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

Integrals Involving $a x + b$

 * $14.59$: Primitive of $\dfrac 1 {a x + b}$


 * $14.60$: Primitive of $\dfrac x {a x + b}$


 * $14.61$: Primitive of $\dfrac {x^2} {a x + b}$


 * $14.62$: Primitive of $\dfrac {x^3} {a x + b}$


 * $14.63$: Primitive of $\dfrac 1 {x \left({a x + b}\right)}$


 * $14.64$: Primitive of $\dfrac 1 {x^2 \left({a x + b}\right)}$


 * $14.65$: Primitive of $\dfrac 1 {x^3 \left({a x + b}\right)}$


 * $14.66$: Primitive of $\dfrac 1 {\left({a x + b}\right)^2}$


 * $14.67$: Primitive of $\dfrac x {\left({a x + b}\right)^2}$


 * $14.68$: Primitive of $\dfrac {x^2} {\left({a x + b}\right)^2}$


 * $14.69$: Primitive of $\dfrac {x^3} {\left({a x + b}\right)^2}$


 * $14.70$: Primitive of $\dfrac 1 {x \left({a x + b}\right)^2}$


 * $14.71$: Primitive of $\dfrac 1 {x^2 \left({a x + b}\right)^2}$


 * $14.72$: Primitive of $\dfrac 1 {x^3 \left({a x + b}\right)^2}$


 * $14.73$: Primitive of $\dfrac 1 {\left({a x + b}\right)^3}$


 * $14.74$: Primitive of $\dfrac x {\left({a x + b}\right)^3}$


 * $14.75$: Primitive of $\dfrac {x^2} {\left({a x + b}\right)^3}$


 * $14.76$: Primitive of $\dfrac {x^3} {\left({a x + b}\right)^3}$


 * $14.77$: Primitive of $\dfrac 1 {x \left({a x + b}\right)^3}$


 * $14.78$: Primitive of $\dfrac 1 {x^2 \left({a x + b}\right)^3}$


 * $14.79$: Primitive of $\dfrac 1 {x^3 \left({a x + b}\right)^3}$


 * $14.80$: Primitive of $\left({a x + b}\right)^n$


 * $14.81$: Primitive of $x \left({a x + b}\right)^n$


 * $14.82$: Primitive of $x^2 \left({a x + b}\right)^n$


 * $14.83$: Primitive of $x^m \left({a x + b}\right)^n$:


 * Three formulas are given for this case:


 * Decrement of Power of $a x + b$


 * Decrement of Power of $x$


 * Increment of Power of $a x + b$


 * The fourth form is not given:


 * Increment of Power of $x$