Question

Integrate:
$\frac{x^2-3x+2}{x^2+3x-10}$

Answer 1

${\int }^{}\frac{x^2-3x+2}{x^2+3x-10}dx$

$={\int }^{}\frac{\left(x-2\right)\left(x-1\right)}{\left(x-2\right)\left(x+5\right)}dx$

$={\int }^{}\frac{\left(x-1\right)}{x+5}dx$

$={\int }^{}\left(1-\frac{6}{x+5}\right)dx$

$I=x-6\log \left(x+5\right)+C$

Hence, this is the answer.