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Integrate x sin(2x) dx
Integrate the original integrand by parts: ∫ xsin(2x) dx Let f'(x) = sin(2x) f(x) = -cos(2x) / 2 Let g(x) = x g'(x) = 1 ∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g'(x) dx ∫ xsin(2x) dx = -xcos(2x) / 2 + ∫ cos(2x) / 2 dx ∫ xsin(2x) dx = -xcos(2x) / 2 + sin(2x) / 4 + C ∫ xsin(2x) dx = sin(2x) / 4 - xcos(2x) / 2 + C aiu
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