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Homework Help: Integral question

  1. Apr 15, 2007 #1
    what is the integral of (tan x)^2

    i added a file in wich i showed the way i tried to solve it

    Attached Files:

    • tan.GIF
      File size:
      118.5 KB
  2. jcsd
  3. Apr 15, 2007 #2
    what is its identity?
  4. Apr 15, 2007 #3
    the integral is:

    (tan x)^2
  5. Apr 15, 2007 #4
    I'm going to ask again, what is its direct trig identity
  6. Apr 15, 2007 #5
    Last edited: Apr 15, 2007
  7. Apr 15, 2007 #6
    the trig identity is tangent

    but my integral is
    tangent square
  8. Apr 15, 2007 #7

    Gib Z

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    Homework Helper


    Are you familiar with what Mathgician said? Its a well known Trigonometric Identity, [itex]\tan^2 x = \sec^2 x -1[/itex]

    Knowing that,

    [tex]\int \tan^2 x dx = \int (\sec^2 x - 1) dx = \int \sec^2 x dx - \int 1 dx = (\int \sec^2 x dx ) - x[/tex]

    For the integral of (sec x) squared, if you don't already know it, try differentiating tan x, what is that?
  9. Apr 15, 2007 #8
    If you are doing integrals right now, you have to have come across the derivative of tanx from differential calc class. No offense, but its the most basic derivative and identity is so common, I just thought you already should have known. I've seen you help many people on this board with integrals, I assumed that you would already knew or maybe you just had a brain fart or something. Its alright I have moments like these also.:cool:
    Last edited: Apr 16, 2007
  10. Apr 16, 2007 #9

    Gib Z

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    In fact, I just look through your attachment right there. You didn't even need Mathgicians or my suggestions for that identity, you got it yourself! 1/cos^2 x is sec^2 x :D You just needed to notice that was the derivative of tan x, instead of using cos^2 x = (1+cos 2x)/2
  11. Apr 16, 2007 #10
    yeeepppp thank you very much

    i got it
    it was right under my nose
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