Inverse sine hyperbolic functions in log form Sinh^-1 (x)= Ln(x+sq(x^2+1^2)

In this video I am scaffolding to discovering Inverse hyperbolic sine function from the definition of Sine hyperbolic function.
Sinh(x)= (e^x-e^-x)/2 swap x and y and then solving for y using quadratic formula by reducing the form into quadratic equations. the video shows all the steps in arriving to the conclusion.
this inverse hyperbolic sine function helps to find the area under the curve of hyperbolic function f(x)=sq(x^2+a^2)