Recursive equation for complexity: T(n) = log(n) * T(log(n)) + n
I suppose you are looking for an asymptotic bound. Notice that the recursion depth is $\log^* n$, that is how often do I have to apply the logarithm recursively to get below 2. Also, the function is increasing. Using these two facts, you can plug in the recursion once and then you  see that you have at most $\log^*$ summands, each of them at most $\log^2 n$ and then the additional $n$. This sum is dominated by $n$. 

$$
\begin{align}
T(n)&amp;=\log(n) T(\log n)+n=\log n \log\log n \;T(\log\log n)+\log^2(n)+n \\
&amp;\le \log^*n\log^2n+n=O(n)
\end{align}
$$

Clearly $T(n)\ge n$ and thus $T(n)=\Theta(n)$.