JAMB 2001 · UME · Q38

Evaluate $\displaystyle\int 2(2x - 3)^{\frac23}\,dx$ .

Worked solution (try it first)

Add one to the power: $\frac23 + 1 = \frac53$ .
Divide by the new power $\frac53$ and by 2, the derivative of $2x - 3$ .
So the integral is $2 \times \dfrac{(2x - 3)^{5/3}}{\frac53 \times 2} = \frac35(2x - 3)^{\frac53} + k$ , option D.