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

Example of Use of Primitive of $\dfrac 1 {\paren {a x + b}^2}$

$\ds \int \frac {\d x} {\paren {x - a}^2} = -\frac 1 {\paren {x - a} } + C$

Proof

\(\ds \ds \int \frac {\d x} {\paren {a x + b}^2}\)

\(=\)

\(\ds -\frac 1 {a \paren {a x + b} } + C\)

Primitive of $\dfrac 1 {\paren {a x + b}^2}$

\(\ds \)

\(=\)

\(\ds -\frac 1 {\paren {x - a} } + C\)

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