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## Homework Statement

evaluate integral if R=[0,1]x[0,1]

[tex]\iint_R ln[(x+1)(y+1)]dA[/tex]

## The Attempt at a Solution

[tex]\int_{0}^{1}\int_{0}^{1} ln[(x+1)(y+1)] dydx[/tex]

by parts

[tex]u=ln[(x+1)(y+1)]; du = \frac{1}{(x+1)(y+1)}dy;dv=dy;v=y[/tex]

[tex]\int_{0}^{1} \Bigg[\frac{y}{(x+1)(y+1)} - \frac{1}{x+1}\int_{0}^{1} 1 - \frac{1}{y+1}dy\Bigg]dx[/tex]

[tex]\int_{0}^{1} \Bigg[\frac{1}{2(x+1)} - \frac{1}{x+1} - \frac{ln(2)}{(x+1)}\Bigg]dx[/tex]

[tex] \frac{1}{2}ln(2) - ln(2) - ln^2(2)[/tex]

not sure what I did wrong but I know thats the incorrect answer