`int3^(x) dx = ?`

Options

A. `3^(x) (log3) + C`
B. `3^(x) + C`
C. `(3^(x))/(log 3) + C`
D. `(log3)/(3^(x)) + C`

Answer

To solve the integral \( \int 3^x \, dx \), we can follow these steps:

### Step 1: Identify the integral form
We recognize that the integral of an exponential function \( a^x \) can be expressed in a standard form. The formula for integrating \( a^x \) is:
\[ \int a^x \, dx = \frac{a^x}{\ln(a)} + C \]
where \( C \) is the constant of integration.

### Step 2: Apply the formula
In our case, \( a = 3 \). Therefore, we can apply the formula:
\[ \int 3^x \, dx = \frac{3^x}{\ln(3)} + C \]

### Step 3: Write the final answer
Thus, the integral \( \int 3^x \, dx \) evaluates to:
\[ \int 3^x \, dx = \frac{3^x}{\ln(3)} + C \]

### Summary of the solution:
\[ \int 3^x \, dx = \frac{3^x}{\ln(3)} + C \]