Suppose we have a real-valued function $g \colon \mathbb{R} \to \mathbb{R}$ (here, assume that we do not know the closed-form of $g$), and define its composition function $f$ by $f(x) := \exp (g(x))$.
Let $\mu$ be the standard normal distribution.
Is it possible to get an analytical form of the integration $\int f(x) \mu(\mathrm{d}x)$? If so, how to reach that?