WAEC Further Mathematics 2023 Paper

$\int(2x + 1)^3 dx$

Using substitution method, Let $u = 2x + 1$

$\; \frac{du}{dx}=2 \Rightarrow du=2dx \Rightarrow dx=\; \frac{du}{2}$

=$\int\; \frac{u^3}{2} du = \; \frac{1}{2} \int u^3 du$

=$\; \frac{1}{2} \left( \; \frac{u^4}{4} \right) = \; \frac{u^4}{8}$

$\therefore \; \frac{1}{8} (2x + 1)^4 + k$