$$ 22.\,\int\!\! \frac{dx}{ax^2+b} = \left \{ \begin{array}{cc} \!\!\!\!\frac{1}{\sqrt{ab}}\arctan \sqrt {\frac {a}{b}}x +C & \textrm (b>0) \\ \frac{1}{2 \sqrt{-ab}} \ln\Big \vert \frac { \sqrt {a}x - \sqrt {-b}}{\sqrt{a}x+ \sqrt{-b}} \Big \vert + C & \textrm (b<0) \end{array} \right. $$

$$ 23.\,\int\!\! \frac{x} {ax^2 +b} dx = \frac{1}{2a} \ln \vert ax^2+b \vert +C $$

$$ 24.\,\int\!\! \frac{x^2}{ax^2+b} dx= \frac{x}{a} - \frac{b}{a} \int\!\! \frac{dx}{ax^2+b} $$

$$ 25.\,\int\!\! \frac {dx} { x(ax^2+b)} = \frac {1}{2b} \ln \frac {x^2}{ \vert ax^2+b \vert } +C $$

$$ 26.\,\int\!\! \frac {dx}{x^2(ax^2+b)} = - \frac{1}{bx} - \frac{a}{b} \int\!\! \frac {dx}{ax^2+b} $$

$$ 27.\,\int\!\! \frac{dx}{x^3(ax^2+b)} = \frac {a}{2b^2} \ln \frac { \vert ax^2+b\vert }{x^2} - \frac{1}{2bx^2} + C $$

$$ 28.\,\int\!\! \frac{dx}{(ax^2+b)^2} = \frac{x}{2b(ax^2+b)} + \frac{1}{2b} \int\!\! \frac {dx} { ax^2+b} $$