Uppgift 5

$$\begin{aligned} \iint_D\frac1{(1+y)^3}\,dx\,dy &=\int_0^1\left(\int_x^1\frac1{(1+y)^3}\,dy\right)dx =\int_0^1\left[-\frac1{2(1+y)^2}\right]_x^1dx\\ &=\int_0^1\left(-\frac1{2(1+1)^2}-\left(-\frac1{2(1+x)^2}\right)\right)dx\\ &=\left[-\frac x8-\frac1{2(1+x)}\right]_0^1=-\frac18-\frac14+\frac12=\frac18. \end{aligned}$$