Finding the integral I've come across the following integration problem online:
$$\int{\frac{x^3}{x^4-2x+1}}\,\,dx$$
This is beyond my current knowledge of integrals, but it seems to be a very interesting integration problem.  Would anyone be able to give a tip on how to being solving the expression?
If there are any techniques, please elucidate - i.e. substitution, trigonometric identities, etc.
Thanks!

You would start by factoring the denominator as $(x-1)(x^3+x^2+x-1)$ and then writing 
$$
\frac{x^3}{x^4-2x+1} = \frac12 \left[ \frac{1}{x-1} + \frac{x^2-1}{x^3+x^2+x-1}\right]
$$
The first term is easy to integrate.  The second term can be integrated by factoring the denominator and doing a similar trick; unfortunately, the expressin is an ugly mess involving things like 
$$\sqrt[3]{17 + 3\sqrt{33}}$$
so the closed form integral must be pretty ugly.
