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Homework Help: Integration problem (check my work)

  1. Feb 12, 2007 #1
    1. The problem statement, all variables and given/known data

    (integrate)((cos(x)/(7*sin(x)+21))

    2. Relevant equations



    3. The attempt at a solution

    I actually solved it, but I fear it might be wrong (that and my calculator says a different answer).

    Anyway, I factored a 1/7 out of the equation, to make the equation (1/7)(integrate)((cos(x)/(sin(x)+21)). I subsituted (sin(x)+21) for u, and made du cos(x).

    This made the integral (1/u), which I turned into ln(u). Now I had (1/7)*ln(u). I just rewrote that into ln(u)/7, then subbed sin(x)+21 into u, making the answer ln(sin(x)+21)/7.

    Did I do anything wrong here?
     
  2. jcsd
  3. Feb 12, 2007 #2
    if i understood what you wrote it should be like this after factoring the 1/7
    (1/7)(integrate)((cos(x)/(sin(x)+3))
     
  4. Feb 12, 2007 #3

    HallsofIvy

    User Avatar
    Science Advisor

    Yes. The denominator is 7sin(x)+ 21= 7(sin(x)+ 3).
     
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