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.
Answer
$\frac{x^{n+1}}{n+1} + C$
Answer for screen readers
The integral of $x^n$ is $\frac{x^{n+1}}{n+1} + C$
Steps to Solve
- Identify the form of the function to be integrated
The power rule for integration is used for functions of the form $x^n$.
- 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.
- Adding the constant of integration
Include the constant $C$ to express the general form of the integral.
The integral of $x^n$ is $\frac{x^{n+1}}{n+1} + C$
More Information
The constant of integration $C$ accounts for any constant that could have been differentiated to yield the integrated function.
Tips
A common mistake is to forget the constant of integration $C$ when finding the indefinite integral.
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