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What is the value of the improper integral

Source: Brazil Undergrad MO - Galois-Noether 2018 #22

November 26, 2019
Brazilian Undergrad MOcollege contestcalculusintegration

Problem Statement

What is the value of the improper integral 0πlog(sin(x))dx \int_0 ^ {\pi} \log (\sin (x)) dx?