Integration of Rational Functions By Partial Fractions

I have this problem that needs to be solved by integration by partial fractions and I can't seem to get the right answer. Here's the problem as written:

"Find with respect to , use the constant ."

So, I have:

and

If , then

and

If , then

So,

Unfortunately, this is not the answer. I greatly appreciate if anyone can point out where I've gone wrong. I have a feeling it was a generally small, but ultimately large, error. It is entirely possible that I have made an arthimetic mistake, by the way.

Thanks for your consideration,

Austin Martin