I may as well finish how I done it. Overkill, yes. I wish I would have saw that Frullani thing right off. I am familiar with it.It did not occur to me. I will remember to look around for it from now on.
This is OK if exists. Which works
if C = -1/2.
With C = -1/2, we get:
To save typng, I went on and eventually wound up with said solution.
I like all of the methods. That is why I like to post an occasional integral.