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VTRMC 2015 Problem 5

    Evaluate ∫0∞arctan⁡(πx)−arctan⁡(x)xdx\int^\infty_0\frac{\operatorname{arctan}(\pi x)-\operatorname{arctan}(x)}xdx (where 0≤arctan⁡(x)<π20\le\operatorname{arctan}(x)<\frac\pi2 for 0≤x<∞0\le x<\infty ).

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