2019-06 Simple but not too simple integration

Compute the following integral  \[ \int_{0}^{\pi/2} \log{ (2 \cos{x} )} dx \].

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About Hyungryul

2003.3-2009.8 KAIST, Undergraduate student in Mathematics 2009.8-2014.8 Cornell University, PhD student in Mathematics 2014.9-2017.2 University of Bonn, Postdoc 2017.3-2021.2. KAIST, Assistant Professor 2021.3-Present. KAIST, Associate Professor