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Integrate (cos^2(x))/(sin^6(x))

  1. Mar 27, 2008 #1
    [SOLVED] ff

    1. The problem statement, all variables and given/known data

    integrate (cos^2(x))/(sin^6(x))

    2. Relevant equations

    Double angles?
    u-sub?

    3. The attempt at a solution

    I tried using double angles but im really not sure what to do I havnt seen any like this... I have only done stuff without fraction like integrating cos^3x sin^5x can anyone just start me off please
     
    Last edited: Mar 27, 2008
  2. jcsd
  3. Mar 27, 2008 #2

    tiny-tim

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    Hi n77ler! :smile:

    Hint: it's cosec^6(x) - cosec^4(x).

    Does that help … ? :smile:
     
  4. Mar 27, 2008 #3
    hmm kind of Im not sure where you got that though. The division in an integral can be changed to subtration i guess... but im not sure how you are getting the two csc's. I know it is 1/sin but not sure other than that
     
  5. Mar 27, 2008 #4

    tiny-tim

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    cos^2(x)/sin^6(x)

    = (1 - sin^2(x))/sin^6(x) = 1/sin^6(x) - 1/sin^4(x)

    = cosec^6(x) - cosec^4(x). :smile:
     
  6. Mar 27, 2008 #5
    right, god lol I'm not functioning well right now.
     
  7. Mar 27, 2008 #6
    ok so i seperate those into two different integrals and then integrate right
     
  8. Mar 27, 2008 #7
  9. Mar 27, 2008 #8
    meh gave up cause it was to much parts so i went back to start and found an easier way lol...

    (cos^2x/sin^2x ) (1/sin^4x) and then cot^2xcsc^4x and solved...thanks tho :)
     
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