Double Integrals and Polar Coordinates

Hi there,

First off, I'm having a bit of trouble changing this integral's bounds so that I can evaluate it starting by integrating the dx part first. Any helps/tips will be appreciated.

$\displaystyle \int_1^3{\int_0^{\ln{x}} xdy}dx$

Second, I've just finished learning how to change variables into polar coordinates, but I'm still a bit confused on how to go about doing so. Here is an example I'm trying to evaluate, but I'm not quite sure where to start:

$\displaystyle \int_0^4{\int_{\sqrt{x}}^2{e}^{y^3}dy}dx$

Thanks.