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Calculus Level 5

\[\large \int _{ 0 }^{ 1 }{ \left( \frac { { \cot }^{ -1 }\left( \sqrt { { x }^{ 2 }+2 } \right) }{ \left( { x }^{ 2 }+1 \right) \left( \sqrt { { x }^{ 2 }+2 } \right) } \right) }dx \]

If the integral above equals to \(\dfrac { { \pi }^{ A } }{ B } \) for positive integers \(A\) and \(B\), find \(A+B\).

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