Your notation is a little confused for the limit. However, 1/ln(2) is the correct answer. Certainly, your setup looks fine.
For the integral:
Using the substitution:
I am getting the following for my new terminals:
To get my new terminals I have simply plugged the values of my old terminals into my u substitution (u=lnx).
When I evaluate the integral I wind up with a limit that needs to be evaluated, as follows:
When I evaluate that I come up with:
Have I done something wrong here?
I tried to correct that last line, but somehow wound up making creating a double thread. I am not coming up with 1/ln(2). I am coming up with 1/ln(-ln(2)). I know that isn't right.
Can you tell me where I am going wrong?
Oh... and I did mean to say "add up the fractions" not "add up the constants".