Which methods to use to integrate $\int{\frac{x^4 + 1}{x^2 +1}}\, dx$ I have this integral to evaluate:
$$\int{\frac{x^4 + 1}{x^2 +1}}\, dx$$
I have tried substitution, trig identity and integration by parts but I'm just going round in circles. 
Can anyone explain the method I need to work this out?

Let's try some imaginary stuff.
$\dfrac{x^4}{x^2+1}=\dfrac{Ax^3}{x+i}+\dfrac{Bx^3}{x-i} \implies A=B= \dfrac{1}{2}$
$\dfrac{x^4+1}{x^2+1}= \dfrac{1x^3}{2(x+i)}+\dfrac{1x^3}{2(x-i)}+\dfrac{1}{x^2+1}$
