What is the integral of 1 dx?

Understand the Problem

The question is asking for the integral of the function 1 with respect to the variable x, which is a basic concept in calculus. The high-level approach to solve it involves applying the rules of integration.

Answer

The integral of 1 with respect to $ x $ is $ x + C $.

Steps to Solve

Identify the integral to solve
We want to find the integral of the function 1 with respect to the variable ( x ). This can be written as:
$$ \int 1 , dx $$
Apply the basic integration rule
The integral of a constant (in this case, 1) with respect to ( x ) is simply the constant multiplied by ( x ). Thus, we will have:
$$ \int 1 , dx = x + C $$
where ( C ) is the constant of integration.
Final expression
Representing the result clearly, we can say:
The integral of 1 with respect to ( x ) is:
$$ x + C $$

The integral of 1 with respect to ( x ) is ( x + C ).

More Information

This integral shows a fundamental rule in calculus where integrating a constant results in that constant multiplied by the independent variable, plus a constant of integration. The constant ( C ) represents any constant value since the process of integration can only determine the function up to a constant.

Tips

Forgetting to include the constant of integration ( C ) at the end of the result. Always remember that indefinite integrals have an arbitrary constant.

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