3 Attachment(s)

Steps in integration problem

Hi, while working on some integration problems today, I came across this one:

Attachment 19466

I multiplied it out:

Attachment 19468

(Edit: it's supposed to say x^2+2x in the first term)

And with some trial and error I got an answer:

Attachment 19467

When I differentiate this I get back what I started out with.

But trial and error isn't usually the best way to get an answer, so can anyone tell me which steps I need to take here?

Should I be using U-substitution?