CIE A Level Maths: Pure 1复习笔记6.1.4 Reverse Chain Rule

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

• 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)