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

Jun 23, 2018

$2 \arctan \left({x}^{2}\right) + c$

#### Explanation:

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

Use this immediate integral: $\int \frac{f ' \left(x\right)}{1 + {\left[f \left(x\right)\right]}^{2}} = \arctan \left[f \left(x\right)\right] + c$

Write your integral in this way: $2 \int \frac{2 x}{1 + {\left[\left({x}^{2}\right)\right]}^{2}}$

So the result is: $2 \arctan \left({x}^{2}\right) + c$