Essentially I am trying to compute the following integral:
$\int_{-\infty}^{\infty} e^{x(t-\lambda)} dx $ and I arrive at $\left[\frac{\lambda e^{x(t-\lambda)}}{t-\lambda}\right]^\infty_{-\infty}$
And this should equal to $\frac{\lambda}{\lambda-t}$ but I can't really understand why.
I can understand at least when the limit is $-\infty$, why it would equal $0$. But when the limit is $\infty$ how do we get any answer that is not $\infty$.
Any insight is appreciated.