How do I compute this integral? I'm wondering how to compute the integral $$ \int_2^3\int_0^\sqrt{3x-x^2}\frac{1}{(x^2+y^2)^{1/2}}\,\mathrm{d}y\mathrm{d}x. $$ Clearly it is too complicated to do it directly, so I'm guessing you have to do some change of variables. But what kind of change? This is not really a sphere, so I don't think that polar coordinates would be so good.

You'll actually want to use polar coordinates. Set your first integral to y, square that y, and you should see you can move x to the left-hand side. You can then turn this into your r value for polar coordinates. You'll also note that it's mapping a sphere in the upper-right coordinate (which allows you to pick the theta values). From there it's a rather simple integration. I'll purposely leave the work to you, if you need clarification let me know.  
