How can I handle divergence that appears in many physical problem?

Question

I came across with the following type of integration with singularity.

$$\int_{s_2=0}^{s_2=\infty}\int_{s_1=0}^{s_1=s_2}\left(\frac{1}{s_2-s_1}\right)^{3/2} \,ds_1\,ds_2 \, .$$ How can I solve it?

Answer 1

This seems like a straightforward application of the usual rules, applying the power rule gives

$$\int_0^{\infty}{1\over 2}(s_2-s_1)^{-1/2}\bigg|_{s_1=0}^{s_1=s_2}\,ds_2$$

which of course is divergent.