Integrate the following :
`intx^(5)dx`

Explanation

To solve the integral \( \int x^5 \, dx \), we will follow the standard procedure for integrating a power of \( x \).

### Step-by-Step Solution:

1. **Identify the Power of \( x \)**:
The function we are integrating is \( x^5 \). Here, the exponent \( n \) is 5.

2. **Use the Power Rule for Integration**:
The power rule for integration states that:
\[ \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \]
where \( C \) is the constant of integration.

3. **Apply the Power Rule**:
- Here, \( n = 5 \).
- We add 1 to the exponent: \( n + 1 = 5 + 1 = 6 \).
- We then divide by the new exponent: \( \frac{x^{6}}{6} \).

4. **Include the Constant of Integration**:
After performing the integration, we must add the constant of integration \( C \).

5. **Write the Final Answer**:
Therefore, the integral \( \int x^5 \, dx \) is:
\[ \int x^5 \, dx = \frac{x^6}{6} + C \]

### Final Answer:
\[ \int x^5 \, dx = \frac{x^6}{6} + C \]

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