How to Simplify an Integrand by Dividing the Denominator into the Numerator?

[Ateowa]

I've just started fundamental Integration, so I don't know too many tricks, and every once and a while my textbook does something that I can't follow. In this case, it's not in the actual solving of the integral so much as it simplifying the function. Here's the problem:

\int \ \frac{8x^{3}dx}{4x^{2}+4x+5}

In my textbook, it says "We can rewrite the given integral by dividing the denominator of the integrand into the numerator. Doing this, we obtain:"

\int \ 2x-2-\frac{2x-10}{4x^{2}+4x+5}

I have absolutely no idea how to do that. I thought I might be able to pull it off with long division or synthetic division, but I don't really know how to do it. I tried doing a quick google to find out what to do, but it's all division with a single root. I'm sure it's actually really simple, but I just can't figure it out.

Sorry if this is in the wrong section. I figured because it was in the middle of solving a Calculus problem, this was the forum to put it in. Thanks in advance!

 

[benorin]

Use polynomial long division (quickie tutorial in that http://www.mathsrevision.net/alevel/pages.php?page=1.)

 

[Ateowa]

I knew it was something simple that I was missing...

Thanks a bunch, benorin. Now I can finish up that problem and turn in for the night!