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Integration by parts

  1. Feb 11, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex]\int(sin(x)^{-1}), dx[/tex]

    2. Relevant equations

    *By Parts Formula: f(x)g(x) - [tex]\int(g(x) f'(x)) dx[/tex]

    Also for d/dx sin(x)^{-1} I used 1/sqrt(1-x^{2})

    3. The attempt at a solution

    Just started learning this method, I tried letting f(x) = sin(x)^{-1} and g(x) = dx but nothing really simplified, can someone help with selecting the correct g(x) and f(x), Thanks
    Last edited: Feb 11, 2009
  2. jcsd
  3. Feb 11, 2009 #2


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    Is the function you're trying to integrate here the inverse function of sin(x)? If so, it should be denoted [tex]\arcsin(x)=\sin^{-1}(x)[/tex]

    This isn't a formula, since you haven't specified what it is equal to! The formula I would use is [tex]\int v du=uv-\int udv[/tex]. Is this the formula you have been taught? If not, what is the formula you have been taught?
  4. Feb 11, 2009 #3
    Yes, the problem is asking for the integral of arcsin(x), and also yes, that is the formula we are using, my "u's" and "v's" look a lot alike sometimes so I replaced them with f(x) and g(x), sorry about the confusion
  5. Feb 11, 2009 #4


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    Ok, so your selection was [itex]u=\sin^{-1}(x) \,\, , \,\, dv=dx[/itex], right? So, what went wrong? This is the choice that I would make!
  6. Feb 11, 2009 #5
    Ok nevermind I got it now, I was working towards an answer to this problem that my 89 gave me but I typed it in wrong, I see how to to it now, the answer being:

    x*arcsin(x) + sqrt(1-x^2)

    Thanks for your help
  7. Feb 11, 2009 #6


    Staff: Mentor

    Plus a constant
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