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The value of the integral \({\int }_{1/2}^{2}\frac{{\tan }^{-1}x}{x}dx\) is equal to [JEE Main 2023, 29 Jan (Shift 2)]

Q1

The value of the integral \({\int }_{1/2}^{2}\frac{{\tan }^{-1}x}{x}dx\) is equal to

[JEE Main 2023, 29 Jan (Shift 2)]

a

\(\pi \log _e 2\)

b

\(\frac{1}{2} \log _e 2\)

c

\(\frac{\pi}{4} \log _e 2\)

d

\(\frac{\pi}{2} \log _e 2\)

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