The maximum possible integral value of

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

The maximum possible integral value of tan⁡−1β−tan⁡−1αβ−α\dfrac{\tan^{-1}\beta-\tan^{-1}\alpha}{\beta-\alpha}, where 0<α<β<30<\alpha<\beta<\sqrt{3}, is

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