TITLE: Integral of $1/\sinh(x)$
QUESTION [5 upvotes]: Can you help me find the integral 
$$
\int{\frac{1}{\sinh(x)}dx}?
$$

REPLY [2 votes]: Arturo's answer brought to mind yet another way of computing this integral: cheat by using the formula $$\sinh x = -i \sin ix,$$ where $i = \sqrt{-1}$.  You can manipulate the imaginary units like ordinary (real) constants for the purposes of integration, and the result follows from the formula for $\int \csc x\,dx.$
Admittedly, the answer you'll get will have imaginary units in them, but you should be able to get rid of those via similar formulas (such as $\cos ix = \cosh x$, for example.)