Who's up to the challenge? 2

Calculus Level 4

\[ \int _{ 1 }^{ 2 }{ \frac { dx }{ 5{ x }^{ 2 }+2x+5 } } = \frac { 1 }{ c\sqrt { d } } \text{ arccot} \left(a\sqrt { \frac { b }{ c } } \right) \]

If \(a,b,c\) and \(d\) are positive integers that satisfy the equation above, with \(b,c\) coprime, find \(a+b+c+d\).

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