(x-2)/(x^2+x^4) dy
I tried this way, but the result didn't seem right.
(AX+B)(X^2+1)+(C)/(X)+(D)/(X^2)
All integrals are standard forms. Omitting the C's:
$\displaystyle \int \frac{1}{x^2} \, dx = \int x^{-2} \, dx = - \frac{1}{x}$.
$\displaystyle \int \frac{-x + 2}{x^2 + 1} = - \int \frac{x}{x^2 + 1} \, dx + \int \frac{2}{x^2 + 1} \, dx = - \frac{1}{2} \ln |x^2 + 2| + 2 \tan^{-1} x$.