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Trig integral

  1. Apr 7, 2007 #1
    The question is to evaluate the integral in the attachment.

    Using trig substition, I've reduced it to ∫ (tanz)^2 where z will be found using the triangle. I just need to integrate tangent squared which I can't seem to figure how to do. I tried using the trig identity (secx)^2 - 1 but I don't know what to do after.
     

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  2. jcsd
  3. Apr 7, 2007 #2

    arildno

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    That is a good move.

    Hint:
    What do you get if you differentiate tan(z)?
     
  4. Apr 7, 2007 #3
    I get (sec(z))^2)
     
  5. Apr 7, 2007 #4

    arildno

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    That is to integrate tan, I said differentiate it!
     
  6. Apr 7, 2007 #5
    Yes, sorry I realized I had made a mistake so when I differentiate tan, I get sec^2 ...
     
  7. Apr 7, 2007 #6

    arildno

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    Indeed, so therefore you DO know an anti-derivative for sec^2, don't you?

    Therefore, you should be able to find an anti-derivative for tan^2(z)=sec^2(z)-1
     
  8. Apr 7, 2007 #7
    So simple... thanks a lot
     
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