Quote:
Originally Posted by R.D. Silverman
Your thinking is correct......
Integration by parts combined with the definition of li(x).
[li(x) is not an elementary function]

Interesting. We never covered li(x) in Calc, but we did cover the sine integral in Ordinary Differential Equations (if you count doing one homework problem covering a topic). Looking it up, li(x) is dx/ln x whose domain depends upon the bounds of the integral. I assume that you let dv = 1/log x (easier to integrate) and u = 1/(log x)^2 when you did tabular integration by parts? However, I am not familiar with using this method when you have one term that will not differentiate to zero. How is it done when you have two transcendental functions? (A brief search on the internet was not very helpful regarding this).
I apologize, this is not my homework problem but I am always eager to learn something new