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.