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)