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

Problem

(∫_^)(x2−9*x+2*d(x))

Solution

1. Identify the integral as a sum of power functions, which allows for 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 each term individually: the integral of x2 is (x3)/3 the integral of −9*x is −(9*x2)/2 and the integral of 2 is 2*x

4. Add the constant of integration C to represent the family of antiderivatives.

Final Answer

(∫_^)(x2−9*x+2*d(x))=(x3)/3−(9*x2)/2+2*x+C

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