Evaluate int 2x 3 frac 1 2 delta x - JAMB Mathematics 2014 Question

(\int (2x + 3)^{\frac{1}{2}} \delta x)

let u = 2x + 3, (\frac{\delta y}{\delta x} = 2)

(\delta x = \frac{\delta u}{2})

Now (\int (2x + 3)^{\frac{1}{2}} \delta x = \int u^{\frac{1}{2}}.{\frac{\delta x}{2}})

( = \frac{1}{2} \int u^{\frac{1}{2}} \delta u)

( = \frac{1}{2} u^{\frac{3}{2}} \times \frac{2}{3} + k)

( = \frac{1}{3} u^{\frac{3}{2}} + k)

( = \frac{1}{3} (2x + 3)^{\frac{3}{2}} + k)