Primitive of x over Root of a x squared plus b x plus c/Examples/x over Root of x^2 + 4 x + 5

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

 * $\ds \int \dfrac {x \rd x} {\sqrt {x^2 + 4 x + 5} } = \sqrt {x^2 + 4 x + 5} - 2 \map \ln {x + 2 + \sqrt {x^2 + 4 x + 5} } + C$

Proof
From Primitive of $\dfrac x {\sqrt {a x^2 + b x + c} }$ with: