# AQA A Level Maths: Pure复习笔记8.2.6 Harder Substitution

### Harder Substitution

#### What is integration by substitution?

• Make sure you are familiar with Reverse Chain Rule and Substitution (RCR)
• In more difficult questions the substitution will be given to you

#### How do I integrate using a given substitution?

• The process is very much the same as before but expect the algebra to be trickier

• STEP 1: Differentiate the substitution and rearrange
• STEP 2: Replace all parts of the integral
• all x terms should be replaced with equivalent u terms, including dx
• if a definite integral change the limits from x to u too
• STEP 3: Integrate and either
• substitute x back in or
• evaluate the definite integral using the u limits
• STEP 4: Find c, the constant of integration, if needed