Primitive of Root of a x squared plus b x plus c over x

Theorem
Let $a \in \R_{\ne 0}$.

Then:
 * $\displaystyle \int \frac {\sqrt {a x^2 + b x + c} } x \ \mathrm d x = \sqrt {a x^2 + b x + c} + \frac b 2 \int \frac {\mathrm d x} {\sqrt {a x^2 + b x + c} } + c \int \frac {\mathrm d x} {x \sqrt {a x^2 + b x + c} }$