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Calculus Level 5

I=0xln(4x)14x4+x2+1dx\large I = \int_{0}^{\infty}\dfrac{x \ln{(4x)}}{\frac{1}{4}x^{4}+x^{2}+1} \,dx

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

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

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