If `f(x)=int(x^8+4)/(x^4-2x^2+2)dxa n df(0)=0,t h e n` `f(x)` is an odd function `f(x)` has range `R` `f(x)` has at least one real root `f(x)` is a monotonic function.

Options

A. `f(x)` is an odd function
B. `f(x)` has range R
C. `f(x)` has at least one real root
D. `f(x)` is a monotonic function

Answer

A, B, C, D

Explanation

`int ((x^(8)+4+4x^(4))-4x^(4))/(x^(4)-2x^(2)+2)dx`
`=int((x^(4)+2)^(2)-(2x^(2))^(2))/((x^(4)-2x^(2)+2))dx`
`=int((x^(4)+2-2x^(2))(x^(4)+2+2x^(2)))/((x^(4)-2x^(2)+2))dx`
`=(x^(5))/(5)+(2x^(3))/(3)+2x+C`