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Is there a way to solve this recurrence using master theorem:

$$T(n) = 4T(n/2) + Θ(n^2/\log n)$$

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As mentioned by @Yuval Filmus in the comment, you can use the extension of the master theorem (case 2b). The result is $T(n) = \Theta(n^2 \log\log{n})$.

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