Identify the integral expression.

The integral to evaluate is given as:

The differential $dx$ indicates that the integration is with respect to $x$.

Since $t$ is not the variable of integration $x$, $e^{-t}$ is considered a constant during this integration.

The integral of a constant $k$ with respect to $x$ is $kx + C$.
In this case, $k = e^{-t}$.

The final answer is $x e^{-t} + C$.