substitute ...
Why would you want to "modify" a number? And why did you not answer my questions?
Your original integral was and skeeter suggested that you make the substitution u= ln(x) so that du= (1/x)dx.
So
You should know that no such substitution will "move" dx into the denominator. There simply is no such thing as " "!
NO! All that is happening is 1/2 is being taken out of the integral as a factor. It is NOT a part of the substitution!
Well your book is clearly wrong. What do you get if you differentiate 2 ln(x) ? You should get 2/x, which is clearly not the same as your integrand...
The book says the answer is , though ???