Question

Integration of (x -1/x)^2 ?

Answer 1

`x^3/3-2x-1/x+C`

Explanation:

`I= int (x-1/x)^2dx`

Expand integrand

`I= int (x^2-2+1/x^2)dx`

Apply linearity

`I= int x^2 dx -int 2 dx +int 1/x^2dx`

Apply power rule to each term

`I = x^3/3 -2x - 1/x +C`