The problem is to evaluate the indefinite integral of $x^n$ with respect to $x$, i.e., $\int x^n \, dx$.

1. Problem Description

The problem is to evaluate the indefinite integral of $x^n$ with respect to $x$, i.e., $\int x^n \, dx$.

2. Solution Steps

To solve the indefinite integral $\int x^n \, dx$, we use the power rule for integration, which states:

$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ for $n \neq -1$

where $C$ is the constant of integration.

3. Final Answer

The solution to the integral is:

$\frac{x^{n+1}}{n+1} + C$