Question

x3+2x2+4x+3/x+1 dx (интеграл 2 и 0)

Answer 1

$intlimits^2_0 frac{x^3+2x^2+4x+3}{x+1} , dx= intlimits^2_0 frac{(x^3+x^2)+(x^2+x)+(3x+3)}{x+1} , dx =\\= intlimits^2_0 frac{x^2(x+1)+x(x+1)+3(x+1)}{x+1} , dx= intlimits^2_0 frac{(x+1)(x^2+x+3)}{x+1} , dx =\\= intlimits^2_0 (x^2+x+3) , dx= (frac{x^3}{3}+frac{x^2}{2}+3x)Big |_0^2= frac{8}{3} +2+6=2frac{2}{3}+8=10frac{2}{3}$