What is the integral of 5?
Understand the Problem
The question is asking for the integral of the constant function 5. This involves finding the antiderivative with respect to a variable, typically presented as 'dx'. The result will be a linear function plus a constant of integration.
Answer
$5x + C$
Answer for screen readers
The integral of the constant function 5 is $5x + C$.
Steps to Solve
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Identify the integral We start with the integral of the constant function 5, which we can express as: $$ \int 5 , dx $$
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Apply the integral rule for constants The integral of a constant $c$ with respect to $x$ is given by: $$ \int c , dx = cx + C $$ where $C$ is the constant of integration.
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Substitute the constant into the formula In this case, we substitute $c$ with 5: $$ \int 5 , dx = 5x + C $$
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Write the final answer The final result is expressed as: $$ 5x + C $$
The integral of the constant function 5 is $5x + C$.
More Information
Integrating a constant function results in a linear function. The constant of integration, $C$, represents any constant value since there are infinitely many antiderivatives differing by a constant.
Tips
One common mistake is forgetting to include the constant of integration, $C$. It's important to always add $C$ when finding the antiderivative.
