How do I perform this logarithmic integral?

Use integration by parts.

hint: [imath]\displaystyle \int u \ dv = uv - \int v \ du[/imath]
 
Have you used the "hints" provided in the problem statement (u = x and dv = e^x dx) !

What did you get?

Did you follow the advice provided in response #2?

Please show us what you have tried and exactly where you are stuck.

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