Exponential integral Ei series

Theorem: The following formula holds: $$\mathrm{Ei}(x) = \gamma + \log x + \displaystyle\sum_{k=1}^{\infty} \dfrac{x^k}{kk!}; x>0,$$ where $\mathrm{Ei}$ denotes the exponential integral, $\log$ denotes the logarithm, and $\gamma$ denotes the Euler-Mascheroni constant.

Proof: █