Choose the correct answer of the given question
`int 2^x dx = ___ +c`

Options

A. `2^x log2`
B. `2^x/(log2)`
C. `2^x log x`
D. 2logx

Answer

To solve the integral \( \int 2^x \, dx \), we can use the formula for the indefinite integral of an exponential function. The formula states:

\[ \int a^x \, dx = \frac{a^x}{\log a} + C \]

where \( a \) is a constant and \( C \) is the constant of integration.

### Step-by-Step Solution:

1. **Identify the constant \( a \)**:
In our case, we have \( a = 2 \).

2. **Apply the formula**:
Using the formula for the integral of \( a^x \):
\[ \int 2^x \, dx = \frac{2^x}{\log 2} + C \]

3. **Write the final answer**:
Thus, the integral \( \int 2^x \, dx \) can be expressed as:
\[ \int 2^x \, dx = \frac{2^x}{\log 2} + C \]

### Final Answer:
\[ \int 2^x \, dx = \frac{2^x}{\log 2} + C \]