Primitive of Reciprocal of a x + b

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Theorem

$\displaystyle \int \frac {\d x} {a x + b} = \frac 1 a \ln \size {a x + b} + C$


Proof

\(\displaystyle \int \frac {\d x} {a x + b}\) \(=\) \(\displaystyle \frac 1 a \int \frac {\map \d {a x + b} } {a x + b}\) Primitive of Function of $a x + b$
\(\displaystyle \) \(=\) \(\displaystyle \frac 1 a \ln \size {a x + b} + C\) Primitive of Reciprocal

$\blacksquare$


Sources