<s>[INST] What is the indefinite integral of $\sqrt[4] {\tan \left( x\right) }$ $$\int\sqrt[4] {\tan \left( x\right) } dx$$
I'm really stuck right now with this integral, so any kind of advice would be appreciated. 
Perhaps a pretty nifty substitution that can save me from partial fraction decomposition.
 [/INST] $$ \small \left( x^2 + \sqrt{2 + \sqrt 2} \; x + 1 \right)  \left( x^2 - \sqrt{2 + \sqrt 2} \; x + 1 \right) \left( x^2 + \sqrt{2 - \sqrt 2} \; x + 1 \right) \left( x^2 - \sqrt{2 - \sqrt 2} \; x + 1 \right) = x^8 + 1 $$
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