Question

How do you integrate by substitution `int root3(1-2x^2)(-4x)dx`?

Answer 1

`= 3/4 (1- 2x^2)^(4/3) + C`

Explanation:

let `y = 1- 2x^2, dy = color(red)((- 4x) dx)`

`int root3(1-2x^2)color(red)((-4x) dx)`

`= int root3y \ color(red)(dy)`

`= int y^(1/3) \ color(red)(dy)`

`= (3 y^(4/3))/4 + C`

`= 3/4 (1- 2x^2)^(4/3) + C`