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?