Найти неопределенный интеграл dx/[latex] \sqrt{4-x^2[/latex]

[latex] \int\limits {1/ \sqrt{4-x^2} } \, dx =1/2 \int\limits {1/ \sqrt{1-x^2/4} } \, dx = \int\limits { 1/\sqrt{1-t^2} } \, dt =[/latex][latex]arcsint+C=arcsin(x/2)+C[/latex] t=x/2⇒dt=1/2dx

[latex]\displaystyle \int\frac{dx}{\sqrt{4-x^2}}=\int\frac{dx}{\sqrt{4\left(1-\frac{x^2}{4}\right)}}=\int\frac{dx}{2\sqrt{1-\frac{x^2}{4}}}=\int\frac{dx}{2\sqrt{1-\left(\frac{x}{2}\right)^2}}=[/latex] [latex]\displaystyle =\int\frac{\frac{1}{2}dx}{\sqrt{1-\left(\frac{x}{2}\right)^2}}=\int\frac{d\left(\frac{x}{2}\right)}{\sqrt{1-\left(\frac{x}{2}\right)^2}}=arcsin\left(\frac{x}{2}\right)+C.[/latex]