Solving a Tricky Integral Homework Problem

[iatnogpitw]

Homework Statement

Okay, here's the problem: integrate ((x^3) - 1) / ((x^3) + x) dx

Homework Equations

What is the solution and the method?

The Attempt at a Solution

I know this involves partial fractions, which I attempted to no avail, since the numerator is the same degree as the denominator. I even factored the numerator into (x - 1)((x^2) + x + 1), but I can't seem to figure out what to do.

 

[diazona]

$$\int \frac{x^3 - 1}{x^3 + x}\mathrm{d}x$$
If factoring doesn't help, I'd try splitting it into a sum of two integrals.

If you're really stuck, mouseover this for a clue:

Spoiler

x^3 - 1 = (x^3 + x) - (x + 1)

 

[Mark44]

Or you can simply divide the numerator by the denominator using polynomial division.