Year 13/A2 Pure Chapter 11.5 (Integration)

Following on from using u- substitutions to integrate functions of the type kf'(𝑥)[f(𝑥)]ⁿ and kf(a𝑥 + b), we now need to look at more complicated substitutions which are not so obvious. Such trickier substitutions tend to be explicitly given to you to use by the examiner, or you may encounter a question which demands an integral is solved using a substitution.

More often that not, with these substitutions, you will need to rewrite instances of the original variable in terms of the substituted variable.

This lesson is meant as preparation for Exercise 11E, page 307 of the Pearson Edexcel Pure Mathematics Year 2/A2 Textbook.

Introduction: 0:00

Solution to Warm-Up Q1: 1:32
Solution to Warm-Up Q2: 5:02
Solution to Warm-Up Q3: 8:52
Solution to Warm-Up Q4: 12:06

INTEGRATION BY SUBSTITUTION - PART II - SUBS PROVIDED

Introduction and explanation: 17:15

Worked Example 1a): 18:10
Worked Example 1b): 24:50

Worked Example 2: 31:18

A "Special" Substitution" - Introduction: 35:42
Worked Example 3: 36:22

INTEGRATION BY SUBSTITUTION - PART II - SUBS NOT PROVIDED

Introduction: 40:47

Worked Example 4a): 41:16
Worked Example 4b): 48:53

Suggested Exercises: 53:44