Primitive of x over a x + b squared/Also presented as

Primitive of $x$ by Power of $a x + b$: Also presented as

This result is also seen presented in the form:

$\ds \int \frac {x \rd x} {\paren {a x + b}^2} = \frac 1 {a^2} \paren {\ln \size {a x + b} + \frac b {a x + b} } + C$

Also see

• Primitive of $x$ by $\paren {a x + b}^n$ for general $n$
• Primitive of $x$ over $a x + b$ for the case when $n = -1$

Sources

• 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Front endpapers: A Brief Table of Integrals: $9$.