Evaluate the following integrals:
To Find :
Now, let be written as (2x – 4) -1 and split
Therefore ,
=
=
Now solving,
Let = u dx =
Thus, becomes
Now , = = =
=
Now solving,
=
=
Let x – 2 = y dx = dy
Then becomes
Formula Used: = log |x +|+ C
Since is in the form of with change in variable.
Hence = log |y +|+ C
= log |y +|+ C
Now, since x – 2 = y and dx = dy
= log |(x-2) +|+ C
Hence = log |(x-2) +|+ C
Therefore , =
log |(x-2) +|+ C
=
log |x - 2 +|+ C