What is the integral of 3x?

The integral of a function helps us find the area under its curve. For the function 3x, we can calculate the integral using basic rules of integration.

Finding the Integral

To integrate 3x with respect to x, we apply the power rule of integration. The power rule states that the integral of x raised to the power n is:

• ∫ x^n dx = (x^(n+1))/(n+1) + C, where C is the constant of integration.

Applying the Power Rule

In this case, we have:

• n = 1 (since x is the same as x^1)

Now, we can integrate:

• ∫ 3x dx = 3 * (x^(1+1))/(1+1) + C
• ∫ 3x dx = 3 * (x^2)/2 + C
• ∫ 3x dx = (3/2)x^2 + C

Final Result

The integral of 3x is:

(3/2)x^2 + C

Here, C represents the constant of integration, which accounts for any constant value that could be added to the function without changing its derivative.