for the 1st problem, you're ok ... the two expressions only differ by a constant.
My answer was :
Apparently, the answer given was with which gives the answer:
So, are these answers the same or was I just wrong?
The answer given is:
Where did the sign change come from or is the given answer wrong?
The first one is correct. As for the second one, I can't really check your work but perhaps you should re-evaluate it. Alternatively, if you expand the numerator and use polynomial division, you will get a much simpler integral to evaluate (and the answer would be the one given in the book).