Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to
1. $e^{e^{-x}}$
2. $e^{-e^{-x}}$
3. $e^{-e^{x}}$
4. $e^{-x}$