I'm doing my thesis on a math-heavy topic (Telecommunication engineering ftw) and got stuck with this integral: $\mathbf{\mathcal{R}_{1}}=\int_{0}^{\beta}\frac{e^{-2^{C_{0}}\zeta x}e^{-\frac{\tau x}{\beta -x}}}{x+\sigma}dx$
Is there any clue? I have an intuition that the result will be something that has Ei(x) in it.
p.s: I have rewritten the integral into more readable format (grouped constants)
$\int_{0}^{\beta}\frac{e^{-A x}e^{-\frac{\tau x}{\beta -x}}}{x+\sigma}dx$