[tex]\displaystyle I =\int \dfrac{x}{\sqrt{x^2+4}}\, dx \\ \\\\ \text{Facem schimbarea de variabila: }\\ \\ \sqrt{x^2+4} = t \Rightarrow \Big(\sqrt{x^2+4}\Big)' \, dx = t'\, dt \Rightarrow \dfrac{(x^2+4)'}{2\sqrt{x^2+4}}\, dx = dt \Rightarrow \\ \\ \Rightarrow \dfrac{2x}{2\sqrt{x^2+4}}\, dx = dt \Rightarrow \dfrac{x}{\sqrt{x^2+4}}\, dx = dt \\ \\\\ I = \int\, dt = \int 1\, dt = t+C = \sqrt{x^2+4}+C[/tex]
