<s>[INST] Integration of $\frac{1}{(1+x^4)^\frac{1}{4}}$ This question has been puzzling me a lot. This is in the middle list of question(meaning its moderately tough). I have tried everything i could think of. 
My try: $$\int \frac{1}{x(1+\frac{1}{x^4})^\frac{1}{4}}dx$$
$$-\frac{1}{4}\int \frac{-4x^4}{x^5(1+ \frac{1}{x^4})^\frac{1}{4}}dx$$
putting $$1 + \frac{1}{x^4} = t \iff x^4=\frac{1}{t-1} \iff dt = -\frac{4}{x^5}dx$$ and substituting in the integral,
$$-\frac{1}{4}\int \frac{1}{(t-1)t^\frac{1}{4}}dt$$ 
And Now I am stuck here.
 [/INST] Try this let $t^4 = 1 + x^{-4}$ 
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