Evaluate the following integrals:
To Find :
Now, let x + 2 be written as (2x + 1) +
and split
Therefore ,
=
=
Now solving,
Let = u
dx =
Thus, becomes
Now , =
=
) =
=
Now solving ,
Now, can be written as
i.e,
Here , let x + = y
dx = dy
Therefore, can be written as
Formula Used: =
log |x +
|+ C
Since is of the form
with change in variable.
=
log |y +
|+ C
= log |y +
|+ C
Since , x + = y and dx = dy
=
log |(x +
) +
|+C
Therefore,
=
log |x +
+
|+C
Hence ,
=
+
log |(x +
)+
|+C
Therefore , =
+
log |(x +
)+
|+C