Primitive of Hyperbolic Cosine Function

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Theorem

$\displaystyle \int \cosh \left({x}\right) \ \mathrm d x = \sinh \left({x}\right) + C$

where $C$ is an arbitrary constant.


Proof

From Derivative of Hyperbolic Sine Function:

$\dfrac{\mathrm d}{\mathrm d x} \left({\sinh \left({x}\right)}\right) = \cosh \left({x}\right)$

The result follows from the definition of primitive.

$\blacksquare$


Sources