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say v=x dv=1
du=sin3x u= -1/3cos3x
use the formula
Integral of vdu = uv - integral of udv
du=sin3x u= -1/3cos3x
use the formula
Integral of vdu = uv - integral of udv
ossoss87
use integration by parts
xsin3x
thanks!
xsin3x
thanks!
Integration parts states:
INT v(du/dx) dx = uv - INT u(dv/dx) dx
As you want to differentiate v and integrate u, you need to decide whether to take x or sin3x as v and so take the other as du/dx. Clearly if you differentiate x you get 1, which has greatly simplified the expression. Differentiating sin3x isn't going to help you in any way except getting a loop of trignometric ratios.
v=x, dv/dx=1. du/dx=sin3x, u=(-1/3)cos3x.
INT xsin3x dx = (-1/3)(x)(cos3x) + INT (1/3)cos3x dx
=(-1/3)(x)(cos3x) + (1/9)(sin3x) + C
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