WAEC 2023 · Paper 1 · Q34

Evaluate: $\displaystyle\int (2x + 1)^3\,dx$ .

Worked solution (try it first)

Raise the power by one and divide by the new power: $\dfrac{(2x + 1)^4}{4}$ .
Divide also by 2, the coefficient of $x$ inside the bracket: $\dfrac{(2x + 1)^4}{4 \times 2}$ .
So the integral is $\frac{1}{8}(2x + 1)^4 + k$ , option D.