Question

Integrate the following eqn



y = dx / (e^x - e^-x)​

Answer 1

$y = ( {e}^{x} - {e}^{ - x} ) \: dx \\ \\ integrating \: rhs \: we \: get \\ \\ {e}^{x} - ( - {e}^{ - x} ) + c\\ = {e}^{x} + {e}^{ - x} + c \\ = {e}^{x} + \frac{1}{ {e}^{ x} } + c \\ = \frac{ { {(e}^{x} )}^{2} + 1}{ {e}^{x} } + c \\ = \frac{ {e}^{2x} + 1}{ {e}^{x} } + c$