Now Here are few examples for you. If You Have any confusion regarding them you can comment below. So I will help you out. Thanks Example No. 1 Integrate . Solution:- Let
and
So That
and .
Therefore:
.
Example No. 2 Integrate . Solution: Let
and
so that
and .
Therefore,
.
Example No. 3
Integrate . Solution: Let
and
so that
and .
Therefore,
.
Example No. 4
Integrate Solution: Let
and
so that
and .
Therefore,
.
Example No. 5
Integrate Solution: Let and so that
and .
Therefore,
.
Example No. 6
Integrate Solution: Let
and
so that (Don't forget to use the chain rule when differentiating .)
and .
Therefore,
.
Now use u-substitution. Let
so that
,
or
.
Then
+ C
+ C
+ C .
Example No. 7
Integrate . Solution: Let
and
so that
and .
Therefore,
.
Example No. 8
Integrate Solution: Let
and
so that
and .
Therefore,
(Add in the numerator. This will replicate the denominator and allow us to split the function into two parts.)
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