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Homework Statement
∫ln(x+1)/(x+1)2dx from a=1, b=2
(Answer is -ln3/3+ln2/2+1/6)
Homework Equations
∫fdg=fg-∫gdf
The Attempt at a Solution
Let u = (x+1), du=dx
∫lnu/u2du
Let f=lnu , df = 1/udu, g=-1/u, dg=1/u2du
=-lnu/u+∫1/u2du
=[-lnu+1/u] 1->2
Using Fundamental Theorem of Calculus plug in a,b
=[-ln(2+1)/(2+1)-(-ln(1+1)/(1+1)]
=-ln3/3+ln2/2
What did I miss in order for me not to get 1/6 in the answer? Help would be great!
Thanks