What is a composite function?

• A?composite?function?involves one function being applied after another
• A composite function may be described as a “function of a function”

How do I integrate linear (ax+b) functions?

• All the above can be deduced using?reverse?chain?rule
  • However, spotting them can make solutions more efficient

What is reverse chain rule?

• The?Chain Rule?is a way of differentiating two (or more) functions
• Reverse?Chain?Rule?(RCR) refers to?integrating?by?inspection
  • spotting that chain rule would be used in the reverse (differentiating) process

How do I know when to use reverse chain rule?

• Reverse?chain?rule?is used when we have the?product?of a?composite?function?and the?derivative?of its?second?function
• Integration is trickier than differentiation; many of the shortcuts do not workHow do I integrate using reverse chain rule?

• If the product?can?be identified, the?integration?can be done “by?inspection”
  • there may be some “adjusting?and?compensating” to do
• Notice a lot of the "adjust?and?compensate?method” happens mentally
  • this is indicated in the steps below by quote marks

• Differentiation can be used as a means of checking the final answer
• After some practice, you may find Step 2 is not needed
  • Do use it on more awkward questions (negatives and fractions!)
• If the product?cannot?easily be identified, use?substitution

What is integration by substitution?

• When reverse chain rule is difficult to spot or awkward to use then?integration?by?substitution?can be used

How do I integrate using substitution?