Perform the following indefinite integration.
Often, one writes the substitution as and
and attempts to write the integrand as
. One is then charged with
integrating
. We conclude that
.
Making the substitution
, so that
we have
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Writing
, we find
Thus,
Integrate:
Set . Then
.
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Integrate
Set
so that
.
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Integrate
Set
so that
.
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Integrate
Set
. Then
.
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Set
so that
.
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Why are these answers different?
So,
.