Primitive of Constant

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Theorem

Let $c$ be a constant.

$\displaystyle \int c \rd x = c x + C$ where $C$ is an arbitrary constant.


Proof

Let:

$\displaystyle \map F x = \int c \rd x$

From the definition of primitive:

$\map {F'} x = c$

From Derivative of Function of Constant Multiple:

$\map {D_x} {c x} = c$

From Primitives which Differ by Constant:

$\map {D_x} {c x + C} = c$

Hence the result.

$\blacksquare$


Sources