(1997C, 2M)
$$ \begin{aligned} & \qquad \int _0^{\pi / 4} \log \frac{1+\tan x+1-\tan x}{1+\tan x} d x \ & \qquad I=\int _0^{\pi / 4} \log \frac{2}{1+\tan x} d x \Rightarrow I=\int _0^{\pi / 4} \log 2 d x-I \ & \Rightarrow \quad 2 I=\frac{\pi}{4} \log 2 \Rightarrow \quad I=\frac{\pi}{8}(\log 2) \ & \text {
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