Primitive of Reciprocal of Root of a x squared plus b x plus c/Examples

Examples of Use of Primitive of $\dfrac 1 {\sqrt {a x^2 + b x + c} }$

Primitive of $\dfrac 1 {\sqrt {2 + 4 x - 3 x^2} }$

$\ds \int \dfrac {\d x} {\sqrt {2 + 4 x - 3 x^2} } = \dfrac 1 {\sqrt 3} \map \arcsin {\dfrac {3 x - 2} {10} } + C$

Primitive of $\dfrac 1 {\sqrt {x^2 + 4 x + 5} }$

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

Primitive of $\dfrac 1 {\sqrt {2 x - x^2} }$

$\ds \int \dfrac {\d x} {\sqrt {2 x - x^2} } = \map \arcsin {x - 1} + C$

Primitive of $\dfrac 1 {\sqrt {2 x + x^2} }$

$\ds \int \dfrac {\d x} {2 x + x^2} = $