Answer
See explanation below.
Work Step by Step
Let $F(x)$ be an antiderivative of $f(x),\qquad F'(x)=f(x)$
By the rule for derivatives of a constant multiple,
$[k\cdot F(x)]'=k\cdot F'(x)=k\cdot f(x)$
So, $k\cdot F(x)$ is an antiderivative of $k\cdot f(x)$
We write this as
$\displaystyle \int k\cdot f(x)dx=k\cdot F(x) +C$
$=k(F(x)+C_{1})\ \ $, where $C_{1}$is a constant, $C_{1}=\displaystyle \frac{C}{k}$
where we defined $F$
$=k\displaystyle \cdot\int f(x)dx$
The integral of a constant multiple is the constant multiple of the integraI.
