Final answer:
The integral of 2x is found by applying the power rule for integration, which results in x^2 + C, where C is the constant of integration.
Step-by-step explanation:
To find the integral of 2x, you need to apply the basic rules of integration. The integration process requires you to identify the power of the variable x and increase it by one, then divide by the new power and include the constant of integration. Here's the step-by-step process:
- Identify the function to integrate: 2x.
- Apply the power rule for integration, which states that the integral of x^n dx is (x^(n+1))/(n+1) + C, where C is the constant of integration.
- Since the power of x in 2x is 1, apply the rule: Integral(2x dx) = 2 * Integral(x dx).
- Integral(x dx) is x^2/2.
- Multiply by the constant 2: 2 * (x^2/2) = x^2.
- Add the constant of integration C: x^2 + C.
Therefore, the integral of 2x with respect to x is x^2 + C, where C represents the constant of integration.