To integrate the function 3x with respect to x, you will apply the power rule for integration. The power rule states that the integral of x raised to the power n is given by:
∫ x^n dx = (x^(n+1))/(n+1) + C (where C is the constant of integration).
In this case, the function is 3x, which can be rewritten as 3 * x^1. Applying the power rule:
- Identify n: Here, n = 1.
- Apply the power rule: Increase the exponent by 1 (1 + 1 = 2) and divide by the new exponent:
- The integral of 3 * x^1 becomes: 3 * (x^(1+1))/(1+1) = 3 * (x^2)/2.
- Finally, don’t forget to add the constant of integration C.
Putting it all together, the integral of 3x is:
∫ 3x dx = (3/2) x^2 + C
This means when you calculate the integral of 3x with respect to x, you get (3/2) times x squared, plus a constant C.