You have uploaded an image containing a set of double integrals. I will analyze the image and solve any of the problems you choose. Which integral should I begin solving for you?

Here is a summary of the problems in the image:

1. Integral 9:
   $\int_0^1 \int_0^1 \frac{x}{(xy+1)^2} \, dy \, dx$

2. Integral 10:
   $\int_{\pi/2}^{\pi} \int_1^2 x \cos xy \, dy \, dx$

3. Integral 11:
   $\int_0^{\ln 2} \int_0^1 x y e^{y^2 x} \, dy \, dx$

4. Integral 12:
   $\int_3^4 \int_1^2 \frac{1}{(x+y)^2} \, dy \, dx$

Let me know which one you'd like me to work on or if you'd like detailed steps for multiple problems.