A calculus problem by Saarthak Marathe

Calculus Level 5

\[\large \displaystyle I= \int^{1}_{0} \dfrac { \tan^{-1}(\sqrt{2+x^2})}{(1+x^2)\sqrt{2+x^2}} \,dx \]

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

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

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