Perform the following indefinite integration.
Often, one finds two functions and
so that the
integrand may be written as
where
.
If we succeed in so doing, then from the equality
If is easier to evaluate than is
, then the
method succeeds.
Take and
so that
and
. Then,
Integrate:
Take and
so that
and
.
Integrate
Set and
so that
and
.
Then
Set and
so that
and
.
Then
Substituting, we have
Adding
and dividing by
gives
Integrate
Set and
so that
and
.
Integrate
Note that
. Via the substitution
(with
) we find that
Set and
(so that
and
).