Determine the asymptotic growth of the recurrence T(n)=3T(n/3)+nlnnT(n) = 3T(n/3) + \frac{n}{\ln n}T(n)=3T(n/3)+lnnn.
Θ(nloglogn)\Theta(n \log \log n)Θ(nloglogn)
Θ(nlogn)\Theta(n \log n)Θ(nlogn)
Θ(n)\Theta(n)Θ(n)
Θ(nlog2n)\Theta(n \log^2 n)Θ(nlog2n)