Sorry, are you referring to actual integration by parts, cause I don't see the need to use it.
Your original equation can be simplified to
Long division should give you
The first one is integrating a constant. You should be able to do that...
The second one is integrating a single x. That should be easy too
The third one, you can integrate it directly if you're comfortable, or simply use the substitution u = x + 19 (remember the limits change during substitution, so turn the u back into x after integrating or change your limits)
The fourth one integrates into a log.