Question

Integrate the following functions.
$\int \frac{1}{\sqrt{(2-x{)}^2+1}}dx.$

Answer 1

$\int \frac{1}{\sqrt{(2-x{)}^2+1}}dx=\int \frac{1}{\sqrt{(x-2{)}^2+1}}dx=log|(x-2)+\sqrt{(x-2{)}^2+1}|+C[\because \int \frac{dx}{\sqrt{x^2+a^2}}=log|x+\sqrt{x^2+a^2}|]$