Question

срочно!!!¡ интеграл

Answer 1

$int frac{(x+8)dx}{(x+2)(x+3)(x-1)} =Q\\ frac{x+8}{(x+2)(x+3)(x-1)}= frac{A}{x+2}+ frac{B}{x+3}+frac{C}{x-1}\\x=-2:; ; A= frac{6}{1cdot (-3)}=-2\\x=-3:; ; B= frac{5}{-1cdot (-4)} = frac{5}{4}\\x=1:; ; C= frac{9}{3cdot 4}= frac{3}{4}\\Q=-2int frac{dx}{x+2}+frac{5}{4} int frac{dx}{x+3}+ frac{3}{4}int frac{dx}{x-1}= \\=-2, ln|x+2|+frac{5}{4}, ln|x+3|+frac{3}{4}, ln|x-1|+C$