Primitive of Function of a x + b

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$\ds \int \map F {a x + b} \rd x = \frac 1 a \int \map F u \rd u$

where $u = a x + b$.


\(\ds u\) \(=\) \(\ds a x + b\)
\(\ds \leadsto \ \ \) \(\ds \frac {\d u} {\d x}\) \(=\) \(\ds a\) Derivative of Function of Constant Multiple: Corollary
\(\ds \leadsto \ \ \) \(\ds \int \map F {a x + b} \rd x\) \(=\) \(\ds \int \frac {\map F u} a \d u\) Primitive of Composite Function
\(\ds \) \(=\) \(\ds \frac 1 a \int \map F u \rd u\) Primitive of Constant Multiple of Function