Limit to Infinity of Exponential Integral Function

Theorem
Let $\Ei: \R_{>0} \to \R$ denote the exponential integral function:


 * $\map \Ei x = \ds \int_{t \mathop = x}^{t \mathop \to +\infty} \frac {e^{-t} } t \rd t$

Then:
 * $\ds \lim_{x \mathop \to \infty} \map \Ei x = 0$