Find arsinh(x) in terms of x

let y=arsinh(x)x=sinh(y)=(e^y - e^-y)/22x=e^y - e^-y2x*e^y=e^y-1 (multiply bye^y)0=(e^y)²-2xe^y-1This is a quadratic in e^y with coefficients: a=1,b=-2x,c=-1Usinng the quadratic formula (and simplifying):e^y=x +/- sqrt(x²+1)but e^y=x-sqrt(x²+1) isn't possible as e^y>0 for all y.so e^y=x+sqrt(x²+1)y=ln(x+sqrt(x²+1))arsinh(x)=ln(x+sqrt(x²+1)).(Note that sqrt(x) is standard notation for 'the square root of x' on computers).