Why does Wolfram Alpha get this domain wrong?

Question

I wanted to check on Wolfram if the domain of $\dfrac{\log |x|}{\arctan \left(x\right)\left(x-2\right)^{\frac{1}{3}}}$ I calculated was correct.

According to Wolfram it is $\{x \in \mathbb{R} : x>2 \}$

I put the function into Desmos and the plot shows that in $0$ and $2 $ the function diverges, as I had calculated myself.

Why doesn't WA show that?

Answer 1

Wolfram can use two conventions for the cubic root: principal or real-valued. The former returns a complex number, which can be ruled out.

Answer 2

You're confusing the cube root, which exists for all real numbers and the function $x^{1/3}$, which is defined only for $x>0$, as its definition is $$x^{1/3}\stackrel{\text{def}}{=}\mathrm e^{\tfrac13\ln x}.$$