The following diagram shows part of the graph of \(y = \frac{x}{x^2 + 2}\) for \( x\geq 0\).
The shaded region \(R\) is bounded by the curve, the \(x\)-axis and the line \(x = c\).
The area of \(R\) is \(\ln{3}\).
Find the value of \(c\).[6]
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