The diagram shows part of the curve \(y = 1 - \frac{4}{(2x+1)^2}\). The curve intersects the x-axis at \(A\). The normal to the curve at \(A\) intersects the y-axis at \(B\).

(i) Obtain expressions for \(\frac{dy}{dx}\) and \(\int y \, dx\).

(ii) Find the coordinates of \(B\).

(iii) Find, showing all necessary working, the area of the shaded region.