Given that \(\mathrm P(x)=(x-2)\sqrt{2x+1}\), find \(\dfrac{\mathrm dP}{\mathrm dx}\), giving your answer in the form \(\dfrac{ax-1}{\sqrt{2x+1}}\) where \(a\) is an integer.[3]
Hence find the value of \(\displaystyle\int_0^4\dfrac{6x-2}{\sqrt{2x+1}}\,\mathrm dx\).[3]
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