A calculus problem by Saarthak Marathe

Calculus Level 5

I=01tan1(2+x2)(1+x2)2+x2dx\large \displaystyle I= \int^{1}_{0} \dfrac { \tan^{-1}(\sqrt{2+x^2})}{(1+x^2)\sqrt{2+x^2}} \,dx

Find the value of 1000I\lfloor{1000I}\rfloor.

Notation: \lfloor{\cdot}\rfloor denotes the floor function (greatest integer function).

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