sin7x dx
$\displaystyle \int sin (7x) \ dx$
Let $\displaystyle {\color{red}u = 7x} \ \Rightarrow \ du = 7 dx \ \iff \ {\color{blue}dx = \frac{du}{7}}$.
So: $\displaystyle \int \sin ({\color{red}7x}) {\color{blue} \ dx} = \int \sin {\color{red}u} \ {\color{blue} \frac{du}{7}} = \frac{1}{7} \int \sin u \ du$
which is a standard integral.