Crazy Integral Question. Please Help!!!

The initial question I have is to evaluate the following indefinite integral:

(from: calculus, early transcendentals textbook by James Stewart 6th custom edition for MA110. Question from: sec. 7.4 question #37)

The question seems to require some completing the square of the denominator, substituition, and partial fraction integration. I thought I was on the right track although I have been trying for about 5 hours now and I can't get the same answer as the book which is really frustrating.

The answer according to my book is:

If anyone has some time then I would really appreciate the help.

NOTE: The step I got to and think I am right is:

This is just after i finished making the integral into partial fractions. Also if you were wondering what I used as my substitution.

So ya I got a little stuck here. I have tried finding the integrals seperately although I can't seem to get it to work and it is hard to see where my errors are because the integrals are all seperate and I can't know if even 1 is right. My work so far may also be wrong too though (Doh)

Thanks in advance for your help,

Luke