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Integral of 1/sinh^2(x/2)

  1. Mar 16, 2013 #1
    Hi dear members,
    I have a problem with the following integral:

    Integral 1/sinh^2(x/2) from -inf to +inf =-2 coth(x/2)

    must I consider it as a principal value integral???

    Thank you
  2. jcsd
  3. Mar 16, 2013 #2


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    If you're integrating wrt x, you can't have x in the RHS.
  4. Mar 16, 2013 #3


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    Just to be clear, are you trying to evaluate
    ##\int_{-\infty}^{\infty} \frac{1}{\sinh ^2(x/2)} \, dx##
  5. Mar 16, 2013 #4


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    once you put limits on the integral (a definite integral, not an indefinite integral), it is no longer a function of x. is it the anti-derivative you want to prove?
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