9.4.9 Curvilinear integrals

(3) Problem: Calculate the line integral over the closed polygonal \( A B C D A \) using Ostrogradsky-Green formula: \[ \begin{array}{l} A(3 ; 2), \quad B(6 ; 2), \quad C(6 ; 4), \quad D(3 ; 4) \\ \oint_{L} \sqrt{x^{2}+y^{2}} d x+y\left[x y+\ln \left(x+\sqrt{x^{2}+y^{2}}\right)\right] d y \end{array} \]