$$ 29.\,\int\!\! \frac{dx}{ax^2+bx+c}dx= \left \{ \begin{array}{cc} \!\!\! \frac{2}{\sqrt{4ac-b^2}} \arctan \frac {2ax+b}{\sqrt{4ac-b^2}}+C & \textrm (b^2<4ac) \\ \frac {1}{\sqrt {b^2-4ac}} \ln \Big \vert \frac {2ax+b-\sqrt{b^2-4ac}} {2ax+b+ \sqrt{b^2-4ac}} \Big \vert +C & \textrm (b^2>4ac) \end{array} \right. $$

$$ 30.\,\int\!\! \frac{x}{ax^2+bx+c} dx = \frac{1}{2a}\ln \vert ax^2+bx+c \vert - \frac{b}{2a} \int\!\! \frac {dx}{ax^2+bx+c} $$