Question

How do you integrate `int(4x)/(x^4 +1)` using partial fractions?

Answer 1

`2arctan(x^2) +c`

Explanation:

I believe that you can't use partial fractions because `Delta<0` and you can't decompose the denominator

Use this immediate integral: `int(f'(x))/(1+[f(x)]^2) = arctan[f(x)] + c`

Write your integral in this way: `2int(2x)/(1+[(x^2)]^2)`

So the result is: `2arctan(x^2) +c`