Integral dupla quociente x entre 0 e 1 e y entre -3 e 3

[pri28]

∫∫ (xy^2)/ (x^2+1) dydx {(x,y)/ 0≤x≤1, -3≤y≤3}

[Fraol]

\(\int_{0}^{1}\int_{-3}^{3} \frac{xy^3}{x^2+1}dydx = \\\\ \int_{0}^{1} \frac{x}{x^2+1}dx \cdot \left ( \frac{1}{3}y^3 \right )_{-3}^3 = \\\\ 18 \int_{0}^{1} \frac{x}{x^2+1}dx = 18 \cdot \left ( \frac{1}{2} ln(x^2+1) \right )_0^1 = \\\\ 9 \cdot ln(2)\)