Consider the transformation given by

x = u +t^2

y= t - u^2

z= u + s + t

I computed the derivative of the transformation then used the inverse function theorem to show that the transformation is locally invertible. Now I want to write a triple integral in terms of the variables (u,s,t)

I cant find a way to solve (u,s,t) in terms of x,y,z

The subsitituitons just go in circles.