How do i find the lapalace transorm of this intergral using the convolution theorem? $$\int_0^{t} e^{-x}\cos x \, dx$$
In the book, the $x$ is written as the greek letter "tau". Anyway, I'm confused about how to deal with this problem because the $f(t)$ is clearly $\cos t$, but $g(t)$ is not clear to me. 
Please help. 

So the transform becomes $\frac{s}{s^2 + 1} \frac{1}{s-1}$ with the shift $s+1$. 
