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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
.
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