Answer
$x^{2}+1$ for all real numbers $x$.
Work Step by Step
Start with given expression: $|x^{2}+1|$.
Since $x^{2}+1$ must be positive for all $x$, the absolute value is the same as what is inside the absolute value for all $x$:
$|x^{2}+1|=x^{2}+1 $ for all $x$.
