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Explore a challenging mathematical problem in this 26-minute video that delves into calculating the definite integral of (ln(cos x))^2 over the interval 0 to pi/2. Learn how to apply Fourier series and other advanced techniques to solve this complex integral. Gain insights into advanced calculus and mathematical problem-solving strategies as the instructor guides you through the step-by-step solution process. This video is part of a comprehensive playlist on advanced mathematical concepts and is suitable for students and enthusiasts looking to enhance their understanding of complex integrals and mathematical analysis.