Valentine's Day! 2

Calculus Level 3

\[ \large \int_2^{14} \dfrac{1402}{x^2+16x+28} \, dx \]

If the integral above is equal to \( \dfrac ab \ln\left( \dfrac cd\right) \), where \(a,b,c\) and \(d\) are positive integers and \(\gcd(a,b) = \gcd(c,d) = 1\), find \(a+b+c+d\).

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