Question

Integrate the function $\frac{1}{\sqrt{(2-x{)}^2+1}}$

Answer 1

$I=\int \left(\frac{1}{\sqrt{(2-x^2)+1}}\right)let2-x=tthendx=-dtthereforeI=\left(\frac{1}{\sqrt{(1+t^2)}}\right)=-log|t+\sqrt{1+t^2}|+c=-log\left|\right(2-x)+\sqrt{(2-x{)}^2+1}|+c$