Project Updates... Stuck!

Currently, I am reading up one of the research papers that were given by Prof. While reading and coding in high level langauge, I came across this interestingly strange mathematical stuff named as: Incomplete elliptical integral of the second kind.

Like this:

My first reaction: Oh God! What is that???? Not taught in my engine courses..... How?

Lets' turn to Google and see what does it showed up in the searches:

Elliptic integral

Elliptic Integral of the Second Kind (Complete)

Elliptic integrals of the first and second kind and Elliptic Integral Overview and a quick calculator is here (link).

Great! But how to code it?

- wong chee tat :)