Integrating: $ \;\int \frac{1}{x^2+3x+2} dx $ How can I solve the following integral:
$$ \int  \frac{1}{x^2+3x+2} dx $$
Should I proceed by changing the variable (substitution)? or should I use integration by parts? Or another method altogether?
Thank you!

Just for fun, I tried it another way.
Complete the square
$$
\frac{1}{x^2+3x+2} = \frac{1}{(x+\frac{3}{2})^2-\frac{1}{4}}
$$
Change variables $y=x+\frac{3}{2}$
$$
\int\frac{dx}{x^2+3x+2} = \int\frac{4}{4y^2-1} = {-2\;\mathrm{atanh}(2y)+C}
$$
Substitute back
$$
\int\frac{dx}{x^2+3x+2}=-2\;\mathrm{atanh}(2x+3) + C
$$
Check by differentiating
$$
\frac{d}{dx}\;\big(-2\;\mathrm{atanh}(2x+3)\big)
=\frac{-4}{1-(2x+3)^2} = \frac{1}{x^2+3x+2}
$$
OK
