Integral of $(3-x)/(x+2)$

Question

Will someone explain how to solve this integral: $$\int \frac{3-x}{x+2} dx =\, ?$$

Answer 1

There are a couple of ways to do it. I like this approach: rewrite the numerator as $5-(x+2)$ and then split it into two integrals.

Answer 2

Hint:

$\displaystyle \int \frac{3-x}{x+2} dx=\displaystyle \int\frac{3}{x+2}dx-\bigg[\int \frac{x+2}{x+2}dx-\int\frac{2}{x+2}dx\bigg]$