Hello In the following integral which I obtained from Wolfram, what is the physical meaning (e.g. in a heat conduction problem) of $\displaystyle \sqrt{-\sinh^{2}(bx)}$. Thanks.
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Unfortunately, your attachment didn't work and without a link to the Wolfram citation, it is impossible to answer your question.
Originally Posted by HallsofIvy Unfortunately, your attachment didn't work and without a link to the Wolfram citation, it is impossible to answer your question. This is Wolfram link: Wolfram Mathematica Online Integrator
This is the integral according to Wolfram: $\displaystyle \int\frac{dx}{\cosh^{3n+1}(bx)}=\frac{\sinh(bx)\co sh^{-3n}(bx)}{3nb\sqrt{-\sinh^{2}(bx)}}\,_{2}F_{1}\left(\frac{1}{2},-\frac{3n}{2};\frac{2-3n}{2};\cosh^{2}(bx)\right)$
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