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Find the value of the following integral:
∫0∞1x(tan−1πx−tan−1x) dx. \displaystyle\int_{0}^{\infty} \dfrac{1}{x} \left(\tan^{-1} \pi x - \tan^{-1}x\right)\,dx.∫0∞x1(tan−1πx−tan−1x)dx.
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