Primitive of x squared over a x squared plus b x plus c/Examples

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

Primitive of $\dfrac {6 x^2 + 10 x + 5} {3 x^2 + 4 x + 2}$

$\ds \int \dfrac {6 x^2 + 10 x + 5} {3 x^2 + 4 x + 2} \rd x = 2 x + \dfrac 1 3 \ln \size {3 x^3 + 4 x + 2} - \dfrac 1 {3 \sqrt 2} \arctan \dfrac {3 x + 2} {\sqrt 2} + C$