shorter solution for this problem, and is my answer correct??
Any help would be highly appreciated. Thanks.