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Integral of sech x

  1. Dec 9, 2011 #1

    sharks

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    The problem statement, all variables and given/known data
    I believe there might be a mistake in this statement from my online notes. A typo error in the last line, maybe?
    http://s1.ipicture.ru/uploads/20111209/K6L7AWhS.jpg


    The attempt at a solution
    In the last line, from what i worked out, it should be (1/2)tan^(-1)(tanh... instead of 2tan^(-1)(tanh... Correct?
     
  2. jcsd
  3. Dec 9, 2011 #2
    Nope it is right. I would make two substitutions instead of one just because it is easier for me to think through that way. I would substitute u=(x/2) and then s=tanh(u) yielding the simple integral 2∫1/(s^2+1)ds=2tan^-1(s)=2tan^-1(tanh(u))=2tan^-1(tanh(x/2))+C

    edit: The du for your equation would be .5sech^2(x/2)dx so you would pull a 2 out in front of the integral.
     
  4. Dec 9, 2011 #3

    sharks

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    Thank you, PCSL. I see it now.
     
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