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 $x$