Evaluate the following integrals :
`int x^(15)dx`
(a and b are constant)

Answer

To evaluate the integral \( \int x^{15} \, dx \), we will follow the standard procedure for integrating a power of \( x \).

### Step-by-Step Solution:

1. **Identify the integral**: We start with the integral \( \int x^{15} \, dx \).

2. **Apply the power rule of integration**: The power rule states that if \( n \) is a constant, then:
\[ \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \]
where \( C \) is the constant of integration.

3. **Substitute \( n = 15 \)**: In our case, \( n = 15 \). Thus, we apply the power rule:
\[ \int x^{15} \, dx = \frac{x^{15+1}}{15+1} + C \]

4. **Simplify the expression**: Now, we calculate \( 15 + 1 = 16 \):
\[ \int x^{15} \, dx = \frac{x^{16}}{16} + C \]

5. **Final result**: Therefore, the integral evaluates to:
\[ \int x^{15} \, dx = \frac{x^{16}}{16} + C \]

### Final Answer:
\[ \int x^{15} \, dx = \frac{x^{16}}{16} + C \]