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Integrate x sin(2x) dx

Integrate x sin(2x) dx

Grade:12

2 Answers

grenade
2061 Points
6 years ago
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
Gman Namg
420 Points
6 years ago
thank u

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