# Homework Help: Tricky Intregral

1. Dec 21, 2009

### iatnogpitw

1. The problem statement, all variables and given/known data
Okay, here's the problem: integrate ((x^3) - 1) / ((x^3) + x) dx

2. Relevant equations
What is the solution and the method?

3. 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.

2. Dec 21, 2009

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

Last edited: Dec 21, 2009
3. Dec 21, 2009

### Staff: Mentor

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