Primitive of Cosine Function/Corollary

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Corollary to Primitive of Cosine Function

$\displaystyle \int \cos a x \ \mathrm d x = \frac {\sin a x} a + C$

where $C$ is an arbitrary constant.


Proof

\(\displaystyle \int \cos x \ \mathrm d x\) \(=\) \(\displaystyle \sin x + C\) Primitive of $\cos x$
\(\displaystyle \implies \ \ \) \(\displaystyle \int \cos a x \ \mathrm d x\) \(=\) \(\displaystyle \frac 1 a \left({\sin a x}\right) + C\) Primitive of Function of Constant Multiple
\(\displaystyle \) \(=\) \(\displaystyle \frac {\sin a x} a + C\) simplifying

$\blacksquare$


Also see


Sources