If \( \lim _{a \rightarrow \infty} \frac{1}{a} \int_{0}^{\infty} \f...

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If \( \lim _{a \rightarrow \infty} \frac{1}{a} \int_{0}^{\infty} \frac{x^{2}+a x+1}{1+x^{4}} \cdot \tan ^{-1}\left(\frac{1}{x}\right) d x \) equal to \( \frac{\pi^{2}}{k} \)
\( \mathrm{P}^{17} \)
WV where \( k \in N \), then \( k \) equals to
(1) 4
(2) 8
\( (3)^{1} \quad 16 \)
(4) 32
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