I've understood that, to find the transfer function of a system, given its weight function, Laplace transform should be used.
I.e. if $$w(t)=50\,\cdot(e^{-5t}\,-\,e^{-10t})\,\cdot\,u(t)$$ then
$$W(s) = \int\limits_0^\infty w(t)\,e^{-st}\:dt$$
How is this solved further? I understand that w(t) is inserted into the formula for the transfer function W(s), but cannot obtain the correct answer through sequential math steps.
The final answer should be:
$$ W(s) = \frac{5}{(1+0.2s)(1+0.1s)}$$