Primitive of p x + q over a x squared plus 2 b x plus c/Examples

Examples of Use of Primitive of $\dfrac {p x + q} {a x^2 + 2 b x + c}$

Primitive of $\dfrac {2 x + 1} {3 x^2 + 4 x + 2}$

$\ds \int \dfrac {2 x + 1} {3 x^2 + 4 x + 2} \rd x = \dfrac 1 3 \ln \size {3 x^2 + 4 x + 2} - \dfrac 1 {3 \sqrt 2} \map \arctan {\dfrac {3 x + 2} {\sqrt 2} } + C$