Evaluate the indefinite integral:
$\int (3 x^{2} + 3 x - 6) d x = ◻ + C$

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Answer

The indefinite integral of the function $3 x^{2} + 3 x - 6$ with respect to $x$ is $x^{3} + \frac{3}{2} x^{2} - 6 x + C$ .

Steps

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 $3 x^{2} + 3 x - 6$ with respect to $x$ is $x^{3} + \frac{3}{2} x^{2} - 6 x + C$ .

Evaluate the indefinite integral:∫(3x2+3x−6)dx=◻+C

Answer

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Evaluate the indefinite integral:
$\int (3 x^{2} + 3 x - 6) d x = ◻ + C$