Let , ( ) where

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

Let ∫0acot⁡−1(ex)+cot⁡−1(e−x)tan⁡−1a+tan⁡−1x⋅dxx2+1=πpln⁡q\int_0^a \frac{\cot^{-1}(e^x) + \cot^{-1}(e^{-x})}{\tan^{-1} a + \tan^{-1} x} \cdot \frac{dx}{x^2 + 1} = \frac{\pi}{p} \ln q, (a>0a > 0) where p,q∈Np, q \in \mathbb{N}, then find the minimum value of (p+q)(p + q).

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