Test for convergence of the series $sum_{n=2}^inftyfrac{1}{(ln n)^{ln n}}$

Could I have a hint for testing the convergence of the following series please?

$$\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$$

Edit

The integral test does not work because $\int_1^n\frac{1}{(\ln x)^{\ln x}}dx$ has not an elementary primitive.

Thank You.

Answer

Alternate hint:

$$(\ln n)^{\ln n} = n^{\ln \ln n}.$$