Primitive of Cosine of a x + b/Proof 1

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Corollary to Primitive of Cosine Function

$\ds \int \map \cos {a x + b} \rd x = \frac {\map \sin {a x + b} } a + C$


Proof

\(\ds \int \cos x \rd x\) \(=\) \(\ds \sin x + C\) Primitive of $\cos x$
\(\ds \leadsto \ \ \) \(\ds \int \map \cos {a x + b} \rd x\) \(=\) \(\ds \frac 1 a \paren {\map \sin {a x + b} } + C\) Primitive of Function of $a x + b$
\(\ds \) \(=\) \(\ds \frac {\map \sin {a x + b} } a + C\) simplifying

$\blacksquare$


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