AQA A Level Maths: Pure复习笔记8.2.9 Integration using Partial Fractions

What are Partial Fractions?

• This is the reverse process to adding (or subtracting) fractions
  • The common polynomial denominator is split into factors
• Make sure you are familiar with the notes on Partial Fractions

How do I integrate using partial fractions?

• Fractions with linear denominators can be integrated (See Integrating Other Functions)

• A fraction with a polynomial denominator (degree 2+) can be integrated by …
  • … splitting using partial fractions
  • … integrating each partial fraction

• STEP 1: Factorise denominator, if needed
• STEP 2: Express as partial fractions
• STEP 3: ‘Adjust’ and ‘compensate’ each term so it can be integrated (See Reverse Chain Rule)
• STEP 4: Integrate each term (usually involves ln) and simplify