Solving Partial Fractions Integral: x^2+5x+2 / x^4+x^2+1

[tangur]

Hi I need some help getting started with this integral

$$\int \frac {x^2+5x+2}{{x^4+x^2+1}}dx$$

Thanks in advance

 

[Astronuc]

Try working the denominator -

$$x^4+x^2+1 = (x^4+2x^2+1)-x^2$$

then use the identity

$$x^2-y^2 = (x+y)(x-y)$$

 

[Astronuc]

You were on the right track.

To eliminate the $$x^3$$ term, C=-A.

Then find 3 equations in three unknowns A, B, D.