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Homework Help: A trigonometric substitution problem

  1. Nov 22, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex]\int[/tex]sin3cos2xdx



    3. The attempt at a solution

    I've successfully solved this problem by factoring out 1 sinx and changing the sin2x to (1-cos2x then assigning u=cosx and du=-sinx and so on.

    What I'm wondering is why does letting u=sin3x in the original integral not work. Then du=3cos2xdx and there is a cos2x in the original integral. Why does this fail? Please and thank you :)
     
  2. jcsd
  3. Nov 22, 2008 #2
    Well, the reason that doesn't work is that that is not the correct derivative. the derivative is 3sin(x)^2*cos(x) :) remember taking the derivative of v^3 is 3v^2*dv (where I let v=sin(x))
     
  4. Nov 24, 2008 #3
    Thanks very much. I don't know what I was thinking
     
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