Quote:
Originally Posted by Primeinator
Apparently I am rusty on my calculus as well. I have been through all the basic calculus classes (13) but I cannot seem to remember how to integrate that before you plug in your bounds. It is not possible to make a usubstitution either of u=log x or 1/log x... The only thing I can think of is integration by parts  tabular method but I do not see how this would work when you have one term that will never differentiate to zero. Dr. Silverman, how did you get this answer?

Your thinking is correct......
Integration by parts combined with the definition of li(x).
[li(x) is not an elementary function]