2.73: Integration from a second derivative

0606/23/O/N/18 — Question 4 · 6 marks

It is given that d2ydx2=2x+3(x+1)4\dfrac{\mathrm{d}^{2}y}{\mathrm{d}x^{2}} = 2x + \dfrac{3}{(x+1)^{4}}.
(i)
Find dydx\dfrac{\mathrm{d}y}{\mathrm{d}x}, given that dydx=1\dfrac{\mathrm{d}y}{\mathrm{d}x} = 1 when x=1x = 1.
[3]
(ii)
Find yy in terms of xx, given that y=3y = 3 when x=1x = 1.
[3]