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Calculus Level 5

\[\large I = \int_{0}^{\infty}\dfrac{x \ln{(4x)}}{\frac{1}{4}x^{4}+x^{2}+1} \,dx\]

\(I\) is the value of the closed form of the above integral. What is the value of \(\lfloor 100I \rfloor\)?

You may use the fact that \(\ln(2) \approx 0.693147\).

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