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Anti-derivative of a trig equation

  1. May 17, 2012 #1
    1. The problem statement, all variables and given/known data
    I just need to find the anti-derivative of this equation:
    [itex]\int x(sin^2(3x)cos(3x))dx[/itex]



    2. Relevant equations
    [itex]sin^2(x)+cos^2(x)=1[/itex]


    3. The attempt at a solution
    I'm not really sure where to start here. I tried to do a substitution first but couldn't make it work. So then I tried to put sin^2 in terms of cos^2 but that didn't seem to help me out any more. Anyone have an idea of how to tackle this problem? Thanks in advance!
     
  2. jcsd
  3. May 17, 2012 #2

    Curious3141

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    Homework Helper

    Integrate by parts, with u = x, dv = [itex]\sin^2(3x)\cos(3x)dx[/itex].

    To integrate [itex]\sin^2(3x)\cos(3x)dx[/itex], use the substitution [itex]y = \sin(3x)[/itex]
     
  4. May 17, 2012 #3
    Thank you very much. I didn't see the ability to do another substitution right off hand.
     
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