<s>[INST] integrate $ \frac {7x^2 + 2x − 7}{ x^3 − x}$ dx I keep messing up with the integration part of this I think. Before that I have to factor out the $x$ on the bottom, and then set up the $A$ and $B$ right?
Evaluate the integral. (Remember to use $\ln|u|$ where appropriate. Use $C$ for the constant of integration.)
$$\int\frac{7x^2+2x-7}{x^3-x}\,dx$$
 [/INST] HINT:
As $x^3-x=x(x^2-1)=x(x+1)(x-1),$
Using Partial fraction decomposition 
$$\frac{7x^2+2x-7}{x(x-1)(x+1)}=\frac A{x+1}+\frac Bx+\frac C{x-1}$$
Multiply either sides by $x^3-x=x(x^2-1)=x(x+1)(x-1)$
and compare the coefficients of the different power of $x$  to find $A,B,C$
Finally use $\displaystyle \int\frac{dx}{x+m}=\ln|x+m|+C$
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