$\displaystyle \displaystyle \int^{3}_{0} \frac{\big(x^{3}(3-x)\big)^{\frac{1}{4}}}{5-x} \ dx $

There is a worked solution on Wikipedia using contour integration. I find it quite confusing.

Methods of contour integration - Wikipedia, the free encyclopedia

However, you don't have to resort to contour integration to solve the problem. There's a much easier (albeit longer) way.