How to get the general expression of a double integral?

Questions
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1

Hi WC!
I wanted to calculate a distribution function from a density function which is not null only over a certain area.
After searching the documentation, I found a handy function which did exactly what I needed:

Integrate[(2y/x)Boole[y<x<1/y],{y,0,w},{x,0, z}]

When I manually substitute w and z by some concrete values, the expression works as expected. However, I would like to see the general expression. Can I do this somehow or is it not possible in Mathematica?

2

Can you possibly give it any hints about your assumptions for the domains and ranges? And possibly integrate over just some of the non-zero portions?

In[1]:= Assuming[0 < y && 0 < w, Integrate[(2 y/x) Boole[y < x < 1/y], {y, 0, w}, {x, 1/y, y}]]

Out[1]= Piecewise[{{-1, w > 1}}, w^2*(-1 + 2*Log[w])]
3

That’s exactly what I wanted. Thank you!