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How do you intergrate cos^3 [x] .dx

  1. Apr 21, 2004 #1
    could some one please show me the steps to doing this ??
  2. jcsd
  3. Apr 21, 2004 #2


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    [itex] \int cos^3(x)dx [/itex] is a standard problem. Anytime you have an odd power of either sin or cos take one of the out to match with the dx:


    Now we can use [itex]sin^2(x)+ cos^2(x)= 1[/itex] to convert to the other trig function:

    [tex]\int(1- sin^2(x))(cos(x)dx)[/tex]

    and, of course, the whole reason for taking out that orginal "cos(x)" is that
    d(sin(x))= cos(x)dx.

    Let u= sin(x). Then du= cos(x)dx and the integral is

    and that should be easy.
    Last edited by a moderator: Apr 21, 2004
  4. Apr 22, 2004 #3
    Well, I beg your forgiveness for this question b/c its really an irrelevant one.

    Can you please tell me how you use these mathematical symbols like integral sign and superscripts etc in your messages?
  5. Apr 22, 2004 #4
    It's called LaTex Math Typesetting and is really pretty cool. Check out this thread for more information:
  6. Apr 24, 2004 #5
    suddy, if you want a place to check your work, the integrator works fine--- powered by mathematica.

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