# Inspired by Karthik Sharma

Calculus Level 5

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

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

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