The value of ${\int }_{-\frac{1}{\sqrt{2}}}^{\frac{1}{\sqrt{2}}}{\left({\left(\frac{x+1}{x-1}\right)}^{2}+{\left(\frac{x-1}{x+1}\right)}^{2}-2\right)}^{1/2}dx$ is: [JEE Main 2021, 26 Aug (Shift 1)]

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The value of \({\int }_{-\frac{1}{\sqrt{2}}}^{\frac{1}{\sqrt{2}}}{\left({\left(\frac{x+1}{x-1}\right)}^{2}+{\left(\frac{…

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