Question

Пожалуйста♥♥♥♥♥♥♥♥♥♥♥♥♥♥

Answer 1

$int frac{3x^2-2}{(x+1)(x^2+x+1)}dx=int frac{dx}{x+1}+int frac{2x-3}{x^2+x+1}dx=ln|x+1|+int frac{(2x-3)dx}{(x+frac{1}{2})^2+frac{3}{4}} =\\=Big [, t=x+frac{1}{2}; ,; x=t-frac{1}{2},; dx=dt, Big ]=ln|x+1|+int frac{(2t-4)dt}{t^2+frac{3}{4}}=\\=ln|x+1|+int frac{2t, dt}{t^2+frac{3}{4}}-4int frac{dt}{t^2+frac{3}{4}}=\\=ln|x+1|+ln|t^2+frac{3}{4}|-4cdot frac{2}{sqrt3}, arctgfrac{2t}{sqrt3}+C=\\=ln|x+1)+ln|x^2+x+1|-frac{8}{sqrt3}, arctgfrac{2x+1}{sqrt3}+C; .$