Lets start by understanding that this method of integration comes from the rule chain method for example,
(1)
lets integrate both sides of equation 1
we can use the substitution
working with
(2)
then
we make the substitution on the integral and get,
by the fundamental theorem of calcules we get
we use equation (2) and get that
Example #1
Solve the integral
We choose
and
we change the integral to
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