# Integrate using the power rule.

#### Understand the Problem

The question is asking for the application of the power rule in calculus, which is used to find the integral of a function of the form x^n. The power rule states that the integral of x^n is (x^(n+1))/(n+1) + C, where n is not equal to -1 and C is the constant of integration.

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

The integral of $x^n$ is $\frac{x^{n+1}}{n+1} + C$

#### Steps to Solve

1. Identify the form of the function to be integrated

The power rule for integration is used for functions of the form $x^n$.

1. Apply the power rule

The power rule states that the integral of $x^n$ with respect to $x$ is: $$\int x^n , dx = \frac{x^{n+1}}{n+1} + C$$ where $n \neq -1$ and $C$ is the constant of integration.

1. Adding the constant of integration

Include the constant $C$ to express the general form of the integral.

The integral of $x^n$ is $\frac{x^{n+1}}{n+1} + C$

The constant of integration $C$ accounts for any constant that could have been differentiated to yield the integrated function.
A common mistake is to forget the constant of integration $C$ when finding the indefinite integral.