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