How can you define the exponential and logarithmic integrals in terms of the incomplete gamma function?

Question

https://www.wolframalpha.com/input/?i=gamma(0,x)

https://en.wikipedia.org/wiki/Exponential_integral

https://en.wikipedia.org/wiki/Logarithmic_integral_function

For the Euler integral definition, it seems reasonable that $Ei(x)$ and $Li(x)$ can be expressed in terms of the incomplete gamma function, but the engine result shows a more complicated expression that just either of those functions. How can you express only $Ei(x)$ and $Li(x)$ in terms of just the incomplete gamma function?