Question

How do you integrate `(x + 2)^2 / x^(1/3)`?

Answer 1

Expand and integrate term by term.

Explanation:

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

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

`= x^(5/3)+4x^(2/3)+4x^(-1/3)`

`int (x+2)^2/x^(1/3) dx = int (x^(5/3)+4x^(2/3)+4x^(-1/3)) dx`

`= 3/8x^(8/3)+ 4* 3/5 x^(5/3) +4 (3/2)x^(2/3) +C`

Simplify as desired.