I looking to evaluate $$\int_{0}^1\ln(\ln(\frac{1}{x})) dx$$
I know the answer is the Euler-Mascheroni constant, $\gamma$ but how do I get that result?
I've tried differentiating under the integral, but that didn't seem to work. Maybe series could work since $\gamma$ is connected to a lot of series and is defined by using harmonic series.