\[\large \displaystyle \int _{ 0 }^{ 1 }{ \dfrac { \sin { (\tan ^{ -1 }{ x } )\sqrt { \cos ^{ 2 }{ (\tan ^{ -1 }{ x } ) } +4{ x }^{ 2 } } } }{ x } } \, dx\]

The integral shown above can be written as \(A-\dfrac { \pi }{ B }\), where \(A\) and \(B\) are integers. Find the value of \(A+B\).

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