Integral of e^(7x) dx

1. Let $u = 7 x$.

   Then let $du = 7 dx$ and substitute $\frac{du}{7}$:

   $$\int \frac{e^{u}}{7}\, du$$

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

      $$\text{False}$$

      1. The integral of the exponential function is itself.

         $$\int e^{u}\, du = e^{u}$$

      So, the result is: $\frac{e^{u}}{7}$

   Now substitute $u$ back in:

   $$\frac{e^{7 x}}{7}$$

2. Add the constant of integration:

   $$\frac{e^{7 x}}{7}+ \mathrm{constant}$$

The answer is:

$$\frac{e^{7 x}}{7}+ \mathrm{constant}$$