Let \(L\) be the length of the curve \(\displaystyle{y = \frac{1}{4}{x}^2 - \frac{1}{2} \ln x }\) for \(4 \leq x \leq 8.\) If \[L = a+\frac{1}{2}\ln{b} ,\] where \(a\) and \(b\) are positive integers, what is the value of \(a+b?\)

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