Evaluate: (2x + 1)³ dx

Correct Answer is : 18(2x+1)4+k\; 1/8 (2x + 1)^4 + k81(2x+1)4+k

Correct Answer is : 18(2x+1)4+k\; 1/8 (2x + 1)^4 + k81(2x+1)4+k

Test Index

WAEC Further Mathematics 2023 Paper

Question : 26

Total: 40

Evaluate:

\int(2x + 1)^3 dx

Solution:

Concept:

Use the substitution method to integrate a power of a linear expression.

Explanation:

Let

u = 2x + 1

Then

\frac{du}{dx} = 2

, so

du = 2\,dx

and

dx = \frac{du}{2}

Substitute into the integral:

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

Now integrate:

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

Replace

u

with

2x+1

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

Answer:

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

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