Double Integral Calculation with Variable Substitution

[physmatics]

Homework Statement

Calculate the double integral over D
\int\int x*ln(2x + y)/y^3 dx dy
D is the finite area in the xy-plane within the straight lines
2x + y = 1
2x + y = 3
x = y
x = 2y

Homework Equations

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The Attempt at a Solution

I thought it was obvious to make the variable substitution
u = x/y<br /> v = 2x + y
which gives us the boundaries
1 \leq u \leq 2<br /> 1 \leq v \leq 3
So far so good. Now, the problem is that I can't really substitute the whole integral. I thought this would solve itself by the Jacobian, but it turns out to be
y^2/2x + y
which I really don't need.
Should I really use this variable substitution? I don't know what else to do.

 

[tiny-tim]

hi physmatics!

have you tried just substituting v = 2x + y, and keeping y as the other variable?

 

[physmatics]

I wrote the Jacobian as a fraction instead, it turned out to work perfectly :)
Should have looked closer at it!