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VTRMC 2018 Problem 1

    It is known that ∫12x−1arctan⁡(1+x) dx=qπln⁡(2)\int_1^2x^{-1}\arctan (1+x)\ dx = q\pi\ln(2) for some rational number q.q. Determine q.q. Here, 0≤arctan⁡(x)<π20\leq\arctan(x)<\frac{\pi}{2} for 0≤x<∞.0\leq x <\infty.

    Dataset text AI-MO AoPS. Quoted with source.

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