the solution for an integral including exponential integral function

Question

I have the following integral

$$\int_c^\infty{x^{a-1} e^{\ p \ x} \ \mathrm{Ei}(-p\ x) \ \mathrm{d}x}.$$

I'd like you to help me to evaluate it or giving me a hint to proceed.

Answer 1

$$\int{x^{a-1} e^{\ p \ x} \ \mathrm{Ei}(-p\ x) \ \mathrm{d}x}=-p^{-a}\,G_{2,3}^{2,2}\left(p\,x\,\left|\begin{array}{c}1,a\\a,a,0\\\end{array}\right.\right),$$ where $G_{2,3}^{2,2}\left(z\,\left|\begin{array}{c}\dots\\\dots\\\end{array}\right.\right)$ is the Meijer G-Function.