# How do you find the antiderivative of e^(3x)?

Dec 24, 2016

$\int {e}^{3 x} \setminus \mathrm{dx} = \frac{1}{3} {e}^{3 x} + C$
Using $\frac{d}{\mathrm{dx}} {e}^{a x} = a {e}^{a x} \iff \int a {e}^{a x} \setminus \mathrm{dx} = {e}^{a x} + C '$
$\therefore \setminus \int {e}^{a x} \setminus \mathrm{dx} = {e}^{a x} / a + C$
Hence, $\int {e}^{3 x} \setminus \mathrm{dx} = \frac{1}{3} {e}^{3 x} + C$