While I am reading a article, I am stuck with some Lapalce transform.
Let $F(x(t),t)$ be two valued function.
Let's take the Laplace trasnform with resepct to $t$, then the paper says
$$ \int_0^\infty \exp(-\lambda t) F(x(t),t) dt = \widehat{F}(\widehat{x}(\lambda),\lambda) $$ where $\widehat{x}$ is the Laplace transform of function $x$ and $\widehat{F}(x,\lambda) = \int_0^\infty \exp(-\lambda t)F(x,t)dt$.
I can't understand why this relation is valid.