What is the solution to this 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.