Page 2: Advanced Integration Techniques

This page focuses on more complex integration problems commonly found in AQA A Level Maths exam questions by topic. It demonstrates various techniques for handling complicated integrals.

Definition: Partial fractions is a method used to break down complex rational expressions into simpler terms for integration.

Example: For expressions like (2x+1)/(1-3x), using substitution u = 2x+1 simplifies the integration process.

Highlight: When dealing with products of sine and cosine with the same coefficient, double angle formulas should be employed.

Vocabulary: Reverse chain rule - a technique used when integrating expressions of the form kf'(x)/f(x)

The page extensively covers:

• Integration of products involving trigonometric functions
• Handling rational functions through partial fractions
• Complex substitution methods
• Algebraic division techniques before integration

Page 1: Integration of Basic Functions

This page presents fundamental integration rules for trigonometric, exponential, and logarithmic functions essential for A Level Maths topics. The content systematically outlines standard integration results and special cases.

Definition: Standard results are fundamental integration formulas that form the basis of more complex integration problems.

Example: For sin²x and cos²x integration, the double angle formula is used: cos 2x = 1 - 2sin²x

Highlight: The formula booklet contains many standard results, but some key integrations like ex and ax must be memorized.

Vocabulary: IBP (Integration By Parts) - a technique used for integrating products of functions

The page covers essential formulas including:

• Trigonometric functions and their squares
• Exponential and logarithmic functions
• Special identities like 1 + tan²x = sec²x