Evaluate the Integral integral of x^2-7x+3 with respect to x

Problem

(∫_^)(x2−7*x+3*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 the first term x2 to get (x3)/3

4. Integrate the second term −7*x to get −(7*x2)/2

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

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

Final Answer

(∫_^)(x2−7*x+3*d(x))=(x3)/3−(7*x2)/2+3*x+C

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