Reverse Chain Rule (CIE A Level Maths: Pure 1)

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)