Integral of (x-7)(3-2x)^(3/2)

Hey guys, I have this problem I have been trying to solve for the longest time.

Not looking for a complete solution, maybe part of one would be nice.

I'm trying to integrate

So far I have tried 2 ways of going at it.

First I completely expanded the integral

I have no problem integrating

I just simply use the substitution technique.

The next part gets tricky, I'm stumped. Any of the functions with x variables I simply can't seem to do.

I tried substituting by parts by either making or so on and so forth

I went to wolframalpha.com and tried to understand what they did step by step

For example, I tried to integrate just like the site did. They say to substitute and to get

Either I am feeling really dumb right now and the answer is right in from of me or the answer is completely wrong. How did wolframalpha manage to get

=

All help is greatly appreciated