Inspired by Karthik Sharma

Calculus Level 5

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

If the value of the integral above is of the form πbc\dfrac{\pi}{b\sqrt{c}}, where bb, cc are integers and cc is square-free, find the value of 10b+c10b+c.


This is my original problem.
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