Prove

Let $2-x=t$

$\Rightarrow-d x=d t$

$\Rightarrow \int \frac{1}{\sqrt{(2-x)^{2}+1}} d x=-\int \frac{1}{\sqrt{t^{2}+1}} d t$

$=-\log \left|t+\sqrt{t^{2}+1}\right|+\mathrm{C}$   $\left[\int \frac{1}{\sqrt{x^{2}+a^{2}}} d t=\log \left|x+\sqrt{x^{2}+a^{2}}\right|\right]$

$=-\log \left|2-x+\sqrt{(2-x)^{2}+1}\right|+\mathrm{C}$

$=\log \left|\frac{1}{(2-x)+\sqrt{x^{2}-4 x+5}}\right|+C$