Question

Помогите пожалуйста:/

Answer 1

$int frac{2x^3-1}{x^3+3x^2}, dx=int Big (2-frac{6x^2+1}{x^2(x+3)}Big ), dx=Q\\\frac{6x^2+1}{x^2(x+3)}=frac{A}{x^2}+frac{B}{x}+frac{C}{x+3}\\6x^2+1=A(x+3)+Bx(x+3)+Cx^2\\x=0:; ; A=frac{6x^2+1}{x+3}=frac{1}{3}\\x=-3:; ; C=frac{6x^2+1}{x^2}=frac{55}{9}\\x^2, |; 6=B+C; ; ,; ; B=6-C=6-frac{55}{9}=-frac{1}{9}\\\Q=frac{1}{3} int frac{dx}{x^2}-frac{1}{9}int frac{dx}{x}+frac{55}{9}int frac{dx}{x+3}=-frac{1}{3x}-frac{1}{9}, ln|x|+frac{55}{9}, ln|x+3|+C$