Question

Вычислить неопределенный интеграл
$\frac{x^3-9x+13}{(x-1)(x^2-3x+2)}$

Answer 1

$\int \frac{x^3-9x+13}{\left ( x-1 \right )\left ( x^2-3x+2 \right )}dx=\int \frac{x^3-9x+13}{\left ( x-2 \right )\left ( x-1 \right )^2}dx=\int \frac{4x^2-14x+15}{\left ( x-2 \right )\left ( x-1 \right )^2}dx+\int dx\\\int \frac{dx}{x-1}-5\int \frac{dx}{\left ( x-1 \right )^2}+3\int \frac{dx}{x-2}+\int dx\\ln\left | x-1 \right |+\frac{5}{x-1}+3ln\left | x-2 \right |+x+C$