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Need help with a problem

  1. Aug 10, 2008 #1
    This is a problem from my homework set.

    I'm so close but I'm tangled up at the end...

    Integrate/ x arccos(x)dx

    So far I am at

    (x^2)/2 arccosx - Int/ (x^2)/ (2 sqrt(x^2 - 1))

    Can figure out how to integrate this part.
  2. jcsd
  3. Aug 10, 2008 #2


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    I hope you mean sqrt(1-x^2). I would try a substitution like x=sin(u).
  4. Aug 10, 2008 #3
    You are correct. Thankyou!
  5. Aug 10, 2008 #4
    I'm not sure I'm reading this right. Is the part inside the integral,

    x * arccos(x)?

    if so, what about the substitution u = arccos(x), so that x=cos(u), and dx = -sin(u) du? Then it becomes the integral of -u*sin(u)*cos(u) du

    I'd probably try repeated integration by parts to solve the new integral.
  6. Aug 10, 2008 #5
    Never mind, seems it was answered while I was typing :)
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