# How do you find the indefinite integral of int 5^-x?

$\because , \int {a}^{x} \mathrm{dx} = {a}^{x} / \ln a + c , \therefore \int {5}^{-} x \mathrm{dx} = \int {\left(\frac{1}{5}\right)}^{x} \mathrm{dx}$
$= {\left(\frac{1}{5}\right)}^{x} / \ln \left(\frac{1}{5}\right) = \frac{{5}^{-} x}{\ln 1 - \ln 5} = - {5}^{-} \frac{x}{\ln} 5 + C .$