Question

Where does the 1/12 come from in this solution?

Answer 1

`du=12x^2 dx`

Explanation:

`3intx^2/sqrt(4x^3-5) dx`

Let `u = 4x^3-5`, then the differential of `u`,

`du`, is `du=12x^2 dx`

So our integral is

`3int1/sqrt(4x^3-5) (12x^2)/12dx`

`= 3int1/(12sqrt(underbrace(4x^3-5)_u)) underbrace((12x^2)dx)_(du)`

`= 3 int 1/(12sqrtu) du`