Your original integral was and skeeter suggested that you make the substitution u= ln(x) so that du= (1/x)dx.
You should know that no such substitution will "move" dx into the denominator. There simply is no such thing as " "!
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 ???