bounded by y=x^2, y=4, x=0. picture: graph y = x^2, y=4, and x=0 from x=0 to x=2 - Wolfram|Alpha

i set my integral: integrate 0 to 2 [ integrate x^2 to 4 x(1+y^2)^-0.5 dy ] dx

then I tried doing it, first integral results: x[arcsinh(y)] from 4 to x^2

but second integral, how to integrate x*arcsinh(x^2).

edit: is this how

[[x^2⋅arcsinh(x^2)] - [(x^4 +1)^.5]]/2