How do you integrate int 3^xdx?

Mar 17, 2018

The answer is $= {3}^{x} / \ln 3 + C$

Explanation:

Let $u = {3}^{x}$

Taking logs on both sides

$\ln u = \ln \left({3}^{x}\right) = x \ln 3$

Then

$u = {e}^{x \ln 3}$

Therefore,

$\int {3}^{x} \mathrm{dx} = \int {e}^{x \ln 3} \mathrm{dx} = {e}^{x \ln 3} / \left(\ln 3\right) + C$

$= {3}^{x} / \ln 3 + C$