Compute the following double integrals taken on an unit square:

- $\displaystyle \int_0^1\int_0^1\sqrt{x^2+y^2}\,dx\,dy$
- $\displaystyle \int_0^1\int_0^1\frac{dx\,dy}{\sqrt{1+x^2+y^2}}$
- $\displaystyle \int_0^1\int_0^1\frac{dx\,dy}{1-xy}$
- $\displaystyle \int_0^1\int_0^1\frac{dx\,dy}{(2-xy)\ln(xy)}$
- $\displaystyle \int_0^1\int_0^1\frac{1-x}{\{-\ln(xy)\}^{5/2}}\,dx\,dy$