You may use substitution as alternative method, hence you should come up with the notation `5 + 6x = y` .

Differentiating `5 + 6x = y` yields:

`6dx = dy =gt dx = dy/6`

You need to change the variable under integral such that:

`int (5+6x)^2 dx = int (t^2)(dy/6)`

`int (t^2)(dy/6) = (1/6)*(t^3)/3 + c`

`int (t^2)(dy/6) = t^3/18 + c`

`int (5+6x)^2 dx = ((5+6x)^3)/18 + c`

**Hence, evaluating the integral yields `int (5+6x)^2 dx =
((5+6x)^3)/18 + c.`**

The anti derivative of (5 + 6x)^2 has to be determined.

`int (5 + 6x)^2 dx`

=> `int 25 + 36x^2 + 60x dx`

=> `25x + 36x^3/3 + 60x^2/2`

=> `25x + 12x^3 + 30x^2`

**The anti derivative of `(5 + 6x)^2` is** `12x^3 + 30x^2 + 25x
+ C`

## See eNotes Ad-Free

Start your **48-hour free trial** to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Already a member? Log in here.