In college and later the first year of university(Engineering), I was taught that you can multiply the constant of integration by a constant value and it doesn't change, like in these examples:

$$ y = \frac{1}{5}\int dx = \frac{x+C}{5} = \frac{x}{5} + C $$

$$ y = e^{\int dx} = e^{x+C} = Ce^x $$

I get what's happening here, but is it considered bad form to do this? Should I create another constant, say $K$, and let this equal (in the first example) $\frac{C}{5}$ so I can say that $y=\frac{x}{5}+K$, or is it just accepted that it's slightly iffy but everyone understands what you've done?