Primitive of Reciprocal of a x + b/Examples/x - a

Example of Use of Primitive of $\dfrac 1 {a x + b}$

$\ds \int \frac {\d x} {x - a} = \ln \size {x - a} + C$

Proof

\(\ds \int \frac {\d x} {a x + b}\)

\(=\)

\(\ds \frac 1 a \ln \size {a x + b} + C\)

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

\(\ds \)

\(=\)

\(\ds \ln \size {x - a} + C\)

substituting $a \gets 1$, $b \gets -a$

$\blacksquare$

Sources

• 1976: K. Weltner and W.J. Weber: Mathematics for Engineers and Scientists ... (previous) ... (next): $6$. Integral Calculus: Appendix: Table of Fundamental Standard Integrals