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 \(10b+c\).
This is my original problem.
by
Surya Prakash