Level 3 Integration Walkthrough

2025 NCEA Level 3 Integration Question 2(a)

2025 Paper

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Question

\[ \text{Find } \int \frac{10}{(2x+1)^6}\,dx. \]

First walkthrough idea

Hint to try first

Rewrite the integrand as a power of \(2x+1\).

Step 1

Rewrite in power form

This exposes the reverse-chain-rule structure straight away.

Show the first step’s working

This exposes the reverse-chain-rule structure straight away.

Key result

\[ 10(2x+1)^{-6} \]

Walkthrough overview

What this question practises

This 2025 walkthrough is part of AS91579 — Apply integration methods in solving problems.

Method: Reverse chain rule integration of a linear power.

This is Question 2(a) from the 2025 NCEA Level 3 Integration paper for AS91579 — Apply integration methods in solving problems. Use the guided hints to practise the method before revealing the full working.

Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91579.

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Learning summary

Review the method, not only the answer

This walkthrough helps you practise reverse chain rule integration of a linear power. Use the hints to plan the method, then repeat the question without hints and check each step.

Common mistake to avoid

Do not stop after differentiating the outside function; include the derivative of the inside function as a factor.

Continue practising

← Question 1(e) Question 2(b) →