I am trying to find a closed-form expression for the following integral:

with

Neither Maple nor Mathematica will give a ready answer.

If I put to 0, Maple gives me:

With Ei the exponential integral. This is Ok as far as it goes, but I need the integral for .

If I add to the function, Maple can no longer find the integral.

I tried taking the derivative of for clues, and that gives me , and the factor is not what I'm looking for; I need .

Any suggestions? Am I overlooking something obvious?