Integration of (x^2 - x - 11)/(3 - x - 2x^2)

(The answer is - 1/2 x + 11/5 ln |x-1| - 29/20 ln |2x + 3| )

What I've done:

1. Long division. I got - 1/2 + (- 3/2 x - 19/2)/(3 - x - 2x^2).
2. Then I separated out the numerator of (- 3/2 x - 19/2)/(3 - x - 2x^2).
So I got (3/8 ( - 4x - 1) - 73/8) / (3 - x - 2x^2).
That further breaks down into (3/8 ( - 4x - 1)) / (3 - x - 2x^2) - (73/8) / (3 - x - 2x^2).

What I'm trying to do is basically to break it into the f'(x)/f(x) format and the 1/a^2 - x^2 format so I can integrate them.

But after a while this got very complicated and I checked the answer and it clearly doesn't tally, so can anyone help? I think my methods are correct but I slipped up on the calculations somewhere. Thanks.

PS for (3 - x - 2x^2) i think the completed square form is - 2 [ (x + 1/4)^2 - 25/16 ] thanks