Find the following inde finite integrat.
\[
\int 3 x^{2} d x
\]

Step 1 ：The integral of a function is the area under the curve of the function. The integral of a function f(x) from a to b is denoted as ∫f(x)dx from a to b. In this case, we are asked to find the indefinite integral of the function 3x^2.

Step 2 ：The indefinite integral of a function is the antiderivative of the function. The antiderivative of a function f(x) is a function F(x) whose derivative is f(x).

Step 3 ：The power rule for integration states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration. In this case, n=2, so the integral of x^2 dx is (1/(2+1))x^(2+1) + C = (1/3)x^3 + C.

Step 4 ：Therefore, the integral of 3x^2 dx is 3 times the integral of x^2 dx, which is 3*(1/3)x^3 + C = x^3 + C.

Step 5 ：Final Answer: The indefinite integral of \(3x^{2}\) with respect to \(x\) is \(\boxed{x^{3} + C}\), where \(C\) is the constant of integration.