NECO 2022 · Paper 1 · Q60

Evaluate $\int 3\sqrt{x}\,dx$ .

Worked solution (try it first)

Write $3\sqrt{x}$ as $3x^{\frac{1}{2}}$ .
Add 1 to the power and divide by the new power: $3 \times \dfrac{x^{\frac{3}{2}}}{\frac{3}{2}} = 2x^{\frac{3}{2}}$ .
$x^{\frac{3}{2}} = \sqrt{x^3}$ , so the answer is $2\sqrt{x^3} + c$ , option C.