I have,

$$ \int uE^{2}\left(u\right)du $$

where $E$ is the complete elliptic integral of the second kind:

$$ E\left(k\right)=\int_{0}^{\frac{\pi}{2}}d\theta\sqrt{1-k^{2}\sin^{2}\left(\theta\right)} $$

I've tried integrating this by looking for something that differentiates into $E^2(u)$, though can't seem to find anything. Any help?

  • 1
    $\begingroup$ Do you specifically need an anti-derivative? Or would it suffice to obtain the definite integral over some interval? $\endgroup$ – David H Aug 28 '14 at 23:04

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