Ans: (B)
Hint \(: I=\int_{1 / 2014}^{2014} \frac{\tan ^{-1} x}{x} d x=\int_{2014}^{1 / 2014} \tan ^{-1} 1 / t \times t \times\left(-\frac{1}{t^{2}}\right) d t(\) put \(x=1 / t)\)
$$
=\int_{1 / 2014}^{2014} \frac{\cot ^{-1} t}{t} d t
$$
$$
\Rightarrow 2 l=\pi / 2 \int_{1 / 2014}^{2014} \frac{d x}{x} \Rightarrow I=\frac{\pi}{4} \times 2 \log 2014=\frac{\pi}{2} \log 2014
$$
