2024 ACJC H1 Q4

The curve \(C\) has equation \(y = -\ln(x + 1) + \frac{5}{x - 2} + 2\).

1. Show that curve \(C\) has no stationary points.[3]
2. Sketch the graph of \(C\), stating the \(x\)-coordinates of any points of intersection with the \(x\)-axes and the equation(s) of any asymptotes.[3]
3. Find the numerical value of the area bounded by \(C\), the \(x\)-axis and the lines \(x = 3\) and \(x = 5\).[1]