If \( f(x)=\int_{0}^{1} \frac{d t}{1+|x-t|}, x \in R \) \( \mathrm{...

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If \( f(x)=\int_{0}^{1} \frac{d t}{1+|x-t|}, x \in R \)
\( \mathrm{P} \)
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Which of the following is not true about \( f(x) \) ?
(1) \( f(x) \) is decreasing for \( x1 \)
(2) \( f(x) \) is increasing for \( x0 \)
(3) \( f(1)=\log _{e} 2 \)
(4) \( f(1 / 2)=\log _{e}(3 / 2) \)
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