I'm trying to study the convergence of 

$$\int\_{1^+}^{3^-}\frac{1}{\sqrt{(3-x)(x-1)}}dx$$

But I'm not sure how to get started. Any suggestion or tip, for this kind of convergence problem?

The indefinite integral seems [a bit a of a mess](http://integrals.wolfram.com/index.jsp?expr=1%2Fsqrt%28%283-x%29%28x-1%29%29&random=false), involving the hyperbolic sine.

Thanks in advance!