Calculate the integral of a $x!$

Question

How I can calculate this integral:

$$ \int_{-\infty}^{+\infty} \frac{\mu^x}{x!} dx$$

where $\mu$ is a constant number?

I tried to solve it using:

Gamma function of Euler

$\Gamma(x + 1) = x!$

But using this method I couldn't continue

Answer 1

It diverges. As $x\to-\infty$, the integrand grows without bound, regardless of $\mu$.