Hi, I've been working on these integral evaluations and I'm stuck. Any help on any of them would be greatly appreciated, thanks in advance!

1. $\displaystyle \int\frac{2x^3-3x+2}{x^3-x}dx$

My attempt:

$\displaystyle 2x^3-3x+2=\frac{A}{x^2-1}+\frac{B}{x-1}+\frac{C}{x}$ (Tried breaking it down, couldn't get it to work )

2. $\displaystyle \int\frac{x^4+1}{x^3+x}dx$

My attempt:

long division to get $\displaystyle \int xdx-\int\frac{x^2+1}{x^3+x}dx$ (not sure how to show that in Latex)

Then $\displaystyle x^2+1=\frac{A}{X^2+1}+\frac{B}{x+1}+\frac{C}{x}$

Not sure where to go from there...I imagine that I'm missing the same idea in both of these, so any help would be appreciated. Thanks again!