Heavy integral

[janhaa]

Try to solve this integral:

I=\int \frac{\sqrt{\sqrt{x^4+1}-x^2}}{x^4+1}\,{\rm dx}

[dextercioby]

Subbing x^2 =\sinh t will give you something like this

I=\int \frac{\sqrt{\coth t -1}}{\cosh t}{}dt

Feed it now to Mathematica. There's about 50% chances it will return a complicated expression in terms of elliptic integrals.

[janhaa]

Nice substitution, I managed to solve it now.
Thanks

[dextercioby]

Apparently the integral is expressible in terms of elementary functions.