Question

Помогите решить интеграл

Answer 1

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