Indefinite integral of 1/(1+x^4)^(1/4)

[hellais]

We are having problems solving the indefinite integral of the following function:
$$\frac{dx}{\sqrt[4]{1+x^4}}$$
We tried the substitution $$t^4=x^4+1$$, but we got stuck.

Our professor tried solving it, but he also encountered difficulties.
Any suggestion is apreciated.

(wolfram alpha says that the integral is a hypergeometric function, but it must be simpler)

 

[CompuChip]

It's not going to help you solve it, but here's a Wolfram Alpha trick.

 

[tiny-tim]

Hi hellais!

I think you just have to keep substituting again and again …

x² = sinhu, a = tanhu …