Find the inverse Laplace transform of the giveb function by using the convolution theorem.
$$F(x) = \frac{s}{(s+1)(s^2+4)}$$
If I use partial fractions I get: $$\frac{s+4}{5(s^2+4)} - \frac{1}{5(x+1)}$$
which gives me Laplace inverses:
$$\frac{1}{5}(\cos2t + \sin2t) -\frac{1}{5} e^{-t}$$
But the answer is: $$f(t) = \int^t_0 e^{-(t -\tau)}\cos(2\tau) d\tau$$
How did they get that?