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.)
$$\int\frac{7x^2+2x-7}{x^3-x}\,dx$$

Hint : Apply http://en.wikipedia.org/wiki/Partial_fraction_decomposition#Procedure
$$ \frac{7x^2+2x-7}{x^3-x} = \frac{7x^2+2x-7}{x(x^2-1)} = \frac{7x^2+2x-7}{x(x-1)(x+1)} $$
$$ \frac{7x^2+2x-7}{x(x-1)(x+1)} = \frac{A}{x} + \frac{B}{(x-1)} + \frac{C}{(x+1)} $$
You can obtain A,B,C by setting the value of x are 1,-1,0 respectively and compare the coefficient of different power of x i.e 2,1 and 0.
$$ \int (\frac{A}{x} + \frac{B}{(x-1)} + \frac{C}{(x+1)}) dx = \int \frac{A}{x} + \int \frac{B}{(x-1)} + \int \frac{C}{(x+1)}$$
Now, apply this, to get your final answer 
$$ \int \frac{1}{x+k} = ln|x+k| + C$$
