Answer
$\sqrt {4+x^2}+c$
Work Step by Step
Consider the integral $\int \dfrac{x dx}{\sqrt {4+x^2}}$
The given integral can be re-written as: $\int (4+x^2)^{(-1/2)}x dx=(\dfrac{1}{2})\int (4+x^2)^{(-1/2)}(2x) dx$
This implies that $(\dfrac{-1}{2})(\dfrac{(4+x^2)^{1/2}}{1/2})+c=\sqrt {4+x^2}+c$
