Approximation needed

Question

I need the approximation for following function $$f(x)=E_1(x)e^{x}$$ where $E_1(x)$ is the exponential integral. I know the following bounds on the above function (they are obtained from Abramovitz book) $$\frac{1}{2}\ln(1+\frac{2}{x})<e^{x}E_1(x)<\ln(1+\frac{1}{x})$$. Any help in this regard will be much appreciated. Thanks in advance.