$\displaystyle

\int {\frac{{2x^4 }}

{{x^3 - x^2 + x - 1}}dx}

$

This one gets a little bit tricky. So first off I do long division to make the fraction proper:

$\displaystyle

x^3 - x^2 + x - 1\left){\vphantom{1{2x^4 }}}\right.

\!\!\!\!\overline{\,\,\,\vphantom 1{{2x^4 }}}

$

Here is my result. You can check my division although i'm not skilled enough in MathType to show all of it yet.

$\displaystyle

\int {\left( {2x + 2 + \frac{2}

{{x^3 - x^2 + x - 1}}} \right)} dx

$

Now I need to find out a way to simplify that last term.

$\displaystyle

\frac{2}

{{x^3 - x^2 + x - 1}} = \frac{2}

{{x(x^2 - x + 1) - 1}}

$

This is as far as I went. Any help is appreciated. Thanks!