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