If is equal to

MATHEMATICS · Single correct · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

If lim⁡a→∞1a∫0∞x2+ax+11+x4⋅tan⁡−1(1x) dx\lim_{a \to \infty} \frac{1}{a}\int_{0}^{\infty}\frac{x^2+ax+1}{1+x^4}\cdot\tan^{-1}\left(\frac{1}{x}\right)\,dx is equal to π2k\frac{\pi^2}{k}, where k∈Nk\in\mathbb{N}, then kk is (1) 4 (2) 8 (3) 16 (4) 32

Related theory

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