\(\int (2x + 3)^{\frac{1}{2}} \delta x\) let u = 2x + 3, \(\frac{\delta y}{\delta x} = 2\) \(\delta x = \frac{\delta u}{2}\) Now \(\int (2x + 3)^{\frac{1}{2}} \delta x = \int u^{\frac{1}{2}}.{\frac{\delta x}{2}}\) \( = \frac{1}{2} \int u^{\frac{1}{2}} \delta u\) \( = \frac{1}{2} u^{\frac{3}{2}} \times \frac{2}{3} + k\) \( = \frac{1}{3} u^{\frac{3}{2}} + k\) \( = \frac{1}{3} (2x + 3)^{\frac{3}{2}} + k\)