It cannot be evaluated..it is called elliptical integral of second kind.

See:

http://www.ebyte.it/library/docs/math05a/EllipseCircumference05.html

It cannot be evaluated in terms of functions already known to us.

We do not know the anti-derivative of the integrand.

So we define a function called elliptical integral of second kind:-the anti-derivative of the integrand.

There are other such functions too like.

= Sine integral (x)

The function "sine integral" on differentiating gives sin(x) / x