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How do you solve the integral

  1. Feb 21, 2012 #1
    1. The problem statement, all variables and given/known data
    ∫ x sinx cosx dx =


    2. Relevant equations
    note that sinx cosx = (1/2) sin 2x


    3. The attempt at a solution
    1/2) ∫ x sin 2x dx =
    (1/2) [(-1/2)x cos 2x - ∫ (-1/2)cos 2x dx] =
    (1/2) [(-1/2)x cos 2x +(1/2) ∫ cos 2x dx] =
    (-1/4)x cos 2x +(1/4) ∫ cos 2x dx =
    (-1/4)x cos 2x +(1/4)(1/2) sin 2x + c =
    (-1/4)x cos 2x +(1/8) sin 2x + c =
    :bugeye:
     
  2. jcsd
  3. Feb 21, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    That looks just fine. What's the question?
     
  4. Feb 21, 2012 #3
    It seems like you have an answer. So what's the issue?
     
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