Why is it arsinh rather than arcsinh?
Ever wondered why we say arcsin for the inverse of the sine function, but arsinh for the inverse of the hyperbolic sine function? It's because arcsin gives the arc length on the unit circle for a given y-coordinate, whereas arsinh gives an area enclosed by a hyperbola and two rays from the origin for a given y-coordinate. The red shaded area below is equal to arsinh(a), where a is the length of the blue line segment.