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

Problem

(∫_^)(9*x2+2*x−9*d(x))

Solution

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

2. Apply the power rule for integration, (∫_^)(xn*d(x))=(x(n+1))/(n+1) to each term individually.

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 −9 to get −9*x

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

Final Answer

(∫_^)(9*x2+2*x−9*d(x))=3*x3+x2−9*x+C

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