Evaluate the following integrals:
To Find :
Now, let 4x + 1 be written as 2(2x - 1) + 3 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