how to assign integration limits in mathematica after solving a set of inequalities

I have a set of inequalities, for example,

2 x1 >=3 x2 && 0<=x1<=1 && 0<=x2<=1

which can be solved with Reduce. Then I want to do an integration for t开发者_如何学Gohe function f(x1,x2)=1/x1 in the area defined by the inequalities above. In this case, Reduce gives a result

(x1 == 0 && x2 == 0) || (0 < x1 <= 1 && 0 <= x2 <= (2 x1)/3)

Then I can do integration by using

Integrate[Integrate[1/x1, {x2, 0, 2 x1/3}], {x1, 0, 1}]

But these all need my manual intervention. How do I do this in a streamline fashion? Many thanks!

Integrate[1/x1 Boole[2 x1 >= 3 x2 && 0 <= x1 <= 1 &&0 <= x2 <= 1], {x1, -\[Infinity], \[Infinity]}, {x2, -\[Infinity], \[Infinity]}]