Convergence of Improper Integral: $\int_{e^2}^\infty {dx\over x\log\log x}$ Test the convergence of the following integral$$\int_{e^2}^\infty {dx\over x\log\log x}$$
I understand that the problem is only at $\infty$ how to proceed ?

Hint: Your function $\frac{1}{x\log\log x}$ goes to $0$ more slowly than $\frac{1}{x\log x}$. You can comfortably find $\int_{e^2}^M \frac{dx}{x\log x}$ explicitly, and show that it (sedately) blows up as $M\to \infty$. 
