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sqrt(2)* E(x | 1/2)

where E is EllipticE, "the elliptic integral of the second kind" ( http://documents.wolfram.com/mathematica/functions/EllipticE/ ), which says E(k | m) is the integral of sqrt(1 - m sin^2 x)dx from 0 to k. Not that helpful.

Seems like there is a big class of functions like f(x), when you try to automatically integrate them you get a result like "g(x), where g(x) is defined as the integral of f(x)".