# Is there an inverse chain rule for integration?

##### 1 Answer

#### Answer:

Integration by substitution is the inverse of differentiation using the chain rule.

#### Explanation:

Let

A different way to see this is to do n integration by substitution and then check the answer by differentiation.

**Example**

Let

Now, if we check our answer by differentiating, we will use the chain rule.

We could also write the integration using

With

# = int (g(x))^(1/2) g'(x)dx = 2/3(g(x))^(3/2)+C#

#= 2/3(x^3+7)^(3/2)+C#