The diagram shows part of the curve \(y=\ln(2x+1)\) and the normal to the curve at the point \(P(2,\ln5)\).
Find the equation of the normal to the curve at \(P\), expressing your answer in the form \(y=mx+\ln k\), where \(m\) and \(k\) are constants to be found. Give \(k\) in exact form.[4]
Express \(x\) in terms of \(y\) for the curve.[1]
Hence find the area of the shaded region.[5]
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