Question

Помогите решить интеграл

Answer 1

$\int\limits^3_{\sqrt{3}} { \frac{2dx}{9+x^2} }= \int\limits^3_{\sqrt{3}} { \frac{2dx}{9(1+ \frac{x^2}{9})} }=\int\limits^3_{\sqrt{3}} { \frac{2d( \frac{x}{3} )}{3(1+ (\frac{x}{3})^2)} }=\frac{2}{3} arctg(\frac{x}{3})= \\\\ = (\frac{2}{3} arctg(\frac{3}{3}))-(\frac{2}{3} arctg(\frac{ \sqrt{3} }{3}))=\frac{2}{3}* \frac{ \pi }{4} -\frac{2}{3}* \frac{ \pi }{6} =\frac{ \pi }{6} -\frac{ \pi }{9} = \frac{ \pi }{18}$