# Inverse chain rule method

In

calculus, the

**inverse chain rule** is a method of

integrating a

function which relies on guessing the

integral of that

function, and then

differentiating back using the

chain rule. The method is a special case of

integration by substitution.

For example, suppose one wants to find the indefinite integral:

A first guess of the antiderivative might be:

treating (5

`x`+4) as if it were an

`x`. Differentiating back with the chain rule gives:

Hence, the initial guess was off by a factor of 5. Dividing by 5 gives:

This method can be used to find:

and

`g`(

`x`) is a

linear function.