Correct Answer: Option C

Explanation

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

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

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

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

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

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

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

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

There is an explanation video available below.

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