How do you derive the formula of S csch(x)(dx)=ln (tanh (x/2)) +C ?

The integrand can be transformed to functions of tanh (x/2) by first observing that sinh 2A = 2sinh A cosh A,

from which

csch(x) = 1/(2sinh(x/2)cosh(x/2)).

Clever algebra, followed by an application of the Pythagorean properties, produces the desired result. Then substitute u for tanh(x/2). You will have to be clever again to figure out what to substitute for dx in terms of du. The result integral is remarkably simple! Confirm that the formula works by evaluatinng the integral on the interval (1,2), then checking by numerical integration.

This has got me confused!!!