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The value of the integral \({\int }_{1}^{2}\left(\frac{{t}^{4}+1}{{t}^{6}+1}\right)dt\) is: [JEE Main 2023, 29 Jan (Shif…

Q1

The value of the integral \({\int }_{1}^{2}\left(\frac{{t}^{4}+1}{{t}^{6}+1}\right)dt\) is:

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

a

\({\tan }^{-1}\frac{1}{2}+\frac{1}{3}{\tan }^{-1}8-\frac{\pi }{3}\)

b

\({\tan }^{-1}2-\frac{1}{3}{\tan }^{-1}8+\frac{\pi }{3}\)

c

\({\tan }^{-1}2+\frac{1}{3}{\tan }^{-1}8-\frac{\pi }{3}\)

d

\({\tan }^{-1}\frac{1}{2}-\frac{1}{3}{\tan }^{-1}8+\frac{\pi }{3}\)

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