Evaluate the Integral integral of 9x^2+2x-3 with respect to x

Problem

(∫_^)(9*x2+2*x−3*d(x))

Solution

1. Identify the integral as a sum of power functions, allowing the use of the sum rule for integration.

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1) for n≠−1

3. Integrate the first term 9*x2 to get 9⋅(x3)/3

4. Integrate the second term 2*x to get 2⋅(x2)/2

5. Integrate the constant term −3 to get −3*x

6. Simplify the coefficients and add the constant of integration C

Final Answer

(∫_^)(9*x2+2*x−3*d(x))=3*x3+x2−3*x+C

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