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Calculus Level 5

If, \[\int _{ 0 }^{ \infty }{ \frac { { x }^{ 1726 }+{ x }^{ 1725 }+{ x }^{ 1724 }+...+{ x }^{ 2 }+{ x }+1 }{ { x }^{ 1728 }+{ x }^{ 1727 }+{ x }^{ 1726 }+...+{ x }^{ 2 }+{ x }+1 } dx } =\frac { A\pi }{ B } \cot\left( \frac { \pi }{ C } \right) \]

\(A,B,C>0\) and \(gcd(A,B)=1\)

Find: \(A+B+C\)

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