Integral transformation

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I'm trying to do a transformation of an integration, I have that $$\int_{0.5}^1\int_0^{0.5}e^{xy}xydxdy$$

And I want to get that integrate $$\int_0^1\int_0^1 f(x,y)dxdy$$ Where the value of the second integral has the same value as the first, or something quite close

Is there any way to do this?

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Just take $u = 2x$ and $v = 2y-1$