Question

$\int \frac{x+3}{\left(x-1\right)\left(x-2\right)\left(x-3\right)}dx$

Answer 1

$\int \frac{x+3}{(x-1)(x-2)(x-3)}dx$

By partial functions, we get

$\int (\frac{2}{x-1}-\frac{5}{x-2}+\frac{3}{x-3})dx$

$\int \frac{2}{x-1}dx-\int \frac{5}{x-2}dx+\int \frac{3}{x-3}dx$

$2ln(|x-1|)-5ln(|x-2|)+3ln(|x-3|)+c$