The question is as in the title: is $K\_2(\mathbb{Z}[x,x^{-1}])$ known?



What is $K_2(\mathbb{Z}[x,x^{-1}])$?
Bass/Quillen's Fundamental Theorem of Algebraic K-theory gives:
$$K\_n(R[x,x^{-1}])=K\_n(R)\oplus K\_{n-1}(R)\oplus NK\_n(R)\oplus NK\_n(R)$$
where the two identical nil-terms vanish for $R$ regular. 


Because ${\mathbb Z}$ is regular, this gives
$$K\_2({\mathbb Z}[x,x^{-1}])
=K\_2({\mathbb Z})\oplus K\_1({\mathbb Z}) 
\approx 
{\mathbb Z}/2{\mathbb Z}\oplus {\mathbb Z}/2{\mathbb Z}$$


