How do you evaluate the integral int3^(x) dx?

Mar 14, 2018

$\int {3}^{x} \mathrm{dx} = \frac{1}{\ln} 3 {3}^{x} + \text{c}$

Explanation:

We want to find $\int {3}^{x} \mathrm{dx}$.

Make the natural substitution $u = {3}^{x}$ so $\mathrm{du} = {3}^{x} \ln 3 \mathrm{dx}$.

So

$\int {3}^{x} \mathrm{dx} = \frac{1}{\ln} 3 \int 1 \mathrm{du} = \frac{1}{\ln} 3 u + \text{c"=1/ln3 3^x+"c}$