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Indefinate integration

  1. Jan 15, 2007 #1
    Integrte indefinately

    ------------- . dx
    Sin^2 x
  2. jcsd
  3. Jan 15, 2007 #2
    did you not attempt this question?
    the people on this board will be more willing to help after they have seen what you've done.

    also your question is unclear did you mean: [(cos(2x))^(1/2)]/[(sinx)^2] ?

    if so do you know how to integrate by parts
  4. Jan 15, 2007 #3
    I do, but there should also be a way to integrate by substitution
    ive tried a lot but it doesnt seem to be happening
  5. Jan 15, 2007 #4

    Gib Z

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    Try using trig identites. Cos 2x=cos^2 x - sin^2 x = 2cos^2 x -1

    Sin^2 x= 1-Cos^2 x
  6. Jan 15, 2007 #5
    You get stuck after a while
  7. Jan 16, 2007 #6


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    [tex] \int \frac{\sqrt{\cos 2x}}{\sin^{2}x} dx =-\sqrt{\cos 2x}\cot x-E(x,2)-F(x,2) +C [/tex]

    , where E and F are the elliptic integrals of the second and first kind, respectively.

  8. Jan 16, 2007 #7
    We havent covered that kinda integration .
    I need a substitution type result
  9. Jan 16, 2007 #8


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    dextercioby has given you the solution. In general, elliptic integrals cannot be expressed in terms of elementary functions. Are you sure you've written down the question correctly?
  10. Jan 16, 2007 #9
    yeah, it's the right question
  11. Jan 16, 2007 #10
    This cant be the solution I'm only in the twelfth grade
  12. Jan 17, 2007 #11


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    Well, that IS the solution and there's no way you can circumvent it and find another one with only "elementary" functions.

  13. Jan 17, 2007 #12

    Gib Z

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    Bad luck kiddo. If your teacher tells you how to get another result, we want to hear :)
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