Integral of e^(3*x)*dx dx

1. Let $u = e^{3 x}$.

   Then let $du = 3 e^{3 x} dx$ and substitute $\frac{du}{3}$:

   $$\int \frac{1}{9}\, du$$

   1. The integral of a constant times a function is the constant times the integral of the function:

      $$\int \frac{1}{3}\, du = \frac{\int 1\, du}{3}$$

      1. The integral of a constant is the constant times the variable of integration:

         $$\int 1\, du = u$$

      So, the result is: $\frac{u}{3}$

   Now substitute $u$ back in:

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

2. Add the constant of integration:

   $$\frac{e^{3 x}}{3}+ \mathrm{constant}$$

The answer is:

$$\frac{e^{3 x}}{3}+ \mathrm{constant}$$