How do you integrate (ax + b)n?
- The reverse chain rule can be used for integrating functions in the form y = (ax + b)n
- Make sure you are confident using the chain rule to differentiate functions in the form y = (ax + b)n
- The reverse chain rule works backwards
- For n = 2 you will most likely expand the brackets and integrate each term separately
- If n > 2 this becomes time-consuming and if n is not a positive integer we need a different method completely
- To use the reverse chain rule (provided n is not -1)
- Raise the power of n by 1
- Divide by this new power
- Divide this whole function by the coefficient of x
- You can check your answer by differentiating it
- You should get the original function when you differentiate your answer
- Note that this method only works when the function in the brackets is linear (ax + b)
Make sure you can recognise when a question needs to use the reverse chain rule, it may not always be obvious.