Evaluate: `int(x^(2)-5x-1)dx`

Answer

To evaluate the integral \( \int (x^2 - 5x - 1) \, dx \), we will integrate each term of the polynomial separately.

### Step-by-Step Solution:

1. **Write the integral**:
\[ \int (x^2 - 5x - 1) \, dx \]

2. **Break down the integral**:
We can separate the integral into three parts:
\[ \int x^2 \, dx - \int 5x \, dx - \int 1 \, dx \]

3. **Integrate each term**:
- For \( \int x^2 \, dx \):
\[ \int x^2 \, dx = \frac{x^3}{3} \]
- For \( \int 5x \, dx \):
\[ \int 5x \, dx = 5 \cdot \frac{x^2}{2} = \frac{5x^2}{2} \]
- For \( \int 1 \, dx \):
\[ \int 1 \, dx = x \]

4. **Combine the results**:
Putting it all together:
\[ \int (x^2 - 5x - 1) \, dx = \frac{x^3}{3} - \frac{5x^2}{2} - x + C \]
where \( C \) is the constant of integration.

### Final Answer:
\[ \int (x^2 - 5x - 1) \, dx = \frac{x^3}{3} - \frac{5x^2}{2} - x + C \]