Solving an integral using euler method Hy. Can someone please explain me how can I resolve $\int_{0}^{\infty} e^{-(sI-A)t}\,dt$ ? I must have the final result $(sI-A)^{-1}$. I think it has the euler form, for beta integral but I don't know how can I get to that result.

If you wrote the integral correctly, just use the fact that
$$\int e^{kt}=k^{-1}e^{kt}+C$$
where, of course, $k$ is a constant and $C$ is an arbitrary constant. There is no need for a fancy integral such as the beta integral. Finding the definite integral from that is easy, since the limit is easy.
All this, of course, depends on $s$, $I$, and $A$ being real or complex numbers.
