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

Integrals Involving $a x^2 + b x + c$

$14.265$: Primitive of $\dfrac 1 {a x^2 + b x + c}$

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

$14.266$: Primitive of $\dfrac x {a x^2 + b x + c}$

$14.267$: Primitive of $\dfrac {x^2} {a x^2 + b x + c}$

$14.268$: Primitive of $\dfrac {x^m} {a x^2 + b x + c}$

$14.269$: Primitive of $\dfrac 1 {x \left({a x^2 + b x + c}\right)}$

$14.270$: Primitive of $\dfrac 1 {x^2 \left({a x^2 + b x + c}\right)}$

$14.271$: Primitive of $\dfrac 1 {x^n \left({a x^2 + b x + c}\right)}$

$14.272$: Primitive of $\dfrac 1 {\left({a x^2 + b x + c}\right)^2}$

$14.273$: Primitive of $\dfrac x {\left({a x^2 + b x + c}\right)^2}$

$14.274$: Primitive of $\dfrac {x^2} {\left({a x^2 + b x + c}\right)^2}$

$14.275$: Primitive of $\dfrac {x^m} {\left({a x^2 + b x + c}\right)^n}$

$14.276$: Primitive of $\dfrac {x^{2 n - 1}} {\left({a x^2 + b x + c}\right)^n}$

$14.277$: Primitive of $\dfrac 1 {x \left({a x^2 + b x + c}\right)^2}$

$14.278$: Primitive of $\dfrac 1 {x^2 \left({a x^2 + b x + c}\right)^2}$

$14.279$: Primitive of $\dfrac 1 {x^m \left({a x^2 + b x + c}\right)^n}$