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The value of $\int_{- 1}^{3} [\tan^{- 1} (\frac{x}{x^{2} + 1}) + \tan^{- 1} (\frac{x^{2} + 1}{x})] dx$ is

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Correct option is A

∫−13 tan−1⁡xx2+1+tan−1⁡x2+1xdx=∫−13 tan−1⁡xx2+1+cot−1⁡xx2+1dx ∵tan−1⁡x=cot−1⁡1x=∫−13 π2dx=πx2−13=π2[3+1]=2π ∵tan−1⁡x+cot−1⁡x=π2

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The value of ∫−13 tan−1⁡xx2+1+tan−1⁡x2+1xdx is

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The value of $\int_{- 1}^{3} [\tan^{- 1} (\frac{x}{x^{2} + 1}) + \tan^{- 1} (\frac{x^{2} + 1}{x})] dx$ is