Evaluate the following integrals:

To Find :

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

Therefore ,

=

= +

Now solving,

Let = u dx =

Thus,becomes

Now , = = ) =

=

Now solving,

can be written as

i.e,

let = y dx = dy

Therefore , becomes

Formula Used: = + + C

Since is of the form with change in variable .

Hence, = + + C

= + + C

Since , = y and dx = dy

Therefore,

= + + C

i.e, = + + C

hence ,

= + = + + + C