<s>[INST] Evalutate $\int\frac{dx}{x\sqrt{1-\frac{4}{3}x^4}}$ How to integrate
$$\int\frac{dx}{x\sqrt{1-\frac{4}{3}x^4}}$$
Mathematica found
$$\ln x-\frac{1}{2}\ln\left(1+\sqrt{1-\frac{4}{3}x^4}\right)$$
but I can't find a method to arrive at this solution.
 [/INST] Try $u=\sqrt{1-(4/3)x^4}$, $u^2=1-(4/3)x^4$, $2u\,du=-(16/3)x^3\,dx$, together with $dx/x=x^3\,dx/x^4$. 
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