Evaluate the following integrals:

To Find :

Now, let x be written as - (1 - 2x) and split

Therefore ,

=

= +

Now solving,

Let = u dx =

Thus,becomes

Now , = = ) =

=

Now solving,

can be written as

i.e, =

let 2x – 1 = y dx =

Therefore , becomes

Formula Used: = + + C

Since is of the form with change in variable .

Hence, = + + C

= + + C

Since , 2x – 1 = y and dx =

Therefore,

= + + C

i.e, = + + C

hence , = + = = + + + C