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$$T(n) = 4T\left(\frac{n}{2}\right) + \frac{n^2}{\log n}$$

I have the solution here (see example 4 in that pdf), but the problem is that they have solved it by guessing. I couldn't make that guess. So if you are going to go by the guess method too, tell me how should I have made that guess?

Or, I'm actually more interested in knowing some other method that can possibly be used to solve that.

Thanks!

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    Looking at the file you provided, they don't solve the recurrence either, the question and the answer there are to give a big-$O$ of bound for $T(n)$. If that is what you are after, you should say so in your question. I've tagged with "asymptotics". Also the file mentions a Master Theorem which you apparently should know about (mention that as well!), so it's not pure guessing.2012-10-02
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    @MarcvanLeeuwen, yes. Thank you for pointing out. Corrected :)2012-10-02

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