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This lecture covers the integration by parts technique, where if f and g are continuous and differentiable functions, the integral of f(x)g(x) can be computed as f(x)G(x) - ∫f'(x)G(x)dx. Through examples, the instructor demonstrates how to apply this method to functions like cos(x) and sin(x), showcasing the step-by-step process and the importance of correctly identifying f and g functions.