Help understanding a Calculus 2 integral

Okay, so I've basically been practicing Calc 2 integrals non-stop because they're VERY difficult. I'm starting to get it, inch by inch, but there is one method that I just do not understand. Here is an example of my problem....

http://i1057.photobucket.com/albums/...pscf14dc67.png

The first step is what I don't understand. How does the 3w - 1 turn into 3 - 7/(w +2)?

Thanks for the help.

Re: Help understanding a Calculus 2 integral

It **doesn't** $\displaystyle \frac{3w- 1}{w+ 2}$ does. Do the division: $\displaystyle \frac{3w- 1}{w+ 2}= \frac{3w+ 6- 7}{w+ 2}= \frac{3w+ 6}{w+ 2}- \frac{7}{w+ 2}= 3\frac{w+ 2}{w+ 2}- \frac{7}{w+ 2}$.

Re: Help understanding a Calculus 2 integral

I can see that now. A lot of the techniques used in these integrals always seems so cryptic to me... thanks a lot!