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…

Mathematics

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 equals to a. 4 b. 8 c. 16 d. 32

Browse the problem library