How to get indefinite integral of the following?

Question

The question is as following :

$$\int \frac {e^{3x}}3 dx$$

I dont understand what to do when there is a number to the power of $x$. I would greatly appreciate anyones help.

Answer 1

One way to do it is via substitution: $$\int \frac{e^{3x}}{3}~dx$$ And let $$u=e^{3x} \implies du=3e^{3x}~dx \implies du=3u~dx\implies dx=\frac{1}{3u}~du$$

Answer 2

Shortly you can write $$\int \frac { e^{ 3x } }{ 3 } dx=\frac { 1 }{ 9 } \int e^{ 3x }d\left( 3x \right) =\frac { e^{ 3x } }{ 9 } +C$$