(x^2+1)(x-2)(3-x)<0
=>(x-2)(3-x)<0
=>(x-2)(x-3)>0
TH1: \(\left\{{}\begin{matrix}x-2>0\\x-3>0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x>2\\x>3\end{matrix}\right.\)
=>x>3
TH2: \(\left\{{}\begin{matrix}x-2< 0\\x-3< 0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x< 2\\x< 3\end{matrix}\right.\)
=>x<2