Evaluate the indefinite integral:
\[
\int\left(3 x^{2}+3 x-6\right) d x=\square+C
\]
Answer
The indefinite integral of the function \(3x^{2}+3x-6\) with respect to \(x\) is \(\boxed{x^{3} + \frac{3}{2}x^{2} - 6x + C}\).
Step 1 ：The integral of a function is the area under the curve of the function. The integral of a polynomial function can be found by applying the power rule of integration, which states that the integral of x^n dx is (1/(n+1))x^(n+1). In this case, we have a polynomial of degree 2, so we can apply the power rule to each term separately. The constant term -6 can be integrated as -6x. After integrating, we add a constant of integration, denoted by C.
Step 2 ：The indefinite integral of the function \(3x^{2}+3x-6\) with respect to \(x\) is \(\boxed{x^{3} + \frac{3}{2}x^{2} - 6x + C}\).
