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I=∫01tan−1(2+x2)(1+x2)2+x2 dx\large \displaystyle I= \int^{1}_{0} \dfrac { \tan^{-1}(\sqrt{2+x^2})}{(1+x^2)\sqrt{2+x^2}} \,dx I=∫01(1+x2)2+x2tan−1(2+x2)dx
Find the value of ⌊1000I⌋\lfloor{1000I}\rfloor⌊1000I⌋.
Notation: ⌊⋅⌋\lfloor{\cdot}\rfloor⌊⋅⌋ denotes the floor function (greatest integer function).
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