Is the Integral of 1/sinh^2(x/2) a Principal Value Integral?

[Belgium 12]

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

 

[dextercioby]

If you're integrating wrt x, you can't have x in the RHS.

 

[pwsnafu]

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

Just to be clear, are you trying to evaluate
$\int_{-\infty}^{\infty} \frac{1}{\sinh ^2(x/2)} \, dx$

 

[rbj]

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?