Evaluating the integral of arctan from 0 to 1

[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).