JAMB Mathematics 2022 Paper

Question : 14

Total: 39

^3

Solution:

Concept:

Use the reversal of the chain rule for integration.

Explanation:

Let

u = 2x + 1

, so

du = 2\,dx

, which gives

dx = \frac{du}{2}

Substitute into the integral:

\int (2x+1)^3 dx = \int u^3 \cdot \frac{du}{2}

Factor out the constant:

\frac{1}{2} \int u^3 du

Integrate using the power rule:

\frac{1}{2} \cdot \frac{u^{4}}{4} = \frac{u^{4}}{8}

Replace

u

with

2x+1

and add the constant:

\frac{(2x+1)^4}{8} + C

Answer:

\frac{(2x+1)^4}{8} + C

This matches option B.

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