I suspect this is just a technical problem. The issue I encountered is this.
When I tried to hypothesis the form to be nlogn - clogn -dn -f, but some positive just pop up.
Another method I tried is to make the assumption of N>17. In that case, nlog(n+17) will be smaller than nlog2n. So I can always get back to a close form. But that turns out to make the expression too big.
Looking up the web, nothing is really useful. Sounds like I am on my own. My guess is this involves the mechanical the proof and the proof of Master Theorem will likely give me some ideas. I will wait before I look up the solutions. (Let's not spoil it)
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