Help with a Double Integral Problem (Multivariable Calculus)

Find the average value, L, of the function f(x,y) = 5(x+y)lnx over the rectangle
A = {(x,y): 1≤x≤4, 0≤y≤4}.

How exactly would I solve this problem. I tried solving with respect to y first by using integration by parts. The answer I got was incorrect.

Please help (best answer gets 10 points).

Take the double integral and divide by the area of the rectangle.

Int[1≤x≤4, 0≤y≤4] 5(x+y) ln(x) dy dx
Int[1≤x≤4] 5(4x+8) ln(x) dx
640 ln(2) - 195

(640 ln(2) - 195)/12
20.7