Primitive of Function of Constant Multiple

Theorem
Let $f$ be a real function which is integrable.

Let $c$ be a constant.

Then:


 * $\displaystyle \int \map f {c x} \rd x = \frac 1 c \int \map f u \d u$

where $u = c x$.

Proof
Let $u = c x$.

By Derivative of Identity Function: Corollary:
 * $\dfrac {\d u} {\d x} = c$

Thus: