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Calculus Level 5

\[\int _{ 0 }^{ \infty }{ \left( 1-\dfrac { { x }^{ 2016 } }{ 2016+{ x }^{ 2016 } } \right) } \, dx\]

If the integral above can be expressed as \[ b^{-c/b} \pi \csc \dfrac\pi a \]

where \(a,b,c\) and \(d\) are positive integers with \(b,c\) coprime, find \(a+2b+c\).

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