Change of variables Double integral I have 
$$\iint_A \frac{1}{(x^2+y^2)^2}\,dx\,dy.$$
$A$ is bounded by the conditions $x^2 + y^2 \leq 1$ and $x+y \geq 1$.
I initially thought to make the switch the polar coordinates, but the line $x+y=1$ is making it hard to find the limits of integration. 

$$
x+y = r(\cos\theta+\sin\theta) = r\sqrt{2}\sin\left(\theta+\frac\pi2\right).
$$
So
$$
\iint_A \frac{dx\,dy}{(x^2+y^2)^2} = \int_0^{\pi/2} \int_{(\csc(\theta+\pi/4))/\sqrt{2}}^1 \frac{r\,dr \, d\theta}{r^4}.
$$
$$
= \int_0^{\pi/2} \left(\int_{(\csc(\theta+\pi/4))/\sqrt{2}}^1\  \frac{dr}{r^3} \right) \, d\theta
$$
