Can the Indefinite Integral of 1/(1+x^4) be Simplified?

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SUMMARY

The indefinite integral of the function 1/(1+x^4) cannot be simplified easily and is expressed as a hypergeometric function. Attempts to solve the integral using the substitution t^4=x^4+1 have proven ineffective, as both students and their professor faced challenges. Alternative substitution methods, such as x^2 = sinh(u) and a = tanh(u), have been suggested but have not yielded a straightforward solution.

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We are having problems solving the indefinite integral of the following function:
[tex]\frac{dx}{\sqrt[4]{1+x^4}}[/tex]
We tried the substitution [tex]t^4=x^4+1[/tex], 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)
 
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Hi hellais! :smile:

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

x2 = sinhu, a = tanhu … :rolleyes:
 

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