Integrate:

Now I used partial fractions:

and after a lot of working out got the following equations:

Now I tried gauss reducing it, but it was rather long and tedious which gave me:

In my final answer I got:

which was of that right form (due to the logs and arctan) but obviously the values were wrong.

So I was wondering, is there a more efficient way to do this question and solve for A, B, D and E without using gauss reduction?