- 637

- 0

∫x*Sin(x)*Sin(2x) dx = - xSin(2x)Cos(x) + ∫Cos(x) dx

= Sin(x) - xSin(2x)Cos(x) + C

By assuming u = xsin2x, du = 2xcos2x + sin2x, dv = sinx, v = -cosx. And using the Parts formula.

- Thread starter PrudensOptimus
- Start date

- 637

- 0

∫x*Sin(x)*Sin(2x) dx = - xSin(2x)Cos(x) + ∫Cos(x) dx

= Sin(x) - xSin(2x)Cos(x) + C

By assuming u = xsin2x, du = 2xcos2x + sin2x, dv = sinx, v = -cosx. And using the Parts formula.

Staff Emeritus

Science Advisor

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- 17

∫ u dv = uv - ∫ v du

not ∫ v dx

BTW, the key to this is the trig identity

2 sin x cos x = sin 2x

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