$$ 10.\,\int\!\! \sqrt{ax+b} dx= \frac{2}{3a}\sqrt{(ax+b)^3}+C $$

$$ 11.\,\int\!\! x \sqrt{ax+b}dx=\frac{2}{15a^2}(3ax-2b)\sqrt{(ax+b)^3}+C $$

$$ 12.\,\int\!\! x^2 \sqrt{ax+b}dx=\frac{2}{105a^3}(15a^2x^2-12abx+8b^2)\sqrt{(ax+b)^3}+C $$

$$ 13.\,\int\!\! \frac{x}{\sqrt {ax+b}}dx= \frac{2}{3a^2}(ax-2b)\sqrt{ax+b}+C $$

$$ 14.\,\int\!\! \frac{x^2}{\sqrt {ax+b}}dx= \frac{2}{15a^2}(2a^2x^2-4abx+8b^2)\sqrt{ax+b}+C $$

$$ 15.\,\int\!\! \frac{dx}{x\sqrt{ax+b}}=\left \{ \begin{array}{cc} \!\!\!\!\frac{1}{\sqrt{b}}\ln \Big \vert \frac{ \sqrt{ax+b} - \sqrt{b}}{\sqrt{ax+b}+\sqrt{b}} \Big \vert + C & \textrm ( b>0) \\ \frac{2}{-\sqrt{-b}}\arctan \sqrt{\frac{ax+b}{-b}}+C & \textrm (b<0) \end{array} \right. $$

$$ 16.\,\int\!\! \frac{dx}{x^2\sqrt{ax+b}} = - \frac{\sqrt{ax+b}}{bx} - \frac{a}{2b}\int\!\! \frac{dx}{x\sqrt{ax+b}} $$

$$ 17.\,\int\!\! \frac{\sqrt{ax+b}}{x}dx = 2 \sqrt{ax+b}+b \int\!\! \frac{dx}{x\sqrt{ax+b}} $$

$$ 18.\,\int\!\! \frac{\sqrt{ax+b}}{x^2}dx= - \frac{\sqrt{ax+b}}{x}+ \frac{a}{2}\int\!\! \frac{dx}{x\sqrt{ax+b}} $$