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