Book:Murray R. Spiegel/Mathematical Handbook of Formulas and Tables/Chapter 14/Integrals Involving Root of a x squared plus b x plus c

Integrals Involving $\sqrt{a x^2 + b x + c}$

In the following results if $b^2 = 4 a c$, $\sqrt{a x^2 + b x + c} = \sqrt a \left({x + b / 2 a}\right)$ and the results from Integrals Involving $a x + b$ can be used. If $b = 0$ use results from Integrals Involving $\sqrt {x^2 + a^2}$, Integrals Involving $\sqrt {x^2 - a^2}$, $x^2 > a^2$ and Integrals Involving $\sqrt {a^2 - x^2}$, $a^2 > x^2$. If $a$ or $c = 0$ use results from Integrals Involving $\sqrt{a x + b}$.

$14.280$: Primitive of $\dfrac 1 {\sqrt{a x^2 + b x + c}}$

$14.281$: Primitive of $\dfrac x {\sqrt{a x^2 + b x + c}}$

$14.282$: Primitive of $\dfrac {x^2} {\sqrt{a x^2 + b x + c}}$

$14.283$: Primitive of $\dfrac 1 {x \left({\sqrt{a x^2 + b x + c}}\right)}$

$14.284$: Primitive of $\dfrac 1 {x^2 \left({\sqrt{a x^2 + b x + c}}\right)}$

$14.285$: Primitive of $\sqrt{a x^2 + b x + c}$

$14.286$: Primitive of $x \sqrt{a x^2 + b x + c}$

$14.287$: Primitive of $x^2 \sqrt{a x^2 + b x + c}$

$14.288$: Primitive of $\dfrac {\sqrt{a x^2 + b x + c}} x$

$14.289$: Primitive of $\dfrac {\sqrt{a x^2 + b x + c}} {x^2}$

$14.290$: Primitive of $\dfrac 1 {\left({a x^2 + b x + c}\right)^{3/2}}$

$14.291$: Primitive of $\dfrac x {\left({a x^2 + b x + c}\right)^{3/2}}$

$14.292$: Primitive of $\dfrac {x^2} {\left({a x^2 + b x + c}\right)^{3/2}}$

$14.293$: Primitive of $\dfrac 1 {x \left({a x^2 + b x + c}\right)^{3/2}}$

$14.294$: Primitive of $\dfrac 1 {x^2 \left({a x^2 + b x + c}\right)^{3/2}}$

$14.295$: Primitive of $\left({a x^2 + b x + c}\right)^{n + 1 / 2}$

$14.296$: Primitive of $x \left({a x^2 + b x + c}\right)^{n + 1 / 2}$

$14.297$: Primitive of $\dfrac 1 {\left({a x^2 + b x + c}\right)^{n + 1 / 2}}$

$14.298$: Primitive of $\dfrac 1 {x \left({a x^2 + b x + c}\right)^{n + 1 / 2}}$