Transforming parabola to straight line

[turin]

To the moderator: This isn't a HW question, but it probably sounds like one, so I appologize. Please move this to the HW forum if need be.

I have an integration domain inside three intersecting curves. Two of the curves are straightlines and the third is a parabola. These three boundaries are of the form

$$y=Ax \, \qquad y=Bx \, \qquad y=(1+x)^2$$

where A and B are arbitrary constant slopes > 4.
I want to transform the boundary of this domain into a triangle, as simply as possible. Any hints?

 

[Office_Shredder]

You don't just want to turn the parabola into a straight line, you want to keep the other straight lines as straight lines as well.

 

[turin]

You don't just want to turn the parabola into a straight line, you want to keep the other straight lines as straight lines as well.

Correct. I already know how to straighten the parabola, e.g. u=(1+x)^2; that's trivial.

BTW, I don't care about the Jacobian; my #1 priority is straight boundaries for the domain of integration.