Question

How do you integrate `((4x^2-1)^2)/x^3dx`?

Answer 1

`8x^2-8 ln x-1/(2x^2)+C`

Explanation:

`((4x^2-1)^2)/x^3 = (16x^4-8x^2+1)/x^3=16x-8/x+1/x^3`

Thus

`int ((4x^2-1)^2)/x^3dx = int (16x-8/x+1/x^3)dx`
`qquad = 8x^2-8 ln x-1/(2x^2)+C`