Primitive of Function of Constant Multiple

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

Let $c$ be a constant.

Then:


 * $\displaystyle \int f \left({c x}\right) \ \mathrm d x = \frac 1 c \int f \left({u}\right) \ \mathrm d u$

where $u = c x$.

Proof
Let $u = c x$.

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

Thus: