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Homework Help: Trigonometric Integration

  1. Sep 28, 2012 #1
    ∫cos^5 x sin^5 x dx

    I thought I would try to solve this by first doing:

    ∫(1 - sin^2 x) cos^3 x sin^5 x dx

    but would like to know if that's right.

    [Edit] Is the answer something like (sin^6 x) / 6 - (sin^8 x) / 4 + (sin^10 x) / 10 ?[Edit]
    Last edited: Sep 28, 2012
  2. jcsd
  3. Sep 28, 2012 #2


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    How did you get it?

    Take the derivative, to check it.

    Don't forget the constant of integration.
  4. Sep 28, 2012 #3
    I split up the cos^3 x just like I did the cos before. Then used u substitution.

    I did. Thanks, everything's okey dokey now : D
  5. Sep 29, 2012 #4


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    I think simpler would be just to ask - is there any well known formula involving cosx.sin x ?
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