The value of

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The value of ∫010π[tan⁡−1x]dx\int_0^{10\pi}[\tan^{-1}x]dx, where [ ][\,] denotes the greatest integer function, is equal to (1) tan⁡1\tan1 (2) 10π10\pi (3) 10π−tan⁡110\pi-\tan1 (4) None of these

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