Question

How do you find the antiderivative of `(x^(3) + 2x)/(x^(4) + 4x^(2) +2)`?

Answer 1

`int(x^3+2x)/(x^4+4x^2+2)dx=1/4ln|x^4+4x^2+2|+c`

Explanation:

Here,

`I=int(x^3+2x)/(x^4+4x^2+2)dx`

`=1/4int(4x^3+8x)/(x^4+4x^2+2)dx`

`=1/4int(d(x^4+4x^2+2))/(x^4+4x^2+2)dx`

`=1/4ln|x^4+4x^2+2|+c`