Stuck on Last Step of an Integral: Need Help

[cahill8]

Homework Statement

I'm at the last step of an integral but can't seem to get the right answer.

Homework Equations

After many substitutions I finally have \int^1_0 arctan(w)dw which from wiki is a standard integral, =[w \text{ arctan}(w)-1/2 \text{ ln}|1+w^2|]^1_0

The Attempt at a Solution

Evaluating this:
=1*\text{ arctan}(1)-1/2 \text{ ln}|1+1^2|-0+1/2 \text{ ln}|1+0^2|
=\pi/4-1/2 \text{ ln}(2)+1/2 \text{ ln}|1|
=\pi/4-1/2 \text{ ln}(2)
=1/4(\pi-2\text{ ln}(2))

however, the answer is stated as:
1/4(\pi-\text{ ln}(4))

is there something I'm missing?

Thanks for any help

 

[Dick]

ln(4)=ln(2^2)=2*ln(2).