Primitive of p x + q over Root of a x squared plus 2 b x plus c/Examples

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

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

$\ds \int \dfrac {1 + x} {\sqrt {2 + 4 x - 3 x^2} } \rd x = -\dfrac 1 3 \sqrt {2 + 4 x - 3 x^2} + \dfrac 5 {3 \sqrt 3} \map \arcsin {\dfrac {3 x - 2} {\sqrt {10} } } + C$